University of Southern California Dissertations and Theses

Taxicab transportation: operations, equilibrium, and efficiency

(USC Thesis Other)

Taxicab transportation: operations, equilibrium, and efficiency

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content T axic ab Transpor t a tion:
Opera tions, Equilibrium, and Efficien cy
b y
R uda Zhang
A Dissertation Presented t o t he
F A CUL TY OF T HE USC GRADU A TE SC HOOL
UNIVERSITY OF SOUTHERN C ALIF ORNIA
In P artial F ulfillment o f t he
R equirements f or t he Deg ree
DOCT OR OF PHIL OSOPHY
(CIVIL EN GINEERIN G)
Ma y 2018
Abs tra ct
Anal yzing social sys tems such as cities requires a set of f or mal met hods different from
t h ose used f or ph ysical sys tems. Intellig ent entities such as human beings act t o op timize
t h eir o wn objectiv es, whose s tr ategic decision making is cons tr ained b y r ules set up in
t h e social sys tem. T o s tudy urban tr ansportation sys tems, I propose a la w–economics–
engineering fr ame w or k , and applies it specificall y t o taxicab tr ansportation.
This dissertation is effectiv el y an ins titutional anal ysis of taxicab tr ansportation in N e w
Y or k City . It comes in t hree parts: using models of taxi oper ations t o es timate t he spatio-
tem por al dis tribution of taxi demand and suppl y ; using g ame-t heoretic model t o under -
s tand t he equilibrium s tr ategy of taxi driv ers; anal yzing t he effect of regulation on t he
efficiency of taxi tr ansportation sys tem. F or all parts, N e w Y or k City taxi trip recor ds from
2009 t o 2013 are used f or em pirical e v aluation.
P art one models taxi demand and suppl y as non-s tationar y P oisson r andom fields on t he
road netw or k , and pickups result from taxis searching f or im patient passeng ers on s treet
segments. The models pro vide a sim ple, f easible, and reliable met hod in es timating t he
suppl y and demand of s treet-hail taxis at segment le v el of a road netw or k. This es timation
of individual tr a v el decision requires onl y in-v ehicle Global P ositioning Sys tem (GPS) data,
wit hout sur v eilling t he p opulation.
P art tw o f or malizes t he decision making of taxi driv ers as a non-cooper ativ e g ame, which
each taxi in ser vice is a multi-mar k et fir m, e v er y s treet segment is a dis tinct mar k et, and
i
Abs tra ct
fir m s allocate ser vice time across t he s treet netw or k. W e anal yze t he equilibrium, dynam-
ics, and efficiency of t he g ame, and v alidate t hese predictions em piricall y . F urt her more, w e
pro vide an analogy of t his equilibrium t o t her modynamic equilibrium f or a macroscopic
inter pretation.
P art t hree s tudies t he s tr ucture of N e w Y or k City taxi indus tr y . W e propose a g ame
model t o cap ture t he rele v ant tr ansportation ins titutions, and design an efficient mecha-
nism f or taxi tr ansportation, measured b y social v alue. W e also address some issues of
im plementing t he efficient mechanism.
ii
A c kn o wledgments
My PhD research w ould ha v e been im possible wit hout t he tr us t and support of m y advisor
Prof. R og er Ghanem. I am also g r ateful f or all t he prof essors who ha v e taught me and
dedicated t heir time f or m y g r aduation: Prof. Sami Masri, Prof. K etan Sa v la, Prof. K ell y
Sanders, Prof. Juan Carrillo, Prof. Matt he w Kahn, Prof. A dam R ose, and man y o t hers.
My f amil y and m y friends ha v e sho wn g reat support and unders tanding t hroughout all
m y g r aduate y ears. I am deepl y indebt t o t hese lo ving people.
F or t he data and t ools I use in t his research, I w ould lik e t o t hank Henr y F arber of
Princet on U niv ersity f or sharing t he 2009 NY C taxi trip recor ds, and A bhishek N ag ar a j
of U niv ersity of Calif or nia, Ber k ele y f or sharing t he recor ds of 2009-2013. I also t hank
OpenS treetMap (OSM) contribut ors f or NY C map data, and Open Source R outing Ma-
chine (OSRM) contribut ors f or g r aph prepar ation and map matching modules.
My research has been funded b y t he USC Gr aduate School, and t he N ational Science
F oundation Gr ant N o. 14-524, R esilient Inter dependent Infr as tr ucture Processes and Sys-
tems.
iii
C ontents
Abs tra ct i
A c kn o wledgments iii
N omen cla ture 1
1 I ntr oduction 3
1.1 An anal ytical fr ame w or k of urban tr ansportation . . . . . . . . . . . . . . . . 3
1.2 Dynamic models of cities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 T axicab tr ansportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Spatial unit of taxicab tr ansportation . . . . . . . . . . . . . . . . . . . . . . . 14
2 D a t a 16
2.1 T echnology P asseng er Enhancements Project . . . . . . . . . . . . . . . . . . 18
2.2 Data origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 Spatial Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 O pera tions of S treet -hail T axi 45
3.1 Ov er vie w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 T ime sam pling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Suppl y route model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4 Segment-le v el pickup model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 Suppl y and demand dis tributions . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4 Eq uilibrium of T axi Transpor t a tion 80
4.1 Microscopic decision making: economic e quilibir um . . . . . . . . . . . . . . 81
4.2 Solution concep t: N ash equilibir um . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3 Macroscopic inter pretation: t her modynam ic equilibir um . . . . . . . . . . . 96
4.4 Efficiency : t he problem of social cos t . . . . . . . . . . . . . . . . . . . . . . . 99
4.5 Em pirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
iv
C ontents
5 Ef ficien cy of NY C T axi Indus tr y 109
5.1 NY C car indus tries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Or g anization of NY C taxi indus tr y . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3 NY C taxi regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.4 NY C TL C Prog r ams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.5 Game model of NY C taxi indus tr y . . . . . . . . . . . . . . . . . . . . . . . . 142
5.6 Em pirical v alidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Bibliography 146
v
N omen cla ture
Omitted subscrip ts im pl y summation.
Subscr ipt
𝑖 , 𝑗 T axi dr iv er , pla y er ; −𝑖 , opponents
𝑥 , 𝑦 S treet segment, mar k et
𝑠 Suppl y , v acant taxi searching t hrough a s treet segment
𝑑 Demand, po tential passeng er w aiting f or taxi
𝑝 Pickup
Ph ysical q uantity
𝑙 Lengt h of s treet segment
𝑡 T ime;
̄ 𝑡 , mean trip dur ation
𝑠 Share of ser vice time, s tr ategy
𝑣 T r affic speed; ̃ 𝑣 , taxi search speed
𝜇 Occurrence r ate; 𝜇 𝑡 , im patience, t he reciprocal of hailer mean patience
𝜑 Demand fulfillment, 𝜇 𝑝 /𝜇
𝑑 𝜌 Suppl y -demand r atio, 𝜇 𝑠 /𝜇
𝑑 𝜅 Co v er number , hailer mean inter -arriv al time t o mean patience, 𝜇 𝑡 /𝜇
𝑑 ℰ En vironment condition, ( v , 𝜇 𝑑 , 𝜇 𝑡 )
Money item
1
N omen cla ture
Π T rip r e v enue; Π , mean trip re v enue
𝑅 Lease pa yment, rent per lease ter m
𝑓 F uel c os t per unit time
𝑐 Cos t, labor alter nativ e income
𝑢 N et r e v enue, income, pa y off
Φ P o t ential function
𝜙 Mar g inal segment income on ser vice time, 𝜕 𝑢 𝑖 𝑥 /𝜕 𝑠 𝑖 𝑥 2
C h apter 1
Intr oduction
1.1 An an al ytic al framew ork of urb an transpor t a tion
Anal yzing social sys tems such as cities requires a set of f or mal met hods different from
t h ose used f or ph ysical sys tems. Ph ysical sys tems conf or m t o sets of go v er ning equations
which combine conser v ation la w s and cons titutiv e relations. Conser v ation la w s hold b y
logic or belief, while cons titutiv e relations arise from inter actions among com ponents of
a ph ysical matter . Social sys tems on t he o t her hand in v ol v e human beings, whose inter ac-
tions are much less s tr aight f or w ar d t han ph ysical entities. Whereas elementar y particles
obe y basic mechanisms, individuals are r ational decision mak ers. It w ould t hus be coun-
ter productiv e t o extend t he reductionis t ideas of mechanics and mat hematical ph ysics f or
t h e unders tanding of agg reg ate social outcome of individual beha vior .
The defining char acteris tic of a social sys tem is t he in v ol v ement of intellig ent com po-
nents such as human beings. Intellig ent entities act t o op timize t heir o wn objectiv es, whose
s tr ategic decision making is cons tr ained b y r ules set up in t he social sys tem. This leads t o
a dis tinct fr ame w or k f or t he anal ysis and design of social sys tems, as illus tr ated in F ig. 1.1 .
T o anal yze a social sys tem, one needs t o accur atel y model t he leg al ins titutions prescribing
individual actions and social outcomes, and predict t he outcome t hat arises from decen-
3
C hapter 1 Intr oduction
tr alized economic decisions. F rom an engineering perspectiv e, t here are t hree approaches
t o affect t he outcome of a social sys tem—oper ations, cos t reduction, and im plementation,
each tar g eting a different le v el of t he fr ame w or k.
Legal Institution
(rules)
Economic Decision
(optimization)
Social Outcome
(goal) constrain select
Implementation Cost Reduction Operations
Engineering
F igure 1.1: Three roles of engineering in social sys tems
T o illus tr ate t his la w–economics–engineering fr ame w or k , I f ocus on t he t opic of urban
tr ansportation. As a leg al, economic, and engineering problem f or e v er y human agglom-
er a tion, tr ansportation is essentiall y a social sys tem. As t he br anch of go v er nment wit h
legislativ e aut hority , s tate and municipal legislatures set out t he ins titutions, or r ules, of
tr ansportation: t he property rights of land, road, f acility and v ehicle, prescibing t he right
t o o wn, use, char g e, and tr ansf er . These r ules are enf orced b y t he bureaucr acy , which also
build, maintain, and oper ate tr ansportation infr as tr ucture and public tr ansit ser vices jus t
lik e a business. The s tr ategic decision making of t he population can be predicted t hrough
g ame t heoretic models.
The engineering of tr ansportation sys tems comes in t hree aspects. The firs t role is t o
im plement or enf orce ne w mechanisms, such as r adar f or speed detection, IC or RFID
chips f or f are collection, and liv e camer a f or video recor d. Engineering can also reduce
tr anspor ation related cos ts via (1) infr as tr ucture suppl y , such as roads and bridg es, r ail-
w a y f or r apid tr ansit, and inter nal combus tion engine f or aut omobile; (2) tr ansit suppl y ,
such as taximeter f or taxicab, r adio and GPS receiv er f or fleet manag ement ; (3) inf or ma-
tion and com putation, such as real-time tr affic and tr ansit inf or mation from Google Maps
and Citymapper ; v ariable-messag e signs pro viding road condition, dynamic speed limit,
4
C hapter 1 Intr oduction
and time-dependent one-w a y control. By reducing inf or mation and com putation cos ts, t he
population can op timize more frequentl y wit h more op tions and more accur ate op tions.
The t hrid role is t o directl y affect oper ational efficiency , such as road w eat her manag ement,
incident remo v al, and tr affic signal syncing using v ehicle loop detect or and on-r am p me-
ter ,
My dissertation applies t his fr ame w or k t o taxicab tr ansportation, in t hree parts: firs t I
use build models of taxi oper ation t o es timation taxi suppl y and demand; t hen I model
t h e decision making problem of taxi driv ers, anal yzing t heir equilibrium beha vior ; at las t,
I s tudy t he effects of property rights regulation on taxicab tr ansportion in N e w Y or k City ,
and propose a mechanism t hat im pro v es sys tem efficiency . In t he context of urban tr ans-
portation equilibrium, taxi suppl y and demand is part of t he equilibrium outcome, taxi
equilibrium is t he equilibrium s tr ategy of taxi suppl y , taxi regulation deter mines t he effi-
ciency of t he equilibrium under current mechanism.
Ot her w or k s wit h a la w–economics–engineering fla v or include Hirshleif er , DeHa v en,
and Milliman ( 1960 ), Dorfman et al. ( 1962 ), and R o t h ( 2002 ). The inno v ativ e points of m y
fr ame w or k is t hat it f ocuses on im plementation and inf or mation, leg al s tr ucture, and mech-
anism design.
1.2 D yn amic models of cities
Cities are places wit h t he denses t human inter action, and it is t hus im portant t o under -
s tand t he regularity of urban agglomer ations. W it hin t he emer ging field of urban science,
f e w s tudies ha v e manag ed t o build com prehensiv e models t hat explain specific aspects of
cities. T o t his end, recent efforts ha v e used entrop y models (W ilson, 2010 ), r andom w alk
models (Gonzalez, Hidalgo, and Bar abasi, 2008), scaling la w s (Bettencourt, 2013 ), and spa-
tial economic equilibrium (Glaeser , 2008).
5
C hapter 1 Intr oduction
Despite t he dis tinct met hodologies applied t o urban science, one pre v alent perspectiv e
is t o treat a city as a sys tem. Meier ( 1968 ) sees t he metropolis as a tr ansaction-maximizing
sys tem where population density s timulates tr ansactions betw een individual act ors. F or -
res ter ( 1969 ) defines urban sys tem as t he built en vironment and t he inter acting population
wit hin an urban area, where t he built en vironment consis ts of buildings and infr as tr uc-
ture sys tems such as tr ansportation, ener gy dis tribution, and w ater suppl y and treatment.
A modeling met hodology f or urban sys tems is sociodynamics (W eidlich and Haag, 1983 ),
which models t he e v olution of city configur ation as a s t ochas tic process, e v ol ving in accor -
dance wit h a mas ter equation. W eidlich ( 1999 ) used t his fr ame w or k t o s tudy t he im pact
of tr ansportation sys tem on regional de v elopment around cities. Based on models from
non-equilibrium s tatis tical ph ysics, ho w e v er , t his g ener al met hodology dismisses t he pos-
sibility of urban sys tems being in equilibrium.
As urban tr ansportation exhibits dail y , w eekl y and seasonal periodic beha vior , w e be-
lie v e it is reasonable t o s tudy cities as sys tems in dynamic equilibrium, at leas t f or urban
tr ansportation sys tems. In f act, equilibrium met hods ha v e been applied t o tr ansportation
since t he discussion o v er t oll roads in Pigou ( 1920 ) and Knight ( 1924 ). Gener alizing t he
economis ts ’ exam ple, W ar drop ( 1952 ) described tw o beha vior al principles of route choice:
a N ash equilibrium and a P aret o op timal. Beckmann, McGuire, and W ins ten ( 1956 ) pro-
vided t he firs t mat hematical f or mulation of t he problem and pro v ed t he exis tence and
uniqueness of tr affic equilibrium in pure s tr ategies. F or a re vie w of de v elopment in t he
f ollo wing 50 y ears, see f or exam ple Bo y ce, Mahmassani, and N agur ne y ( 2005 ). Ho w e v er ,
a k e y issue of t he af orementioned tr affic equilibrium liter ature is its narro w assum p tion on
individual incentiv es: t hat individuals minimize t heir tr a v el time, or t hat social planners
minimize t he t o tal tr a v el time of t he society . P eople mo v e f or v arious reasons and seldom
beha v e as time minimizers. T o tr ul y unders tand human mobility and successfull y tackle
tr affic cong es tion and related inefficiencies, an equilibrium model of urban tr ansportation
6
C hapter 1 Intr oduction
has t o account f or different incentiv e s tr uctures of t he population.
W e reg ar d t he regularity in urban tr ansportation as t he equilibrium outcome of indi-
vidual decision making in response t o tr ansportation demand and ser vices. This paper ,
in particular , pro vides equilibrium models f or taxi tr ansportation. T axi driv ers are bo t h
ride ser vice pro viders and independent contr act ors. W it h ex og enous tr affic speeds and
passeng er demand, income maximization of taxi driv ers lead t o an economic equilibrium.
W e f or malize taxi driv er decision making as a non-cooper ativ e g ame, sol v e its N ash equi-
librium, and s ho w its s tability under non-equilibrium dynamics. W e also pro vide a macro-
scopic inter pretation of t his equilibrium as a t her modynamic equilibrium, and discuss t he
economic efficiency of s treet-hail taxis. W it h fiv e y ears of N e w Y or k City (NY C) taxi trip
recor ds, w e v alidate t he equi librium in space, o v er time, and under policy chang e, and
examine t he lear ning process of taxi driv ers.
In t his s tudy , w e model t he dynamics of urban tr ansportation sys tem. An urban tr ans-
portation sys tem consis ts of t hree types of elements: infr as tr ucture, v ehicle, and popula-
tion. T r ansportation infr as tr ucture ref ers t o t he fix ed ins tallations including roads, r ail-
w a ys, bridg es, public tr ansit s tations, and f acilities f or par king and tr affic control. V ehicles
are mobile t ools t hat help people mo v e around, such as bicy cles, mo t or v ehicles, and r ail
v ehicles. The population ma y ser v e t heir o wn tr ansportation need or use a tr ansportation
ser vice; in t he latter case, some o t her members of t he population will be w or king as t he
driv er or oper at or , at leas t under current technology . While t he tr ansportation of goods is
also a part of urban tr ansportation, it is no t explicitl y included in t his model, because cur -
rentl y t he tr ansportation of goods in cities alw a ys in v ol v e tr ansportation of people, using
common modes of urban tr ansportation.
An urban tr ansportation sys tem can be partitioned int o multiple subsys tems b y mode
of tr ansportation. Common tr ansportation modes include w alking, biking, driving, public
tr ansit, and f or -hire v ehicle (FHV). F or -hire v ehicle as defined b y public officers ref ers t o
7
C hapter 1 Intr oduction
T able 1.1: Com position and Subsys tems of an U rban T r ansportation Sys tem
Mode Infr as tr ucture V ehicle P opulation
W a lking Side w alk , pedes trian w a y ,
crossw alk , f oo tbridg e.
none pedes trian
Biking Bik e lane, cy cle w a y , bik e s tand. bicy cle cy clis t
Driving R oad, bridg e, tunnel, tr affic
signal, par king lane/lo t.
mo t orcy cle, car , tr uck driv er
FHV (Same as driving.) car driv er , passeng er
T r ansit R oad, bus lane, r ailw a y , bus
s t op, tr ain s tation.
bus, tr am, tr ain oper at or , passeng er
go v e r n ment-regulated s treet-hailed taxi ser vices and prearr ang ed car ser vices. The f or mer
pick s up passeng ers ex clusiv el y on t he s treet, while t he latter dispatches v ehicles based on
ser vice reques t, including liv eries, black cars, and luxur y limousines. These tw o types of
FHV will be sim pl y ref erred t o as taxi and car ser vices, unless t he y become ambiguous. F or
sim p licity , w e ignore o t her possible modes of tr ansportation.
1
T able 1.1 sho w s t he mak eup
of an urban tr ansportation sys tem.
The s tate of an urban tr ansportation sys tem at an y time can be full y described b y t he
la y out of tr ansportation infr as tr ucture, routes of public tr ansit, location of priv ate v ehi-
cles, rental v ehicles, FHVs and public tr ansit fleets
2
, and location of t he population.
3
Our
h ypo t hesis is t hat t he s tate of an urban tr ansportation sys tem is in dynamic equilibrium at
an y giv en time.
There are man y equilibrium concep ts in t he sciences; t hree different but related equilib-
rium concep ts are used in t his s tudy . A t t he microscopic le v el, economic equilibrium ref ers
1
Priv ate sect or car ser vices can be considered as car ser vices oper ated independentl y from t he go v er nment.
Air , w ater , and cable tr ansports are no t ma jor modes of urban tr ansportation. Multimodal trips can be
modeled as multiple single-mode trips.
2
Schedules of public tr ansit are no t necessar y in specifying t he s tate of a tr ansportation sys tem giv en t he
current location of fleets, because schedules do no t pro vide extr a inf or mation o t her t han promised but no t
guar anteed future location of t he fleets.
3
R egulations such as tr anspor ation r ules and control signal s tatuses are no t included in t he s tate of a tr ans-
portation sys tem, because t he y are prescrip tiv e r at her t han descri p tiv e t o t he sys tem.
8
C hapter 1 Intr oduction
t o t he situation when e v er y individual obtains t heir maximum v alue from tr ansportation
decision making, subject t o t he s tate of t he tr ansportation sys tem. N ash equilibrium ser v es
as a solution concep t f or t his decision making process of t he population including tr ans-
portation ser vice oper at ors. Ther modynamic equilibrium pro vides a macroscopic inter pre-
tation of t he equilibrium outcome, where agg reg ate beha viors are perceiv ed as tr ansport
phenomena built up from individual choices.
1.2.1 Micr osc opic decision makin g
T r ansportation, f or people, is t he recurring need t o go t o places o t her t han where t he y are.
The dynamics of urban tr ansportation sys tem t hus natur all y originates from t he decision
making of individuals of t he population. The pos tulate of r ational choice s tates t hat e v er y
individual tries t o maximize t he v alue of t heir choice giv en t he a v ailable alter nativ es. The
situation where t his pos tulate is satisfied f or t he entire population is called an economic
equilibrium. Here w e set up t he decision making problem accor ding t o t his equilibrium
concep t.
Individuals at an y moment ma y consider whet her or no t t o mo v e from t heir current lo-
cation t o ano t her location. The v alue of tr ansportation t o an individual is t hat of teleporta-
tion: mo ving t o t he des tination ins tantaneousl y , wit hout o t her consequences. The v alue of
tr ansportation is ref erenced at t he v alue of s ta ying, so t he latter alw a ys equals zero. Since
teleportation is no t a f easible mode of tr ansportation, t he v alue of an y f easible mode of
tr ansportation is based on t he v alue of tr ansportation, minus t he cos ts and plus t he v alue
an individual associates wit h t hat mode. The cos ts ma y include time, f are, v ehicle dete-
rior ation, consumable material, ph ysical effort, and discomf ort. The v alue an individual
associates wit h a mode of tr ansportation ma y include ph ysical and psy chological benefits.
The tr ansportation dec ision of an individual at an y moment is t hen t o choose among s ta y -
ing and mo ving t o an y o t her location via an y mode of tr ansportation, whiche v er giv es t he
9
C hapter 1 Intr oduction
maximum v alue.
Deno te 𝑣 𝑖 (𝑜, 𝑑 , 𝑡 ) as t he v alue of tr ansportation t o individual 𝑖 t o mo v e from origin 𝑜 t o
des tination 𝑑 at time 𝑡 . Deno te 𝑣 𝑖 𝑚 (𝑜, 𝑑 , 𝑡 ; s (𝑡 )) as t he net v alue individual 𝑖 associates wit h
tr ansportation mode 𝑚 if 𝑖 lea v es 𝑜 f or 𝑑 at time 𝑡 when t he s tate of t he tr ansportation
sys tem is s (𝑡 ) . Deno te tr ansportation modes: 𝑊 , w alking; 𝐵 , biking; 𝐷 , driving; 𝑃 , public
tr ansit ; 𝐹 , f or -hire v ehicle. Then t he op timization problem of an individual is
𝑚𝑎𝑥 (𝑑,𝑚)
𝑣 𝑖 (𝑜, 𝑑 , 𝑡 ) + 𝑣 𝑖 𝑚 (𝑜, 𝑑 , 𝑡 ; s (𝑡 ))
s.t. 𝑚 ∈ {𝑊 , 𝐵, 𝐷, 𝑃 , 𝐹 }
𝑣 𝑖 + 𝑣 𝑖 𝑚 ≥ 0
(1.1)
F or a n y individual 𝑖 and tr ansportation mode 𝑚 , 𝑣 𝑖 = 𝑣 𝑖 𝑚 = 0 if 𝑜 = 𝑑 .
This model applies t o e v er y individual of t he population, reg ar dless of t heir current
activity or nature of w or k. F or people whose jobs are s tationar y , while at w or k , t he v alue of
tr ansportation t o an y place o t her t han t heir current location is neg ativ e. Some people’ s jobs
are mobile, which means f or a lar g e portion of t heir w or k time, t he v alue of tr ansportation
t o some des tinations are positiv e. When people are off w or k , some des tinations ma y ha v e
positiv e v alues of tr ansportation, and t he y will chang e location if t he t o tal v alue is s till
positiv e a f ter inclusion of tr ansportation mode associated v alue.
The specific mode of f or -hire v ehicles is divided int o taxis and car ser vices. While t he
w aiting time f or public tr ansit and prearr ang ed car ser vices are typicall y pro vided t o t he
passeng ers, people w ait f or an indefinite amount of time when hailing f or taxis. Deno te 𝑣 𝑖 𝑇 as t he v alue individual 𝑖 associates wit h taking a taxi wit hout w aiting, and 𝑤 as w aiting
time. Then t he v alue associated wit h taking a taxi is 𝑣 𝑖 𝑇 − 𝑐 𝑖 (𝑤 ) , where 𝑐 𝑖 is t he time cos t
function f or individual 𝑖 . Deno te 𝑃 𝑊 as t he probabilis tic model of w aiting time 𝑊 indi-
vidual 𝑖 has f or hailing taxis, t hen t he individual will s tart hailing when 𝑣 𝑖 𝑇 − 𝔼𝑐 𝑖 (𝑊 ) ≥
10
C hapter 1 Intr oduction
𝑚𝑎𝑥 𝑚∈−𝑇
𝑣 𝑖 𝑚 , where −𝑇 is t he set of tr ansportation modes ex cluding taxi. When t he in-
equality becomes in v alid bef ore 𝑖 g ets pick ed up b y a taxi, t he individual will quit hailing
and choose t he current bes t op tion.
An individual’ s hailing decision o v er time can t hus be f or mall y expressed. Individual
𝑖 will no t consider hailing f or a taxi if 𝑣 𝑖 𝑇 < 𝑚𝑎𝑥 𝑚∈−𝑇
𝑣 𝑖 𝑚 . Ot her wise, based on t he prior
probabilis tic model 𝑃 𝑊 of w aiting time, 𝑖 s tarts hailing if 𝔼𝑐 𝑖 (𝑊 ) ≤ 𝑐 𝑖 (𝑤
0
) , where 𝑤 0
is t he
indifferent w aiting time wit h 𝑣 𝑖 𝑇 + 𝑐 𝑖 (𝑤
0
) = 𝑚𝑎𝑥 𝑚∈−𝑇
𝑣 𝑖 𝑚 . Once s tarted hailing, 𝑖 continu-
ousl y updates 𝑃 𝑊 as if b y Ba y esian inf erence, and also updates 𝑣 𝑖 𝑚 f or all modes 𝑚 . The
individual k eeps hailing until 𝔼𝑐 𝑖 (𝑤 ) > 𝑐 𝑖 (𝑤
0
) . In case t he individual’ s mar ginal time cos t
is cons tant, t hat is, t he individual is risk neutr al, t he criteria f or hailing can be sim plified
t o 𝔼𝑊 ≤ 𝑤 0
.
F igure 1.2: Hailing decision of a h ypo t hetical risk -neutr al individual. Hailing s tarts at 𝑡 𝐻 when indifferent w aiting time 𝑤 0
ex ceeds expected w aiting time 𝔼𝑊 . Hailing
s t ops when expected remaining w aiting time 𝔼(𝑊 − 𝑤 | 𝑊 > 𝑤 ) ex ceeds indif-
f erent w aiting time 𝑤 0
, resulting in hailer patience 𝑡 𝑃 .
11
C hapter 1 Intr oduction
1.3 T axic ab transpor t a tion
T axi tr ansportation cons titutes a k e y com ponent of urban mobility , and is a r are case of
indus trial econom y where detailed and com prehensiv e tr ansaction recor ds are a v ailable.
As metropolitan areas o v er t he w or ld continue t o g ro w in population and econom y , tr affic
cong es tion and induced pollution ha v e w orsened. A v er ag e tr affic dela y in Manhattan Cen-
tr al Business Dis trict increased 28% betw een 2013 and 2017 (Ma y or’ s Office of Oper ations,
2017 ), where an im portant source is g ro wt h in taxi/TN C v ehicles, especiall y unoccupied
ones (Schaller , 2017 ). Increasing search efficiency is t hus k e y t o alle viate t he ongoing in-
crease in cong es tion.
In urban com puting and tr a ject or y mining liter ature, s tudies using taxi GPS recor ds
lar g el y s tarted since 2010. V acant taxi a v ailability has been s tudied b y Phit hakkitnuk oon
et al. ( 2010 ) and Y uan2013 . Man y predictiv e models of taxi demand ha v e been proposed,
despite treating actual pickups as demand, see f or exam ple Chang, T ai, and Hsu ( 2010 ),
Moreir a-Matias et al. ( 2013 ) and T u et al. ( 2016 ). T axi demand and satisfied demand w ere
firs t dis tinguished in Shao et al. ( 2015). F e w s tudies used road netw or k: Cas tro, D. Zhang,
and Li ( 2012 ) predicted tr affic density and es timated road capacity and speed t hreshold;
Zhan2013 and W ang et al. ( 2016 ) es timated tr a v el speed on road segments; Santi et al.
( 2014 ) and Alonso-Mor a et al. ( 2017 ) used road netw or k f or routing shared taxi r ides.
In taxi search friction and matching liter ature, matching functions are commonl y used
t o relate demand and suppl y wit h matches. But t he functions used are eit her agg reg ate
models or obtained b y simulation, and no t cap turing t he char acteris tics of s treet-hail taxis.
F or exam ple, Lagos ( 2000 ) used t he minimum number of hailers and v acant taxis as t he
number of matches, assuming all buy ers and sellers at t he same place match simultane-
ousl y . Y ang2010 and Y ang2011 used t he Cobb-Douglas production function, where meet-
ing r ate is a po w er function of t he numbers of hailers and v acant taxis; t he y also pro v ed
12
C hapter 1 Intr oduction
t h e exis tence of com petitiv e s tationar y equilibrium. F rechette, Lizzeri, and Salz ( 2016 ) used
a matching function obtained from numerical simulation t o es timate t he t o tal number of
hailers in each hour of a typical w eekda y . Their matching function maps from t he numbers
of hailers and v acant taxis t o taxi search time, and t he y es timated demand b y inter polating
and in v erting t he function. Ho w e v er , in t heir simulation, hailers arriv e in batches at fix ed
time inter v als, dis tributed wit h unif or m probability on g rid nodes of each of eight areas in
core Manhattan, and w ait indefinitel y while v acant taxis mo v e as r andom w alk ers. Buch-
holz ( 2017 ) es timates suppl y and demand dis tributions o v er 39 clus ters of census tr acts
f or e v er y 5-minute periods betw een 6am and 4pm w eekda ys. Equilibrium suppl y dis tri-
bution is sol v ed f or each period based o n pre vious v alues, t he mo v ement of occupied taxis,
and driv er decision t o maximize net re v enue. He uses t he equilibrium matching function
deriv ed in Bur dett, Shi, and W right ( 2001 ), which is based on Butters ( 1977 )’ s ur n-ball
matching problem, t hat is, taxis ha v e capacity one and cus t omers arriving at a matched
taxi are rejected.
Different oper ation modes cater t o different tr ansportation demand: s treet-hail, pre-arr ang ement,
and t heir combinations; app-summon.
In analogy , t he taxi indus tr y can be seen as a g ambling. The Manhattan Casino is o wned
b y t he NY C city go v er nment, who deleg ates dail y manag ement t o chief ex ecutiv e TL C. TL C
sells limited edition Medallion tick ets t o pla y ers, each receiving a fix ed amount of time
t ok ens. Gambling occurs at t he Manhattan pool, which is separ ated int o man y pock ets
wit h v ar ying profitability ; t he more t ok ens a pock et receiv es, t he more profit it g ener ates.
Each round pla y ers dis tribute t heir t ok ens across t he pock ets, profit g ener ated b y each
pock et is shared proportionall y b y t ok en contribution. R ounds occur continuousl y wit h
no g ap, so pla y ers taking res t will miss some. When onl y one pla y er is participating, t ok en
dis tribution will mak e all in v es ted pock ets ha v e t he same mar ginal profitability , which is
higher t han all em p ty pock ets. When multiple pla y ers are participating, t ok en dis tribution
13
C hapter 1 Intr oduction
will push pock ets wit h high a v er ag e profitability t o lo w er mar ginal profitability . When all
pla y ers are participating, t ok en dis tributions will mak e all in v es ted pock ets ha v e almos t
t h e same mar ginal profitability , which is higher t han all em p ty pock ets.
1.4 Sp a tial unit of t axic ab transpor t a tion
Here w e ar gue t hat spatial agg reg ation f or tr ansportation anal ysis should use s treet seg-
ments, no t areas or points. In essence, one canno t agg reg ate or a v er ag e f eatures on a net-
w or k b y pro ximity in its embedding spac e.
Using areas t o agg reg ate activities on a road netw or k is counter productiv e, as t he net-
w or k t opology is ignored and e v ents are a v er ag ed t o a measure of a different dimension.
T o predict v acant taxi dis tribution in Lisbon, P ortug al, P hit hakkitnuk oon et al. ( 2010 ) de-
v eloped a naiv e Ba y es model wit h time of da y , da y of w eek , and w eat her as predict ors.
But t he s tudy used square areas of one square kilometer as t he spatial unit, which is uni-
f or m in space but no t in t he under l ying s tr ucture. Space cells canno t be a reasonable pro xy
f or tr ansportation activities because f eatures such as tr a v el demand and tr affic speed are
dis tributed along s treet netw or k s, which is spatiall y highl y heterog eneous. F or reasonable
es t imate of taxi suppl y , a v ailable trip recor ds should be at leas t near t o com plete f or t he
s tudied urban area. In o t her pr actices, t he urban area under s tudy has been discretized b y
census tr acts, neighbor hood tabulation areas (NT A), or taxi zones. Such g eog r aphic parti-
tions are all clus ters of city block s bounded b y s treets, and are typicall y no t designed f or
tr ansportation anal ysis. F or exam ple, census tr act is a spatial unit f or population s tatis tics,
each wit h a com par able size of residential population. Using t hem in g rouping tr ansporta-
tion activities is no t onl y arbitr ar y , but it also separ ates noisy obser v ations g ener ated on
t h e same s treet. Buchholz ( 2017 )’ s mechanism of driv er -hailer matching is har d t o inter pret,
especiall y because t he spatial units are clus ters of census tr acts. F irs t, t he number of v acant
14
C hapter 1 Intr oduction
taxis in each area is counted as suppl y , im pl ying t hat all driv ers ha v e identical contribu-
tion t o searching an area. Second, hailer arriv als and matching are simultaneous at each
period; if multiple hailers are assigned t o one driv er , despite some o t her driv ers ha ving
none, onl y one hailer g ets matched and o t hers do no t s ta y f or t he next period. Since spatial
context is abs tr acted a w a y b y agg reg ation, while a taxi pickup s till requires bo t h parties
t o be at t he same place, it is unclear ho w t his matching process arises from t he s treet le v el.
In addition, t he matching function has an efficiency par ameter wit h no ph ysical inter pre-
tation. Spatial agg reg ation b y lar g e areas is especiall y inappropriate when t he under l ying
f eature is highl y heterog eneous ( see F ig. 2.6 ), which is t he case of taxi tr ansportation where
pickup r ates extend multiple or ders of magnitude. In com parison, tem por al v ariation is
much smoo t her and can be es timated at coarser units.
Some s tudies on urban mobility used s treet intersections f or trip origin and des tination,
which is based on road netw or k and more fine-g r ained, see Santi et al. ( 2014 ), Sag arr a et
al. ( 2015 ), and T achet et al. ( 2017 ). Their t opics co v er taxi sharing po tential and its scaling
la w , and recons tr ucting nor malized origin-des tination (OD) matrix wit h a super -sam pled
model. But taxis canno t pick up nor drop off passeng ers at intersections. By using intersec-
tion as t he spatial unit, segments connecting t o t he same intersection are treated as similar
in tr ansportation related properties. But as s treet segments sharing one intersection typi-
call y ha v e different tr affic directions, v acant taxis will no t be able t o search all t hese seg-
ments in one pass. And also because intersections are typicall y controlled b y tr affic lights,
hailers canno t freel y mo v e t o ano t her s treet segment t o catch a v acant taxi, while t he taxi
ma y s im pl y pass or g et occupied b y ano t her hailer nearb y . Thus, w e t hink it is reasonable
t o claim t hat t he fundamental unit of taxi tr ansportation is s treet segment.
15
C h apter 2
D a t a
The N e w Y or k City (NY C) T axi and Limousine Commission (TL C) s tarted collecting trip
recor d of its Medallion T axis (aka y ello w cabs) using T axi P asseng er Enhancement Pro-
g r am (TPEP) de vice in Januar y 2009. Since t hen, t he TL C has been publishing t his digital
trip recor d continuousl y . R ecent s tudies ha v e used t hese trip recor ds t o s tudy labor sup-
pl y elas ticity of taxi driv ers ( F arber2014 ), taxi pooling po tential (Santi et al., 2014 ), and
tr ansportation sys tems resilience t o natur al hazar ds (B. Dono v an and D. W or k , 2015 ).
The trip recor d contains attributes, among o t hers: latitude, longitude and times tam p of
bo t h pickups and drop-offs; trip dis tance and f are amount. Published trip recor ds till 2014
ma y also contain medallion ID (f or v ehicles) and hack license (f or driv ers), which w ere
remo v ed from published data later b y TL C due t o priv acy concer ns. W e ha v e g at hered trip
recor ds wit h t hese ID fields f or t he y ears from 2009 t o 2013, accounting f or 870 million
individual taxi trips. (Brian Dono v an and D. B. W or k , 2014 ) In our s tudy , w e use t hese
data t o v alidate taxi s teady s tate and t o deriv e t he em pirical cons titutiv e relation f or NY C
taxi trips. The ID fields are indispensable in t he v alidation, because t o es timate model
par a meters w e need t o tr ack a taxi betw een consecutiv e trips.
Bef ore A ugus t 2013, onl y Medallion v ehicles are allo w ed t o pick up passeng ers on t he
s treets in NY C wit hout pre-arr ang ement, af ter which S treet Hail Liv er y (kno wn as g reen
16
C hapter 2 D a t a
cab) s tarted oper ation but did no t pick up momentum bef ore 2014 and are also no t allo w ed
t o pickup wit hin core Manhattan. Thus t he trip recor ds of Medallion taxi during 2009-2013
consis ts all taxi trip recor ds responding t o s treet hailing in NY C during t hat period.
The T axi and Limousine Commission (TL C) controls t he issuing of Medallion licenses t o
oper ate taxi in N e w Y or k City . The t o tal number of Medallions s ta ys cons tant unless TL C
releases ne w Medallions via auction, see F igure 2.1 .
12000 12500 13000 13500
Date
Medallions
2000 2005 2010 2015
F igure 2.1: N umber of N e w Y or k City Medallions o v er time. Shaded area highlights t he
period from 2009 t o 2013, t he firs t fiv e calendar y ears since TPEP sys tems w ere
ins talled in all Medallion taxis b y December 2008. The same 13237 Medallions
are in ser vice during t hat period, untill t he auction of 200 mini-fleet Medallions
on 2013-11-14.
T axi trips in core Manhattan is relativ el y s table o v er a y ear , and dail y patter ns are similar
f or all w eekda ys.
17
C hapter 2 D a t a
2.1 Tec hn ol og y P assen ger Enhan cements Pr oject
On 2004-03-30, along wit h a f are increase, t he TL C Boar d of Commissioners mandated
t h at all medallion taxis shall im plement
1
: (1) aut omated (electronic) trip sheet data collec-
tion and submission, including GPS recor ds; (2) electronic pa yment (credit/debit car d; dis-
pla ys t o tal f are at t he end of trip); (3) text messaging (driv er inf or mation monit or , DIM),
so TL C can send short alphanumeric messag es t o taxi driv ers t o advise f are opportuni-
ties, announce los t property and emer g ency ; and driv ers can repl y wit h pre-prog r ammed
responses. (4) passeng er inf or mation monit or (PIM) on back seat pro vides map f or route
tr acking; ne w s, sports, w eat her , and TL C Saf ety and Public Ser vice Announcements (PS As);
passeng er can mute or tur n off t he PIM f or t heir trip.
TPEP ins tallation s tarted in autumn 2007 and w ere com pleted b y 2008-12-01.
2
Also
t here are Liv er y P asseng er Enhancement Prog r am (LPEP) Pro viders. Y ello w taxi digital
trip recor d collection beg an in Januar y 2009; Green taxi trip data collection be g an since
g r een cabs beg an oper ating in A ugus t 2013.
3
2.1.1 TPEP/LPEP Pr o viders
A TPEP pro vider is a v endor who has contr acted wit h TL C t o ins tall and maintain TPEP
sys tem in T axicabs.
4
There are t hree TPEP pro viders: V eriF one T r ansportation Sys tems
(VTS); Creativ e Mobile T echnologies (CMT); DDS W ireless Inter national (DDS), whose
contr act w as no t continued. Square w as shorted in v ol v ed in t he TPEP 2.0 pilo t prog r am.
Each ser vice pro vider eit her has subcontr acted wit h g ar ag es and meter shops t o ins tall
and ser vice t heir sys tems, or has dedicated f acilities t o pro vide ser vice t o medallion o wn-
ers. There is a cos t t o Medallion o wners in signing contr acts wit h TPEP pro viders, which
1
TL C 2004 Annual R eport
2
TL C TPEP R eques t f or Inf or mation (RFI) 2009-04-14. See also Ir a Golds tein, Inf or mational Ex chang e Con-
f erence letter , 2009-08-19.
3
http://www.nyc.gov/html/tlc/downloads/pdf/press_release_08_03_15.pdf
4
TL C R ules §51-01
18
C hapter 2 D a t a
Medallion o wners are free t o choose. The re v enue g ener ated from ads and on-screen pro-
g r ams fund t he taxicab sys tems so t hat t he y do no t cos t an yt hing f or t he driv ers.
5
Medal-
lion o wners pa y f or equipment maintenance, eit her in a maintenance contr act co v ering all
repairs and replacements or per individual repairs.
CMT
6
w as f ounded in 2005 b y R on Sher man, t he president of t he Metropolitan T axi
Boar d of T r ade (g ar ag e o wners association). Since its f oundation, CMT has been a s tr ate-
gic partner wit h Mobile Kno w ledg e Sys tems, Inc.
7
, a Canada-based f or hire-v ehicle dis-
patch com pan y , t o pro vide integ r ated taxi solution in NY C. CMT consolidated wit h Mo-
bile Kno w ledg e on 2014-10-15, making CMT Group t he lar g es t integ r ated taxi technology
solution pro vider w or ldwide. CMT pro vides free use of equipment and w eb-based man-
ag ement sof tw are (FleetN et).
8
F or TPEP , CMT uses N a vman MD T -860 as DIM, as is used in CMT LPEP . V ehicle/fleet
o w ners and TL C can communicate wit h driv er via FleetN et, CMT’ s w eb portal which also
tr ack s v ehicle locations.
9
CMT ex clusiv el y partners wit h Bank of America f or wireless elec-
tronic pa yment. And T -Mobile pro vides mobile netw or k f or CMT .
10
Electronic pa yment tip presets is 20%, 25% and 30%, or cus t om tip amount. In 2012,
CMT designed a f eature f or t he visuall y im paired t o pa y electronicall y . RideLinQ is t he
pa yment app f or CMT , which does no t pro vide e-hail op tions. Credit Car d Processing F ees
can be char g ed in tw o w a ys. If o wner is t he merchant of recor d, o wners will be char g ed
per electronic pa yment a r ate no t t o ex ceed 25 basis points (0.25%) and 25 cents abo v e
t h e CMT -appro v ed processor’ s merchant frees related t o t he specific car d used. If CMT is
t h e merchant of recor d, o wners will be char g ed b y CMT percent (5%), inclusiv e of CMT -
5
http://www.thirteen.org/metrofocus/2012/04/technology- in- cabs- take- different- routes/
6
http://creativemobiletech.com/
7
http://www.mobile- knowledge.com/
8
http://creativemobiletech.com/solutions/driver- solutions/
freedom- solution/
9
https://fleetnet.cmtnyc.com
10
https://youtu.be/xE- punmYRB0?t=1m22s
19
C hapter 2 D a t a
appro v ed processor’ s merchant f ees related t o t he specific car d used. A ccor ding t o CMT
President Jesse Da vis, t heir sys tem is subtler and quieter t hat VTS, and do no t offer a lo t
of butt ons or f eatures t o na vig ate t o a v oid passeng ers fr us tr ation.
V eriF one T r ansportation Sys tems, Inc.
11
(VTS) w as f or med on 2005-10-24 as a joint v en-
ture of V eriF one Holdings, Inc.
12
( NY SE:P A Y ) and T axitronic S.A .
13
(Interf acom S.A .U .;
Spain-based), f or equipping taxis wit h integ r ated fleet manag ement and cus t omer pa y -
ment sys tems.
14
T axitronic pro vides taximeter manuf acturing, and has been ser vicing t he
NY C taxi indus tr y since 1997; V eriF one pro vides secure electronic pa yment and mobile
adv ertising. VTS g ener ated re v enue from electronic tr ansaction processing f ees and pro vi-
sion of ongoing support ser vices. VTS w as acquired b y V eriF one on 2010-04-02, all oper a-
tions aligned wit hin V eriF one’ s Integ r ated Sys tems or g anization. Amos T amam f ounded
Metro-Shop in N e w Y or k in 1992, and led de v elopment of t he firs t credit car d taximeter . He
w as t he president of T axi T ronic, t he indus tr y’ s lar g es t meter v endor (Mat he w , 2008 ). He
w as t he CEO and President of VTS and has been t he Senior V ice President of T axi Sys tems
at V eriF one Sys tems Inc. since Januar y 2010.
15
VTS uses Micronet N et-960CE-X as DIM, which consis ts of: a SIM car d slo t t o SIM car d
(subscriber identity); Cellular modem antenna connect or (SMA) t o GSM/GPRS Antenna;
GPS antenna connect or (MCX) t o GPS antenna located outdoors wit h a clear vie w of t he
sky ; Inter nal expansion modules f or wireless communication (included in X3 model). The
expansion modules ha v e a GSM/GPRS cellular modem (Mo t orola G24) on Serial P ort 1
(RS-232), which pro vides Quad band 850/900/1800/1900 MHz, GPRS Multi slo t class
10, MO/MT SMS, F AX, and V OICE. It also has a GPS receiv er (T rimble Lassen iQ) on Se-
rial P ort 2, pro viding 12-channel simultaneous oper ation at horizontal accur acy <5 meters
11
http://www.verifonets.com/
12
http://www.verifone.com/
13
http://www.taxitronic.com/
14
http://www.businesswire.com/news/home/20051024005456/en/
VeriFone- Taxitronic- Form- Taxi- Management- Systems- Venture
15
http://daniellesdish2.blogspot.com/2009/10/amos- tamam- taxi- genius.html
20
C hapter 2 D a t a
(50%), <8 meters (90%); and altitude accur acy <10 meters (50%), <16 meters (90%); along
wit h NMEA 0183, TSIP , T AIP pro t ocols. T or taximeter , T axitronic TX -36, consis ts of: a clock
pre-prog r ammed da y light-sa ving time and leap y ears, char g e f or extr as prog r ammaticall y
based on time of da y or b y manual in put ; a frequency counter which measure dis tance
b y wheel re v olution; a cellular modem; a RS-232 port, f or magnetic car d reader , k e ypad,
SIM car d and cellular modem, data ter minals; memor y holds inf or mation on up t o 75 trips
per shif t ; and a receip t printer . The PIM, V eriF one MX870 has a magnetic and smart car d
reader , t ouchscreen (virtual PIN pad) and s ty lus.
GPS antenna receiv es GPS satellite signals and passes t hem t o t he GPS R eceiv er . GPS
receiv er (e.g. SIM808) is a module/chip wit h tr acking and acquisition receiv er channels
which calculate t he coor dinates (also v elocity and time; PVT) from GPS signals; s t or ag e
is op tional. GPRS antenna push coor dinates in IP pack ets t o a centr al ser v er oper ated b y
fleet d ispatchers or municipal manag ers. Some TPEP Sys tems w or k independentl y of t he
taximeter (e.g. GPS/GPRS module ins talled as add-on t o t he taximeter), o t hers do no t (e.g.
TX -36 b y VTS). Driv er ma y continue t he shif t as long as t he taximeter is w or king proper l y .
TL C requires t he driv er t o report sys tem malfunction t o TPEP pro vider and retur n t he taxi
f or repairs wit hin 48 hours.
T axitronic also mak es taximeters f or European mar k ets such as Barcelona. TXD-30 inte-
g r ates taximeter TX -30 wit h data ter minal f or GSM/GPRS cellular modem, and connects
t o T C50 f or pa yment aut horization and communication wit h fleet manag ement or emer -
g e ncy ser vices.
De vice I/O. The DIM, N et-960CE-X, has function k e ys, an alpha-numeric k e ypad wit h
butt ons f or Clear and Enter , and a ro tat or nob. Main assignments of t he function k e ys:
F1 (DR VR ID), hack license number sign in/out (use k e ypad; rejects in v alid number); F2
(FLA T RA TE), out of city nego tiated flat r ate (use k e ypad; amount prom p t t o PIM bef ore
trip); F3 (LAS T REC); F4 (OFF DUTY), off-duty code (use ro tat or knob); F5 (ADD T OLL),
21
C hapter 2 D a t a
t oll amount (use k e ypad; added t o t o tal; TX -36 aut omaticall y detects t olls); F6. Op tions
on t he main menu: 1, texting, f or missing passeng er item; 2, trip his t or y (las t 75 trips),
wit h trip number , driv er number , date, pickup and drop off time, passeng er number , r ate
number , dis tance number , pa yment type, f are breakdo wn (could be used f or reporting); 3,
v oid t he las t electronic pa yment (f or alter nativ e pa yment met hods); 4, settings, f or back
light, v olume, wireless modem s tatus, debug mode.
The taximeter , T axitronic TX -36, in t he v acant mode pro vides inf or mation on date, time
of da y , taxi number , trip summar y inf or mation; K f act or (pulses per mile), r ate chip ID,
check sum, sof tw are v ersion (1.16 or higher). The k e ypad includes: H f or ”HIRED”, which
set r ate code (ro tate from 1 t o 3, manuall y chang e t o 4 be y ond city limit) and t hen passeng er
count (op tions from 1 t o 6); T f or ” TIME OFF”, t o end trip, aka “diseng ag e t he meter”; P f or
print, while in “V A C ANT” (x1, las t receip t ; x3, electronic pa yment t o tals report ; x4, dail y
t o tals report ; x6, las t fiv e trips report ; x7, las t fiv e t olls) F f or function, reset meter t o tals
(f or personal report);
The PIM, V eriF one MX870 and Car d R eader (magnetic s trip reader ; op tionall y RFID
car d reader), pro vides route tr acking (lef t pane) and video content (right pane) during trip.
A t trip end, it sho w s “Medallion number”, “Driv er ID” (0-padded t o 8 digits), pa yment
op tions (“CREDIT C ARD”, “C ASH”), f are breakdo wn (f are + extr a + t olls = t o tal), and TL C
reminder . F or f are under $25, it sho w s tip presets ($2/3/4) and cus t om amount (whole
dollars); f or f are o v er $25, it sho w s tip presets (20/25/30%) and cus t om amount (whole
dollars). Signature is required on receip t.
When an electronic pa yment is rejected b y t he sys tem and t he passeng er has no cash, t he
cab/driv er should go off duty using t he code ”F are Dispute” and sol v e t he issue depending
on t he cause. If t he taxicab is in a “dead spo t” wit h no connection t o t he data netw or k
f or electronic pa yment appro v al, driving t o ano t her location ma y sol v e t his issue. If t he
passeng er’ s credit/debit car d is in v alid or o v er limit, t he driv er should seek out an A TM t o
22
C hapter 2 D a t a
enable t he passeng er t o pa y in cash. If t he taximeter los t communication while processing
electronic pa yment, it will appro v e t he pa yment and indicate “s t ore f or w ar d” on DIM,
which clears upon reconnection and successful processing (VTS recommend approaching
a meter shop if sys tem accumulated t hree flags).
Some recor ded Medallion and hack IDs are inter nal use: Medallion T O WER1 , hack 555555
and 222222 , and com pan y name “ TL C T es t” are VTS demo IDs.
16
Medallion TL C4 , com-
pan y name T axitr onic Demo are TL C demos names. V eriF one later launched a tablet
update t o PIM. W a y2Ride is t he pa yment app f or V eriF one.
DDS
17
, f or mer l y Digital Dispatch Sys tems
18
, w as aut horized t o pro vide t he TPEP sys-
tems, wit h de vices ins talled in appro ximatel y 1100 taxicabs. TL C’ s contr act wit h DDS ex-
pired on 2010-09-30, af ter which DDS w as contr actuall y oblig ated t o ser vice and maintain
its sys tems f or up t o one y ear . TL C tar g eted t o finish sys tem tr ansition b y 2011-04-30, and
reques ted Medallion o wners t o sign up wit h one of t he o t her tw o TPEP contr act ors b y
2010-12-31 and ha v e ne w de vices ins talled as of t he firs t v ehicle inspection on and f ollo w -
ing 2011-02-01.
19
As t he CMT and VTS’ s contr acts f or t he original TPEP expired on 2013-04-22, Square
w as a po tential com petition t o CMT and VTS, whose 2.75% f ee per swipe is among t he
lo w es t in t he indus tr y .
20
Right no w cab driv ers pa y an a v er ag e 5% per tr ansaction.
21
Square,
Jack Dorse y’ s (CEO of Square) mobile pa yments sys tem, has r un a pilo t prog r am f or TPEP
2.0, replacing TPEP in 13 v ehicles wit h iP ads in t he back seat and iPhones in t he front.
22
Square pulled out b y 2012-10-12.
23
16
VTS NY C T axi Sys tems T r aining videos, filmed 2006-09-13, uploaded on 2010-10-22. http://youtu.
be/tM7nSCjmkVI
17
http://www.ddswireless.com/
18
http://www.digital- dispatch.com/
19
TL C Indu s tr y N o tice #10-20 (2010-10-15), #10-22 (2010-10-27), and #10-27 (2010-11-29).
20
http://taxisocial.com/index.php/14- tlc- news/9- tlc- authorizes- creative- mobile- technologies- llc- cmt- and- verifone- inc- as- a- tpep- providers
21
http://www.thirteen.org/metrofocus/2012/04/technology- in- cabs- take- different- routes/
22
https://web.archive.org/web/20121001024702/http://betabeat.com/2012/09/
new- york- city- tlc- taxi- limousine- commission- ehailing- smartphone- apps- ruling- rfp/
23
http://nypost.com/2012/10/15/square- hits- brakes- on- taxi- payment- system- as- new- rules- loom/
23
C hapter 2 D a t a
2.1.2 D a t a dump
TL C R ules demanding electronic trip recor d collection w as passed on 2012-12-14.
24
The
r u les specify : required trip data attributes; on/off-duty s tatus chang e, wit h off-duty codes
and on-duty una v ailable codes (01, Going Home; 02, R elief T ime; 03, Off-Duty ; 04, Def ec-
tiv e Equipment ; 05, N o Char g e; 06, Dispute; 07, U na v ailable – En R oute E-Hail; 08, U n-
a v ailable – En R oute A ccessible Dispatch); On-duty Location P ositioning, t hat t he location
of an on-duty T axicab mus t be cap tured at t he commencement and end of each P assen-
g er f are, and at leas t e v er y 2 minutes (e v er y 5 seconds f or passeng er route map). All data
required t o be collected, tr ansmitted and mus t be maintained b y t he TPEP Pro vider f or
at leas t 3 y ears, ex cep t t hat On-duty Location P ositioning cap tured e v er y 2 minutes mus t
be maintained f or at leas t 6 mont hs. The A ut omatic V ehicle Location (A VL) Sys tem mus t
deter mine t he v ehicle location in On-duty Location P ositioning t o wit hin 15 meters at leas t
98% of t he time and t o wit hin 25 meters at leas t 99% of t he time.
25
Data dum p specification f or TPEP pro viders.
26
TL C R ule required (80) fields in t o tal,
and include tables f or trip data (40), r ate chang e (12), shif t (12), and breadcr umb (6). The
s t or e _and_fwd flag is a DO T need, included in TL C updated technical requirements
f or TPEP .
27
The specification w as updated on 2014-11-06 t o include T axicab Im pro v ement
Surchar g e.
2.2 D a t a origin
TL C originall y released TPEP trip recor ds t o F OIL reques ts. The data consis t of a sub-
set of attributes in TL C’ s database, populated b y data dum ps of TPEP pro viders (CMT ,
24
http://www.nyc.gov/html/tlc/downloads/pdf/tpep_promulgated_12_14_12.pdf
25
TL C R ules §75-03(y), §75-25(b)(5)(i), §75-25(c)(2), §75-25(e)(1), §75-25(h)
26
http://www.nyc.gov/html/tlc/downloads/excel/tpep_data_dump_proposal_v5.
xls
27
http://www.nyc.gov/html/tlc/downloads/pdf/newly_passed_rules_tpep_
updates_2013.pdf
24
C hapter 2 D a t a
VTS, DDS). Subsequent releases on TL C w ebsite and Google BigQuer y ha v e f e w er at-
tributes. I g at hered 2009-2013 trip recor ds wit h ID fields from A bhishek (and F aber). LPEP
trip recor ds w ere release t o F OIL reques ts, and also hos ted on TL C w ebsite wit hout ID
columns.
F reedom of Inf or mation La w ref ers t o NY S Public Officer’ s La w , Article 6, Section 84-
90.
28
On 2012-03-07, f or mer Ma y or Bloomber g signed Local La w 11 of 2012, commonl y
kno w n as t he “Open Data La w”, which amended t he N e w Y or k City adminis tr ativ e code
t o mandate t hat all public data be made a v ailable on a single w eb portal b y t he end of
2018. A ccor ding t o t he la w , a “public data set” is an y com prehensiv e collection of data t hat
is maintained on a com puter sys tem b y or on behalf of a City ag ency .
As no ted b y Daniel B. W or k
29
: “ The NYYT&L Commission does no t res trict publish-
ing t he data, as deter mined from personal communication wit h t he Commission. ’The
data w as disclosed pursuant t o t he NY S F reedom of Inf or mation La w , t heref ore t here is
no licensing res triction on y our publication of t he data. ”’ Moreo v er , t he U niv ersity of Illi-
nois at U rbana Cham paign Ins titutional R e vie w Boar d re vie w ed t heir reques t t o publish
t his dataset, and responded t hat “Since y ou receiv ed t his inf or mation via t he F reedom
of Inf or mat ion La w , and will be anal yzing trip and f are data, y ou are no t considered in-
ter acting or inter v ening wit h human subjects, t heref ore, it has been deter mined t hat t his
project as described does no t meet t he definition of human subjects research as defined
in 45CFR46(d)(f) or at 21CFR56.102(c)(e) and deter mined publication does no t cons titute
human subjects research. ”
T able 2.1 lis ts rele v ant ear l y F OIL reques ts t o TL C.
30
Daniel B. W or k hos ts data re-index ed
as 20 1XDDDDDD in or der of medallion-hack pairs ’ firs t trip recor d of y ear .
31
A bhishek
N ag ar a j shared wit h me 2009-2013 trip data he F OIL ’ d on 2014-02-25, which is a super
28
https://www.dos.ny.gov/coog/foil2.html
29
https://my.vanderbilt.edu/danwork/open- data- 2/
30
https://github.com/ajschumacher/foilfoil
31
https://my.vanderbilt.edu/danwork/open- data- 2/
25
C hapter 2 D a t a
set of F arber and Whong’ s data: On 2014-06-16, Chris Whong shared t he 2013 trip data
(11.0GB)
32
and f are data (7.7GB)
33
, which ha v e original medallion and hack license num-
bers. The GitHub mirror b y @andr esmh on 2014-06-18 is no t t he r a w TL C dum p, ha v e
minimal processing.
34
Their copies of TPEP data a re equiv alent.
T able 2.1: F OIL reques ts t o TL C, 2014-01-01 t o 2015-01-31, f or TPEP data
Date R eques ter Y ears
2014-01-08 Princet on U niv ersity (Henr y S. F arber) 2009
2014-02-11 U niv ersity of Illinois (Daniel B. W or k) 2010-2013
2014-02-25 A bhishek N ag ar a j (MIT Sloan) 2009-2013
2014-03-11 Chris Whong 2013
2014-04-09 AR GUS Inf or mation & A dvisor y Ser vices, LL C
2014-05-02 Samuel Hirshman (RAND)
2014-07-17 Chris tian K oenigsheim
2014-08-26 Har v ar d U niv ersity
2014-09-17 Alex MacKa y (UChicago Econ)
2014-09-18 Ar up
2014-10-09 Center of U rban Science+Prog ress, NYU
2015-01-24 Marc- Ant oine Schmidt (U T oront o, Econ)
NY C TL C will no w den y F OIL reques t f or trip recor ds wit h medallion ID and hack li-
cense, accor ding t o Jerem y W ong in N o v 2015.
35
S tarting Jul y 2016, TL C pro vides onl y (263)
taxi zones
36
ins tead of latitude and longitude coor dinates of taxi trips.
The CS V files on n y c.go v
37
are no t clean: it has inconsis tent schema, meaningless tr ailing
floating points. The CS V files are also hos ted on Google Cloud S t or ag e.
38
TL C claims no
responsibility f or released trip recor ds: “ The data used in t he attached datasets w ere col-
32
http://chriswhong.com/wp- content/uploads/2014/06/nycTaxiTripData2013.
torrent
33
http://chriswhong.com/wp- content/uploads/2014/06/nycTaxiFareData2013.
torrent
34
http://www.andresmh.com/nyctaxitrips/
35
http://chriswhong.com/open- data/foil_nyc_taxi/comment- page- 4/
36
https://toddwschneider.carto.com/viz/2961a180- ffb1- 11e6- a29f- 0e233c30368f/
public_map
37
http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml
38
https://storage.googleapis.com/tlc- trip- data/2009/yellow_tripdata_
2009- 01.csv
26
C hapter 2 D a t a
lected and pro vided t o t he NY C T axi and Limousine Commission (TL C) b y technology
pro viders aut horized under t he T axicab and Liv er y P asseng er Enhancement Prog r ams
(TPEP/LPEP). The trip data w as no t created b y t he TL C, and TL C mak es no represen-
tations as t o t he accur acy of t hese data. ” TPEP data hos ted on Google BigQuer y
39
do no t
ha v e t he tw o ID columns, but ma y ha v e f e w er semantic data errors t han t he TL C F OIL
response.
Green cab trip data is a v ailable from A ugus t 2013 on TL C w ebsite. T able 2.2 lis ts rele v ant
ear l y F OIL reques ts t o TL C.
40
T able 2.2: F OIL reques ts t o TL C, 2014-01-0 1 t o 2015-01-31, f or LPEP data
Date R eques ter N o te
2014-03-13 Andre w Flo w ers - ESPN LPEP T rip Sheet R ecor ds of Boro (Green) cabs
2014-06-02 Epoch T imes NY C Boro T axi trip data - 8/2013 t o current
2014-06-04 Greenber g T r aurig All Boro T axi recor ds containing t he pick -up
and drop-off locations
2014-06-12 Columbia U niv ersity LPEP data f or t he Boro T axicabs
2014-07-28 Des tine Ozuy gur Medallion and S treet Hail Liv er y trip and
f are data from 2010
Green cabs ha v e sho wn im pact in surrounding Boros ear l y on, reaching 1/3 of y ello w
cab trips in Queens and Brookl yn b y Jan 2014. Y ello w cab trips from A ug 2013 ma y be
dropped from (equilibrium) anal ysis.
T rip share of priv ate e-hail pro viders is har d t o es timate. But accor ding t o Uber’ s report
t o TL C
41
, Uber has 5% trips com pared t o y ello w cabs during Apr -Sep 2014. A linear ex-
tr apolation back t o A ug 2013 giv es 3k dail y pickup, 0.6% trips b y y ello w cabs, which is an
o v eres timate.
39
gs://n y c-tlc:y ello w .trips
40
https://github.com/ajschumacher/foilfoil
41
https://github.com/fivethirtyeight/uber- tlc- foil- response
27
C hapter 2 D a t a
2.3 D a t a pr ocessin g
The r a w data is lar g e and has man y issues such as in put error and artif acts, which requires
a sys tematic processing procedure. I design a hier archical data schema t o f acilitate data
v ersioning and processing, s tarting from r a w data (Le v el 0):
• Le v el 1: recons tr ucted recor ds wit h c orrect syntax
• Le v el 2: clean data wit h deriv ed attribute s
• Le v el 3: data mapped ont o regular spatial e lements
• Le v el 4: model output or results agg r eg ated as spatial time-series
T able 2.3 sho w s t he chang e in serialized data size at v arious processing le v els.
T able 2.3: S tandar d sch ema hier arch y file sizes
V ersion Size (csv) Size (csv .gz)
Le v el 1 114GB 32GB
Le v el 2 105GB 29GB
Le v el 3 - -
The principles of real-w or ld data processing can be summarized as: label widel y ; modify
where appropriate; ne v er remo v e.
2.3.1 D a t a c ollection methods
T o handle r a w data correctl y , one needs t o kno w t he data collection met hods firs t. F or
exam ple, it has been no ted t hat driv ers of ten confuse t he ”no char g e” and ”dispute” off-
duty codes wit h cancelling a mis tak en f are r ate selection.
42
Data collection de vice and or der f or trip attributes in TPEP data dum p (21), modeled
ag ains t VTS def ault sys tem configur ation:
42
http://www.nycitycab.com/forum/Replies.aspx?postid=707
28
C hapter 2 D a t a
1. Pre-shif t, DIM (3): v endor_id ; medallion ; hac k_license ;
2. Pre-trip (2):
• T aximeter (2): r at e_code and passeng er_count ;
• DIM: out of city nego tiated flat r ate;
3. On-trip (13):
• T aximeter (7): tr ip_dis t ance , tr ip_time , and f are items ( f ar e_amount ,
e xtr a or sur c har g e , mt a_t ax , t olls_amount , t o t al_amount );
• DIM, GPS antenna + receiv er (6): pic k up_dat e time , pic k up_longitude ,
pic k up_latitude ; dr opof f_dat e time , dr opof f_longitude , dr opof f_latitude ;
4. pos t-trip (3):
• DIM: t oll amount, v oid t he las t electronic p a yment ;
• PIM (2): pa yment_type ; tip_amount , rider in put f or electronic pa yment,
driv er op tionall y report f or cash pa yment ;
• T aximeter , cellular modem (1): s t or e_and_fwd_f lag ;
5. P os t-shif t, DIM: off-duty codes;
The natur al ID f or a trip recor d is: ( medallion , hac k_license , pic k up_dat e time ).
The or der a trip recor d appears in t he r a w data can also be used a unique ID f or tr acing data
lineag e across processing le v els, I name t his ne w attribute as r a w_id . N o te t hat driv er
names canno t uniquel y identify driv ers, especiall y f or Indian, Ir anian and Ar abic names.
2.3.2 S ynt a ctic d a t a cleanin g
Le v el 1 of data processing recons tr uct recor ds t hat are syntacticall y correct and serialize t o
a com pact human-readable f or mat. Syntactic data issues include: line ending wit h carriag e
29
C hapter 2 D a t a
retur ns; em p ty lines (as ro w s of N A); ro w s containing extr a columns.
Specificall y , w e mer g e trip and f are attributes, reco v ere ID v ariables (medallion, hack),
sort and g roup b y tem por al and de vice oper ational attributes. The data ma y be alter na-
tiv el y or dered b y ( medallion , pic k up_dat e time ).
W e also chang e t he schema t o sa v e s t or ag e, see T able 2.4 . Geog r aphic coor dinates shall
be sa v e as fix ed-precision integ er , as GPS de vice onl y pro vide positioning up t o t he sixt h
decimal point of g eog r aphic coor dinates, t he res t are database floating point precision and
can be saf el y rounded off. T imes tam p shall represent full seconds since an epoch. F are
items shall be sa v e as fix ed-precision integ ers t o t he firs t/second decimal point. Useless
columns, such as passeng er count, ma y be remo v ed. T able 2.5 summarizes data sizes at
Le v el 1.
T able 2.4: Le v el 1 data schema (22; or der b y pic k up_dat e time )
A ttributes T ype
v endor f act or wit h 3 le v els (VTS, CMT , DDS)
medallion char acter
hac k integ er
pic k up_dat e time ,
dr opof f_dat e time
POSIXct
r at e integ er
pa yment f act or wit h 5 le v els (cash, credit, no char g e,
dispute, unkno wn)
f lag logical; cellular modem s tatus
dur ation integ er (seconds) or doub le (seconds or min-
utes)
miles double
t o t al , f ar e , e xtr a , tip , t olls , t ax double
fr om_lng , fr om_lat , t o_lng , t o_lat double
passeng er s integ er
r a w_seq integ er
30
C hapter 2 D a t a
T able 2.5: Le v el 1 data s t or ag e sizes
Y ear T rips CS V (t o tal) CS V (trip) F eat her
2009 170896055 55GB 33GB 20GB
2010 169001153 31GB 20GB 13GB
2.3.3 Semantic d a t a cleanin g
Semantic data issues are cases when measurements do no t represent t he under l ying quan-
tity , reg ar dless of data type. F ixing semantic data errors chang es t he meaning of t he data,
and t hus shall be handled wit h caution. Semantic data issues can be separ ated int o elemen-
tar y and com plex issues: elementar y issues in v ol v e onl y one recor d, while com plex ones
relates multiple recor ds. Le v el 2 data processing handles onl y elementar y issues, and also
deriv e v ariables at t he same resolution in time and space as Le v el 1 data.
Gener al semantic data issues include extremes, errors, artif acts, and inconsis tencies. As
of dur ation extremes, f or exam ple, 2 million trips wit hin Manhattan in 2011 las ted less
t h an 1 minute. Errors can happen as medallion in put errors, times tam ps no t correcting
f or da y light sa ving time. and trips wit h identical pickup and drop-off GPS positions. Arti-
f acts in g eog r aphical coor dinate rounding, as seen from a t hin v ertical line do wn t he eas t
riv er . N o te t hat some visual artif acts reflects real phenomenon ins tead of data issue: an
area around WT C ha v e no taxis because it has security barriers since 9/11; locations on
mo t or w a y can be recor ded in fix ed f are trips betw een Manhattan and JFK, because driv ers
ha v e little incentiv e t o s tart meter at t he exact pickup or drop-off location. Inconsis tencies
can happen in man y subsets of t he attributes, such as betw een dur ation and times tam ps,
betw een times tam p and r ush hour or o v er night surchar g es, betw een f are items and t he
t o tal amount, and betw een r ate code and t he o t her attributes. An exam ple of com plex se-
mantic data issue is o v er lapping trips f or one Medallion or hack. N o te t hat MD5 hashes
of m edallion numbers and hack license numbers can ha v e a f e w clashes, such issue can be
resol v ed b y using multiple ID attributes as v ehicle-driv er identifier . In our s tudy , all t hree
31
C hapter 2 D a t a
de vice ID attrbutes (v endor , medallion, hack) are used t o identify a trip sequence.
The handling of semantic data issues depend on one’ s confidence about t he under l ying
causes. If t he fix is e vident, t he issue can be readil y corrected. If t he correct v alue canno t
be inf erred wit h high confidence, one ma y use im putation or sim pl y drop t he recor d in
rele v ant anal yses. F or exam ple, no t all char acter sequences are real Medallion numbers,
which ha v e patter n 0A00 f or canonical Medallions and patter n SB V000 f or SB Vs. Because
Medallion number are entered int o t he DIM and r arel y chang ed, non-canonical licenses
are unlik el y t o be human error and can be saf el y remo v ed. As ano t her exam ple, when a
recor d has non-increasing time s tam ps, one canno t be sure which, or bo t h, time s tam ps
are incorrect. Such errors typicall y canno t be corrected and ha v e t o be remo v ed.
T able 2.6: Le v el 2 data schema (22; or der b y textttmedallion, hac k , pic k up_dat e time )
A ttributes Group
v endor , medallion , hac k ID attributes in DIM
r at e , r ider s T aximeter hire in puts
milec , secs T aximeter counter in centi-mile and
clock measurements in seconds
t o t alc , f ar e c , e xtr ac , t ollc , t ax c , tipc Mone y items in cents
pa yment End-of-trip PIM and DIM in put
pic k up_dat e time , dr opof f_dat e time Clock readings
plng6 , plat6 , dlng6 , dlat6 Pickup/drop-off GPS coor dinates
(F ix edP oint6)
r a w_seq
mar k Flags f or elementar y recor d issues
(BitF ield) replacing modem s tatus
f lag
Driv er income can be easil y deriv ed f or each trip: t he driv er ear ns t he sum of trip f are,
surchar g e, and tips. The firs t tw o attributes are alw a ys included in each recor d; tips are
aut omaticall y recor ded if paid electronicall y , while manuall y in put b y t he driv er if paid in
cash, which is usuall y missing. N o te t hat driv er income per shif t is no t t he t o tal income of
all t he trips made in a shif t, because driv ers ha v e t o pa y f or man y o t her t hings incurred
32
C hapter 2 D a t a
during t he shif t, which ma y include lease cos t, v ehicle sales tax, credit car d processing f ee,
g asoline, and tr affic or par king tick ets.
2.3.4 Sp a tial mappin g
Le v el 3 data processing maps location attributes t o regular spatial and tem por al elements.
In o t her w or ds, t his s tep discretizes (coarsens) t he measurements of time and space. F or
taxi trip recor ds, t he appropriate spatial element is s treet seg ement. Since t he taxi trip
recor ds are already rounded b y second (CMT , DDS) or minute (VTS), t here is no t much
need t o modify time measurements.
Mapping GPS points ont o a road netw or k is essentiall y finding t he road segment where
t h e under l ying measurement t ook place. Assuming GPS error is iso tropic, t he mos t lik el y
s treet segment corresponding t o a measurement is t he one closes t t o t he measurement.
When GPS error is lo w , such as f or places in Brookl yn, it ma y be possible t o deter mine
t h e side of s treet. Ho w e v er , wit h GPS precision at about f our decimal points (11.1m nort h-
sout h), and at 10-20m or lar g er in man y places in do wnt o wn Manhattan due t o urban
can y on effects, locations can at bes t be deter mined t o undirected s treet segments. N o te
t h at GPS accur acy during 2009–2012 has seasonal v ariations: it goes up s tarting in t he
spring, and t hen abr up tl y f alls in t he f all. GPS accur acy im pro v ed o v er time, partl y because
in 2011 R ussia slapped a 25% im port tariff on GPS de vice t hat did no t receiv e GL ON ASS
signals. All t he phone mak ers responded b y switching o v er t o use bo t h GPS and GL ON ASS
simultaneousl y , so GPS receiv ers ha v e more satellites t o lock on t o.
T rip recor d schema at Le v el 3 replaced trip pickup and drop-off longitude and latitude
wit h segment g eometr y ID: pseg , dseg (integ er), whose v alue is N A f or locations a w a y
from t he s treet netw or k.
33
C hapter 2 D a t a
2.3.5 A ggreg a tion
Le v el 4 data processing agg reg ates model outputs or results at coarser obser v ation units,
representing spatial time-series or o t her data models. Data at t his l e v el are much smaller
and do no t ha v e much s t or ag e issue. Depending on t he models used and ques tions ask ed,
multiple f or ms of le v el 4 data exis t, and t hus no t v ersion controled.
F or taxi trip recor ds, deriv ed v ariables at agg reg ate le v el ma y include t he number of
cabs in ser vice, hour l y income, and v acancy r ate. A gg reg ate obser v ation units ma y be hour ,
shif t , s treet segment, medallion, driv er , or t heir combinations.
Besides spatial time-series, data can also be agg reg ated int o g r aph models. The relation
betw een medallion and hack can be used t o categorize hack s int o o wner -oper at or , long-
lease driv er , mix ed-lease driv er , or short-lease driv er . F or exam ple, t he netw or k ma y ha v e
each hack as a node, each connecting shif ts as link , w eighted b y shif t count ; medallion ID is
also affiliated wit h link s. The data s tr ucture is t hus: medallion , fr om_hac k , t o_hac k ,
counts .
2.4 Sp a tial D a t a Pr ocessin g
2.4.1 Manha tt an s treet netw ork
The Manhattan island is a long s trip of land spreading from sout h t o nort h, tilting eas t-
w ar d. The Manhattan island is separ ated from t he Long Island b y t he Eas t Riv er ; separ ated
from N e w Jerse y b y t he Hudson Riv er ; separ ated from Bronx b y t he Har lem Riv er . Ear l y
de v elopment of Manhattan built roads lar g el y par allel t o t he irregular w aterfront on t he
sout her n end, creating w edg es of land in t he inner part of lo w er Manhattan.
In 1807, t he Common Council of N e w Y or k w as g r anted sw eeping po w er b y t he N e w
Y or k S tate Legislature t o regulate s treet cons tr uction in Manhattan nort h of Hous t on S treet.
The Commissioners ’ Plan of 1811 designed 12 s tr aight a v enues at 29 deg rees eas t of tr ue
34
C hapter 2 D a t a
nort h and 155 ort hogonal s treets; alt hough 12t h A v enue is on extended land no w lar g el y
part of t he W es t Side Highw a y . Block widt h betw een A v enues are irregular : 1s t-2nd, 650
f eet (200 m);2nd-3r d, 610 f eet (190 m);3r d-6t h, 920 f eet (280 m);6t h-12t h, 800 f eet (240
m).Lexingt on and Madison A v enues (145 m, 155 m) w ere inter polated betw een 3r d and
5t h af ter t he original plan. The numbered s treets are 60 f eet (18 m) wide reser ving 200 f eet
(61 m) f or block s, resu lting in almos t exactl y 20 block s per mile. F if teen cross t o wn s treets
w ere designated as 100 f eet (30 m) wide f or tw o-w a y tr affic: 14t h, 23r d, 34t h, 42nd, 57t h,
72nd, 79t h, 86t h, 96t h, 106t h, 116t h, 125t h, 135t h, 145t h and 155t h. The g rid w as no t com-
pletel y im plemented be tw een Hous t on S treet and 14t h S t, t he nort h boundar y of Lo w er
Manhattan. The actual boundar y from eas t t o w es t is: Hous t on S treet, Bo w er y , Cooper
Square, 8t h S t, Green wich A v enue, Ganse v oort S treet.
Broadw a y already exis t b y t he time of t he Plan, whose angled crossings wit h A v enues
resulted in v arious public spaces: U nion Square at P ar k A v e (4t h), Madison Square at 5t h,
Her a ld Square at 6t h, T imes Square at 7t h; Columbus Circle at 8t h; Richar d T uck er Square
at 9t h, V er di and Sher man Squares and 10t h, and S tr aus P ar k at 11t h. Broadw a y is a sep-
ar a ted primar y road (FCC: A25) betw een 59t h S t (Columbus Circle) and 169t h S t, unsep-
ar a ted primar y (FCC: A21) t o t he nort h, sout hbound one-directional (FCC: A31) t o t he
sout h.
The road netw or k slightl y chang es o v er time, which affects road netw or k modeling in
our anal ysis. Since 2009, Broadw a y betw een 59t h S t (Columbus Circle) and 14t h S t (U nion
Square) has been reconfigured multiple times b y NY C DO T t o ser v e pedes trian and im-
pro v e tr affic.
43
Green Light f or Midt o wn
44
affected Broadw a y betw een 59t h S t and 23r d
S t , which s tarted on 2009-05-24 and ended in mid- A ugus t same y ear . The project reduced
lanes betw een Columbus Circle and 58t h S t from f our t o tw o; and banned mo t or v ehicles
betw een 47t h S t and 42nd S t (T imes Square), and betw een 35t h S t and 33r d S t (Her ald
43
http://www.nyc.gov/html/dot/html/pedestrians/broadway.shtml
44
https://www.flickr.com/photos/nycstreets/sets/72157622973444484
35
C hapter 2 D a t a
Square).
45
U nion Square R edesign
46
in Sep tember 2010 affected Broadw a y betw een 23r d
S t and 14t h S t, which includes lane and tur n res triction and signal timing chang es.
Manhattan island can be cut int o lengt hwise portions based on t he g rid.
• Lo w er Manhattan: sout h of 14t h S t.
• Midt o wn: 14t h-59t h S t.
• U pper Eas t Side: 59t h-96t h S t, eas t of 5t h A v e.
• Centr al P ar k: 59t h-110t h S t, 5t h-8t h A v e.
• U pper W es t Side: 59t h-110t h S t, w es t of 8t h A v e.
• U pper Manhattan: t he res t of t he Manhat tan island.
Core Manhattan defined b y TL C consis ts of all t hese regions ex cep t U pper Manhattan.
P opular points of interes t in Manhattan as of taxi activity includes: P ennsy l v ania S tation
and Madison Square Gar den, which is a ma jor city and inters tate r ail-tr ansit hub under -
g r ound and an e v ent center abo v e; Gr and Centr al T er minal (GCT); P ort A ut horit y Bus
T er minal (P ABT); Columbus C ircle; and Gr and Ar m y Plaza.
2.4.2 Segment map of c ore Manha tt an
T o contain t he size of t he road netw or k wit hout tr uncating muc h of taxi activity , w e choose
a part of Manhattan where mos t taxi pickups are located, called “core Manhattan”. Core
Manhattan defined b y TL C consis ts of all of t he Manhattan island ex cep t U pper Manhat-
tan; t hat is, t he part of t he Manhattan island bounded t o t he nort h b y Eas t 96t h S treet and
W es t 110 S treet. W e extended t he nort her n boundar y t o 130 S treet, t o include a f e w ho t
45
http://www.nyc.gov/html/dot/downloads/pdf/broadway_report_final2010_
web2.pdf
46
http://www.nyc.gov/html/dot/html/pr2010/pr10_043.shtml
36
C hapter 2 D a t a
spo ts be y ond Core Manhattan, such as Columbia U niv ersity and Har lem-125t h S treet S ta-
tion. T able 2.7 summaries taxi trip origin-des tination (O-D) proportions relativ e t o core
Manhattan, t he air ports, and an ywhere else. Alt hough core Manhattan is small relativ e t o
NY C, it dominates in taxi activity o v er t he city .
T able 2.7: O-D matrix r elativ e t o core Manhattan
Origin/Des tination Core Manhattan Air ports Else where T o tal
Core Manhattan 84.49 1.83 6.16 92.48
Air ports 2.18 0.22 0.98 3.39
Else where 1.59 0.11 2.44 4.14
T o tal 88.25 2.16 9.59 100.0
F or t he road netw or k of NY C, w e use OpenS treetMap data, a community -edited w or ld
map wit h an open license. W e extr act OpenS treetMap data wit hin a bounding pol y gon
containing core Manhattan, and filter f or t he public non-free w a y v ehicular road netw or k.
Specificall y , w e include OSM w a ys whose highw a y tag tak e one of t hese v alues: tr unk ,
pr imar y , secondar y , t er tiar y , unclassif ied , r esidential . W e ex cluded
mo t or w a y because no taxi pickup or drop-off shall be on mo t or w a ys, despite tr ace amount
of ex cep tions.
47
T o mak e t he road netw or k s trongl y connected, w e remo v ed tunnels, bridg es,
and link roads. Rarel y used v alues are ex cluded, such as r oad and living_s tr ee t ; so
are roads no t accessbile b y taxis, such as f oo tw a y and ser vice . The filtered OSM map
has 8928 locations, 11458 edg es, and 2310 tr affic lights.
T o g et s treet segments as w e defined, w e use Open Source R outing Maching (OSRM) L ux en
and V etter ( 2011 ), a routing engine t hat tak es OpenS treetMap data as in put. OSRM creates
a com pressed g r aph f or efficient routing, retaining onl y nodes t hat are locations of penalty ,
including locations connecting more t han tw o segments, or tagg ed as tr affic signal or bar -
rier . W e tap int o t his capability and modified t heir code t o export t he routing g r aph. The
47
V alidated ag ains t Eric F ischer’ s map of 2013 data. Some of t hese recor ds ma y be fix ed-f are trips betw een
Manhattan and JFK, because driv ers ha v e little incentiv e t o oper ate t he taximeter at t he exact pickup and
drop-off location.
37
C hapter 2 D a t a
OSRM com pressed g r aph has 6001 segments, 7055 uni-directional segments, and 13542
maneuv ers (possible mo v es betw een uni-directional segments), see F igure 2.2 .
F igure 2.2: Segmented road netw or k of core Manhattan, colored b y type of tr affic: mos t
segments are one-w a y (g re y), a f e w are tw o-w a y wit hout ph ysical separ ation
(or ang e); f e w er are tw o-w a y s treets wit h ph ysical separ ation (g reen).
The Manhattan g rid w as designed wit h 260 f eet (79 meters) betw een center lines of num-
bered s treets (eas t-w es t), ex cep t f or 15 tw o-w a y s treets which are 40 f eet (12 meters) wider .
Dis tance betw een center lines of a v enues (sout h-nort h) v aries, around 150, 220, 275, and
310 meters. Broadw a y and s treets sout h of Hous t on S treet are build bef ore t he Commis-
sioners ’ Plan of 1811, creating segments of irregular lengt hs, see F igure 2.3 .
GPS recor dings are noisy but reasonabl y accur ate, wit h deg r aded quality in densel y
built area due t o urban can y on effects, see F igure 2.4 . Civilian GPS receiv ers use t he S tan-
dar d P ositioning Ser vice, which has a user r ang e error (RMSE of r ang e error at user’ s
end) about 6 meters Misr a and Eng e ( 2006 ). TPEP v endors ma y use GPS receiv ers of
v arious quality f or t heir sys tems, but mos t appear t o be on par wit h t he s tandar d. F or
exam ple, VTS—a ma jor TPEP v endor—used Micronet N et-960CE-X as t he driv er inf or -
mation monit or , which ships wit h T rimble Lassen iQ GPS receiv er , wit h horizontal error
less t han 5 meters 50% of t he time, and less t han 8 meters 90% of t he time. As a guid-
38
C hapter 2 D a t a
Number of segments
Meters
1400
1200
1000
800
600
400
200
0
0 50 100 150 200 250 300
F igure 2.3: His t og r am of segment lengt h of core Manhattan s treet netw or k. The Manhattan
g rid i s regular , wit h a f e w common lengt hs of s treet segments.
ance, TL C r ules require t he positioning accur acy wit hin 15 meters at leas t 98% of t he time
and wit hin 25 meters at leas t 99% of t he time. Com pared wit h t he typical dis tance of
79 meters betw een s treet center lines, matching GPS locations t o t he neares t s treet seg-
ment w ould be correct in mos t cases ex cep t in do wnt o wn areas. W e use a module wit hin
OSRM t o match GPS locations t o t he neares t segments, where g eog r aphic coor dinates
are tr ansf or med in Mercat or projection f or iso tropic local scales of dis tance. Locations
matched on tw o-w a y s treets are assigned equall y t o bo t h uni-directional segments. Lo-
cations matched on tw o-w a y s treets are assigned equall y t o bo t h one-directional segments
in suppl y and demand es timation. The modified code is a v ailable at https://github.
com/rudazhan/osrm- backend .
GPS receiv ers occasionall y recor d meaningless locations, mos tl y wit h pickup and dropoff
locations bo t h missing. A bout 2.2% recor ds ha v e such issues, dis tributed relativ el y e v en
39
C hapter 2 D a t a
F igure 2.4: GPS recor ds g ener all y align w ell wit h t he road netw or k , but noise can be
significant in areas wit h densel y located high buildings. (A) Pickup counts
in t hree-decimal-point g r aticule in core Manhattan, log arit hmic scale black
t o blue. White circle mar k s P ennsy l v ania S tation - Madison Square Gar den
(P enn/MSG), which has t he highes t taxi pickup frequency in Manhattan. (B)
Pickups counts near P enn/MSG in 2013, linear scale black t o red wit h about
2% high v alues o v erexposed. Lines sho w s teets accessible t o taxis b y t hen.
40
C hapter 2 D a t a
o v e r time but no t across taxis, see F igure 2.5 . A small fr action of taxis consis tentl y report
missing locations, which ma y be eit her t he y ha v e def ectiv e GPS receiv ers ins talled and no t
fix ed af ter w ar ds, or t he driv er uses a GPS jamming de vice t o a v oid tr acking. Ex cep t t hese
cases, w e consider t he o v er all extent of GPS missing v alues as accep table.
Pickup r ate dis tribution is spatiall y highl y heterog eneous, while drop-off dis tribution
is co m par ativ el y e v en, see F igureo 2.6 . The map of pickup-dropoff r atio sugg es ts t hat taxi
driv ers pref er t o head back t o high demand areas af ter a drop-off at a lo w demand location.
Ho t spo ts of taxi pickup are typicall y tr ansportation hubs, e v ent and shopping centers. In
Manhattan, points of interes t wit h t he highes t pickup frequencies include: P ennsy l v ania
S tation and Madison Square Gar den, Gr and Centr al T er minal (GCT), P ort A ut hority Bus
T er minal (P ABT), Columbus C ircle, and Gr and Ar m y Plaza.
2.4.3 D a t a pipeline
Multiple sof tw are are used in spatial data processing. F or map data, w e firs t do wnload
t h e smalles t OpenS treetMap extr act co v ering NY C from OSM extr act mirrors. W e t hen
use osmupdat e and osmium t o filter b y pol y gon and tag t o reduce t he map t o a road
netw or k co v ering core Manhattan. Manual edits of map data is perf or med in JOSM.
F or t he com pressed road netw or k , w e load t he OSM file int o OSRM, which calls osr m-
e xtr act , osr m-contr act , and osr m-dat as t or e in or der . osr m-fr ont end is
used t o visuall y check map connectivity . S treets shall be segmented b y netw or k t opology
r at her t han b y g eometr y , because alt hough s treets wit hin t he Manhattan g rid are s tr aight
f or w ar d t o segment, windy roads (circles, cul de sacs, w aterfront roads, Centr al P ar k , P enn
Sout h, S tuyv esant T o wn) mus t be segmented differentl y . This is wh y w e use OSRM ins tead
of sim pler packag es such as shapel y . Segment ID does no t con v e y inf or mation o t her
t h an an identifier , alt hough w e ma y recode t he segments wit h Huffman coding, t hat is t o
reor der s treet segments b y pickup frequency .
41
C hapter 2 D a t a
0.001 0.005 0.01 0.05 0.1 0.5 1
0.001
0.002
0.005
0.01
0.02
0.05
0.1
0.2
0.5
Proportion of canonical Medallions (13233)
GPS error rate, at least
Either out of bbox
Both out of bbox
Either at (0,0)
Both at (0,0)
Percent of records missing GPS value, vendor weekly average
6
5
4
3
2
1
0
DDS
VTS
CMT
2009 2010 2011 2012 2013 2014
A
B
F igure 2.5: Propo tion of GPS missing v alues. (A) W eekl y time-series, g r a y line sho w s o v er -
all propo tion, about 2.2%. (B) T ail probabilities of GPS error r ate of a Medallion
taxi, log-log scale. Bounding bo x (bbo x) is a lar g e rectangular r ang e o v er g eo-
g r aphic coor dinates, so t hat actual trips tr a v elling be y ond t hat r ang e is highl y
unlik el y .
W e use cus t omized OSRM code f or map matching: r un r out e-dis tr ibution on
a CS V file of unique GPS locations t o create a mapping from t hose locations t o t he seg-
ment ID of t he neares t s treet segment, as measured b y Euclidean dis tance in EPSG:3395
42
C hapter 2 D a t a
F igure 2.6: Char acteris tics of taxi trips in core Manhattan. (U pper) T r ansaction r ate, count
per hour . Color scale is nonlinear as taxi tr ansaction r ate is lar g el y heterog e-
neous in spatial dis tribution. T r ansaction concentr ates in tr ansportation hubs
and e v ent centers; at neighbor hood scale, Midt o wn is t he mos t activ e area.
(Lo w er) Pickup-dropoff r atio, log2 scale. Midt o wn has relativ el y balanced
pickup and drop-off (g re y), s treets leading t o w ar ds Midt o wn ha v e much more
pickups t han drop-offs (red), man y s treets in Lo w er Manhattan, U pper Eas t
Side and U pper W es t Side ha v e much more drop-offs t han pickups (blue). This
reflects t hat taxi drop-offs are more e v enl y dis tributed spatiall y , com pared wit h
pickups. It also sho w s driv ers ’ tendency t o cr uise back t o high demand areas.
projection. The modified prog r am calls S t aticR T r ee::N ear es t() , which does t he
har d-lif t ing.
T o use t he g r aph in o t her prog r ams, w e export it in ex chang e f or mats: OPL f or t he g e-
43
C hapter 2 D a t a
ometric g r aph and CS V f or t he routing g r aph. OPL can t hen be con v erted b y osmium or
ogr2ogr t o o t her f or mats such as GeoJSON . F or GIS functionality , QGIS can be used f or
sim p le task s such as joining columnar non-g eometr y data la y er , while GRASS can be use
f or batch processing. Using R mapping packag es mak es separ ate GIS t ools lar g el y unnec-
essar y .
F or shortes t pat h routing, w e use our o wn im plementation of t he Di jk s tr a algorit hm,
which is combined wit h a gg reg ation routines t o output dis tributions on netw or k s.
T r affic speed can be es timated from t he trip recor ds:
1. P ar ameter g rid: (intersection penalty , speed b y road classification);
a) T r affic speed v ect or (TS V) on edg e-based g r aph (ebg);
i. Mode (maximum lik elihood) of rounded speed of trips short and s tr aight
along tr affic direction;
48
ii. F ill in speed b y road classification f or segments wit h no direct es timate
( (OSMN odeID, speed in km/h) );
b) T rip dur ations b y g reedy routing on tr affic speed;
c) (Subsam ple) matrix nor m of difference from mode of rounded dur ation of recor ded
trips;
2. Pick TS V wit h smalles t difference;
Com pared wit h o t her es timates of tr affic speed, such as DO T field tr a v el time sur v e ys and
bus tr a v el speed, es timates based on taxi recor ds are more accur ate. Dono v an and W or k
also pro vide t heir es timate of NY C tr affic data
49
.
48
NY C DO T 2010 Broadw a y R eport
49
https://uofi.app.box.com/v/NYC- traffic- estimates
44
C h apter 3
Opera tions of S treet -hail T axi
Individual tr a v el decision is fundamental t o human mobility , urban econom y and sus-
tainability , but measuring it is technologicall y challenging and et hicall y contro v ersial. F or
taxis, pre vious s tudies are limited t o taxi s tands or hail mar k ets at agg reg ate spatial units.
W e use in-v ehicle Global P ositioning Sys tem (GPS) data t o es timate t he suppl y and de-
mand of s treet-hail taxis at segment le v el of a road netw or k , wit hout sur v eilling t he popu-
lation. T o t his end, w e model taxi demand and suppl y as non-s tationar y P oisson r andom
fields on t he road netw or k , and pickups result from taxis searching f or im patient passen-
g ers on s treet segments. R elating t his model wit h queueing t heor y giv es pickup r ate, and
modeling driv er income maximization as a symmetric g ame giv es equilibrium suppl y r ate.
W it h 868 million trip recor ds of all 13,237 licensed taxis in N e w Y or k City from 2009 t o
2013—while it w as s till a monopol y mar k et—w e match GPS locations t o s treet segments
f or pickup and suppl y , and demand is es timated b y sol ving nonlinear equations. W e v al-
idate t hat taxi pickups can be modeled as P oisson processes, and t hat demand es timates
are s table at different suppl y le v els and across y ears. Our met hod is t hus sim ple, f easible,
and reliable in es timating s treet-hail taxi activities at a high spatial resolution. Contr ar y
t o common im pression, in high-demand locations s treet-hail taxis out-perf or m tr ansporta-
tion netw or k com panies (TN C) such as Uber , sugg es ting a taxi/TN C regulation chang e t o
45
C hapter 3 Opera tions of S treet -hail T axi
reduce cong es tion and pollution.
3.1 O ver view
T r ansportation decisions of individuals ha v e ne v er been com prehensiv el y recor ded t hrough-
out an y urban agglomer ation, due t o technological and priv acy issues. F or taxicab tr ans-
portation, until hailing from mobile de vices became possible, passeng ers and taxi driv ers
ha v e no inf or mation about each o t hers ’ locations. But wit h taxi GPS receiv ers as ins tr u-
ment, it is possible t o es timate t he suppl y and demand f or taxicab tr ansportation. W e pro-
pose models of taxi suppl y and pickup, and es timate t he suppl y and demand dis tributions
in M anhattan o v er s treet segments and hours of a typical w eekda y , using taxi trip recor ds
in N e w Y or k City betw een 2009 and 2013.
T o unders tand taxi oper ation, one needs t o quantify t he spatial-tem por al patter ns of
taxi activities. More criticall y , while pickup and drop-off inf or mation are easil y measured
(Santi et al., 2014 ), taxi suppl y and demand le v els are of ten of g reater interes t ( Y ang2002 ;
K. W ong, S. W ong, and Y ang, 2001 ). U nf ortunatel y , such attributes are har d t o obtain: taxi
suppl y es timate requires high sam pling r ate GPS tr a ject ories (Zheng et al., 2012 ), which is
challenging t o s t ore, tr ansmit, and process; taxi demand is im possible t o measure wit hout
per v asiv e ins tr umentation on t he entire population since all are po tential taxi passeng ers.
Es timating t hese unmeasured attributes can com plement our insight int o urban mobil-
ity obtained from o t her sources such as smart-car d data (Sil v a, Kang, and Airoldi, 2015 )
and mobile phone data ( Jiang2016 ; De ville et al., 2016 ). It also enables s tudies of suppl y -
demand relation, and com petition betw een taxis and TN Cs. Go v er nments can adjus t taxi
and TN C regulations t o im pro v e tr ansportation efficiency , and tr ansportation oper at ors
can benefit from t his inf or mation t o im pro v e ser vice quality . The current chap ter is t hus
mo tiv ated t o s tudy t he suppl y and demand dis tributions of s treet-hail taxi, and t heir im-
46
C hapter 3 Opera tions of S treet -hail T axi
plication on perf or mance.
In our w or k , suppl y ref ers t o a v acant taxi in ser vice searching f or passeng ers, and de-
mand ref ers t o a po tential passeng er , or hailer , who tries t o hail a taxi on t he s treet, re-
g ar d less t he e v entual mode of tr ansportation. W e no te t hat t he suppl y and demand de-
fined here are no t t hose of a homog eneous good in economics v ocabular y , but actuall y
tw o f act ors of production. W e choose t hese ter ms t o conf or m wit h common unders tand-
ing. This dis tinction is im portant because pre vious s tudies of taxi ser vice ha v e assumed
mar k et clearing at economic equilibrium, which im plies all hailers are e v entuall y pick ed
up ( Y ang1998 ).
W e reg ar d tr ansportation activities as periodic non-s tationar y r andom fields. In o t her
w or ds, e v ents differ at different places, chang e o v er time, and w ould no t be t he same w ere
t h ere independent duplicates of t he w or ld, but t he same r andom entity occurs at regular
occasions in time. T em por al regularity is t he k e y t o unders tand and es timate such r andom
entities. In t he case of taxi tr ansportation, tr affic condition, passeng er demand, and driv er
suppl y are t he rele v ant f eatures. Once t hese en vironment conditions are held s tationar y ,
taxi oper ation can be modeled at equilibrium.
W e build probabilis tic models of taxi pickup on s treet segments, which are related t o
queueing models t o obtain anal ytical f or ms of t he matching functions. Queueing mod-
els ha v e long been applied t o pickup at taxi s tands (K endall, 1951 ), where bo t h taxis and
passeng ers can be w aiting. W e sho w t hat queueing t heor y (Barrer , 1957a , b ; Anck er and
Gaf a rian, 1962 ; Dale y , 1964 ) can also be adap ted t o hail mar k ets where taxis search on
t h e s treet netw or k. Since taxi has long been a go v er nment regulated segment of urban
tr ansportation, f or cities t hat ha v e been collecting taxi GPS tr a ject or y data, our model can
be readil y applied t o es timate taxi demand. If f or technical or his t orical reasons onl y trip
origin-des tination locations are a v ailable, w e also pro vide a sim ple f or mula t o es timate t he
equilibrium suppl y route dis tribution. T o sho w case our met hod, w e es timated t he spatial-
47
C hapter 3 Opera tions of S treet -hail T axi
tem por al dis tributions of taxi suppl y and demand in Manhattan, NY C. As ride-hiring mar -
k ets in cities w or ldwide ha v e been fr agmented b y TN Cs, it is har der no w t o es timate t he
com plete demand dis tribution from a single source of data. But our met hod s till applies
t o t he demand seeking s treet-side ser vice. And b y com paring es timated taxi demand dis-
tributions bef ore and af ter TN C entr y , w e can ha v e a detailed unders tanding of TN Cs ’
im pact on taxi tr ansportation. W e sho w t hat s treet-hail taxis perf or m better t han TN Cs in
high demand locations, which can inf or m current taxi and TN C regulations.
Our s tudy s tands out in se v er al fronts. In data com pleteness and time span, w e use trip
recor ds of all 13237 licensed taxicabs of a monopol y mar k et across 5 y ears. All f eatures are
es t imated at s treet segment le v el, t he highes t spatial resolution achie v ed. W e dis tinguish
demand intention from actual pickup, and relate t hem via a mechanis tic model. W e model
taxicab demand as a non-s tationar y P oisson r andom field on t he s treet netw or k; and t he
es t imation of equilibrium suppl y requires onl y location at pickup.
The fr ame w or k of t his chap ter roughl y comes in t hree parts, illus tr ated in F igure 3.1 .
F i rs t , match all trip recor ds of NY C y ello w cabs on a map of s treet segments. Then w e can
com pute pickup r ate and es timate equilibrium suppl y r ate. A t las t, w e propose a segment-
le v el pickup model which relates pickup r ate t o suppl y and demands r ates, and hailer
im p atience. Demand r ate can be es timated b y in v erting t he pickup r ate function.
3.2 Time s amplin g
Alt hough w e ha v e fiv e y ears of trip recor ds, no all t he y ears ha v e accep table data qualities.
The mos t significant incident is t hat TL C’ s contr act wit h DDS expired on 2010-09-30, which
had TPEP sys tems ins talled in about 1100 taxis and t hese taxis need t o tr ansition t o t he re-
maining tw o v endors b y 2011-04-30. In f act, DDS did no t report trip recor ds in F ebr uar y
and March 2010, and ter minated reporting on 2010-08-01. Mos t Medallion o wners con-
48
C hapter 3 Opera tions of S treet -hail T axi
trip records
segment map
trips
between
segments
Map
Matching
supply trips
routing graph
edge weights
(transaction rate)
supply
routes
Shortest
Path
Routing
supply rate
demand rate
impatience
(assumed)
transaction
rate
Segment
Transaction
Model
F igure 3.1: Outline o f data pipeline. Colors indicate direct data dependency . F irs t, trip
recor ds are matched ont o a segmen ted map, which can be agg reg ated t o g et
pickup r ates, and tr acing a driv er betw een pickups giv es trip recor ds of taxi
suppl y . Equilibrium suppl y r ates can be es timated using a f or mula of pickup
r ates, t o tal search time, tr affic speed and segment lengt hs. F inall y , using t he
segment pickup model wit h assumed hailer im patience, demand r ates can be
sol v ed as an im plicit function of pickup and suppl y r ates.
tr acted wit h DDS tr ansitioned t o CMT , which sa w increasing dail y reporting Medallions
from Oct ober 2010 till F ebr uar y 2011. T r ansitions happened t hr oughout 2010, lea ving g aps
in trip recor d collection. Alt hough DDS contr acted wit h onl y a fr action of Medallion taxis,
t h e tr ansition violated data com pleteness in 2010, which w e do no t include in our anal y -
sis. W e also do no t use t he 2009 data, because t he discontinuity in time mak es it har d t o
com pare wit h t he later t hree y ears, and it also has its o wn data issues as t he ear l y s tag e of
t h e TPEP prog r am. W e ins tead f ocus our anal ysis on t he 2011-2013 data.
F ig. 3.2 sho w s t he annual patter ns of taxi pickups on w eekda ys in 2012, o t her y ears ha v e
similar patter ns, wit h floating dates of ma jor e v ents. Dail y activ e Medallions are mos tl y
cons tant t hroughout a y ear , and drops on leg al holida ys and se v ere w eat her conditions.
The U nited S tates f eder al holida ys include fiv e Monda y holida ys, plus Independence Da y ,
V eter ans Da y , Thank sgiving, Chris tmas and N e w Y ear . Based on t he obser v ed patter ns,
49
C hapter 3 Opera tions of S treet -hail T axi
Independence
Thanks-
giving
MLK Washington Memorial Labor Columbus
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
0.6
0.7
0.8
0.9
1
1.1
1.2
Spring Summer Fall Winter
Relative daily trips
Medallions count Fri
Thu
Wed
Tue
Mon
F igure 3.2: Dail y trips and activ e Medallions in 2012 w eekda ys, relativ e t o annual median.
Gr a y bars mar k public holida ys, g r a y lines f or popular inf or mal holida ys, light
blue lines f or se v ere w eat her e v ents. Annual taxi activity can be categorized
int o f our seasons, bounded b y holida ys. Hurr y cane Sandy in f all 2012 caused
lar g e dis r up tion.
w e categorize annual taxi activity int o f our seasons: spring season from Martin L ut her
King Jr . (MLK) Da y t o Memorial Da y ; summer season t o Labor Da y ; f all season t o Thank s-
giving; and winter season t o MLK Da y next y ear . Bo t h t he spring and f all seasons ha v e
s table w eekl y pickup patter ns, especiall y from T uesda y t o Thursda y , as mos t of t he city’ s
population are at w or k. In t he summer season while man y people tak e v acations, taxi pick -
ups s teadil y decrease. In t he winter season taxi activity g r aduall y increases till Chris tmas,
while hea vil y disr up ted during t he holida y season and b y w eat her conditions. W it hin t he
r ang e of each season w e ex clude certain da ys as ex cep tions t o t he regular season. Specifi-
call y , w e ex clude Monda y holida ys and T uesda ys af ter as people retur n t o w or k , and ex-
clude from W ednesda y bef ore Memorial da y till t he holida y , as people of ten tak e lea v e f or
an extended v acation. P articular t o NY C, W e ex clude Saint P atrick’ s Da y f or its popular an-
50
C hapter 3 Opera tions of S treet -hail T axi
5am 8 12pm 4 8 12am 4
Fri
Thu
Wed
Tue
Mon
8
6
4
2
0
Pickups in core Manhattan, Spring 2012
15-minute average with IQR band, thousands
F igure 3.3: Pickups in core Manhattan, w eekda ys in spring season 2012. Solid lines sho w
15-minute a v er ag e pickups in t housands, wit h inter quantile-r ang e (IQR) band.
Lines s tart from 5am and continue int o 4:45am next da y , when mos t night shif ts
end. The drop in 4pm indicates common s hif t chang e of da y and night shif ts.
nual par ade, and ex clude Good F rida y which is a non-tr ading da y at The N e w Y or k S t ock
Ex chang e (NY SE). W e ex clude winter s t or ms and ice s t or ms as identified b y t he N ational
Centers f or En vironmental Inf or mation (N CEI).
1
W e also ex clude da ys when eit her of t he
tw o ma jor v endors has zero or t oo f e w trips reported, o v er 5% GPS positions missing, or
o v er 3% recor ds containing non-increasing time s tam ps; t hese data issues tend t o be cor -
related. W e choose t he spring season f or its regularity and dur ation, as w e pref er a lar g er
sam ple size f or es timation.
Despite near l y cons tant suppl y of taxis on w eekda ys, taxi pickups are s trongl y affected
b y da y of w eek. Among w eekda ys, Monda ys ha v e t he lo w es t pickups, while F rida ys ha v e
t he highes t. T o tal pickups g r aduall y increase from T uesda y t o Thursda y , wit h almos t iden-
tical pickup patter ns wit hin each da y . If w e pick short time inter v als of a da y , v ariations
in tr ansportation activities become negligible. W e ma y t hen reg ar d each time inter v al as a
1
N CEI S t or m Ev ents Database. https://www.ncdc.noaa.gov/stormevents
51
C hapter 3 Opera tions of S treet -hail T axi
clus ter of obser v ations of t he same r andom field, independent from each o t her as t he y are
dis tantl y placed on t he time axis. W e no te t hat da y light sa ving time (DS T) does no t appear
t o cause immediate drif t in taxi activities: pickup patter ns continue t o f ollo w t he nominal
time of da y . W e choose t he AM peak from 8am t o 9am T uesda ys t o Thursda ys in spring
seasons, as t he y ha v e t he mos t similar taxi and tr ansportation activities.
Giv en a time inter v al, w e need t o choose t he rele v ant sub-sequences of trips f or each
taxi, t o deter mine t he actual pickups in t his time inter v al and t he search efforts t hat lead
t o t hese pickups. This procedure is im portant because wit hin a short time inter v al each taxi
does no t mak e man y trips, careless counting ma y t hus cause lar g e error . F ig. 3.4 sho w s a
diag r am of sub-sequence selection. F or an hour -long inter v al lik e 8am-9am, w e firs t put
a half-hour buffer on each end and select trips o v er lapping wit h t he extended inter v al. In
t h is case, all trips t hat ends no later t han 7:30am and s tarts ear lier t han 9:30am. The 30-
minute buffer is im posed t o deter mine if a taxi is in ser vice immediatel y bef ore and af ter
t h e chosen inter v al. N o w f or t he extended sub-sequences of each taxi, a trip is counted as
wit hin t he time inter v al if t he pickup time s tam p is on or af ter 8am and bef ore 9am. N o te
t h at no t all v endors report time s tam ps t o seconds, so t here are onl y 60 unique v alues of
time wit hin an hour -long inter v al. Since w e onl y consider taxi activity in core Manhattan,
pickups out of t he region are no t counted. T o count suppl y time, w e sort t he extended
sub-sequences of each taxi b y pickup time s tam ps, and con v ert t he trip recor ds int o search
recor ds b y linking t he drop-off attributes wit h t hose of t he next pickup. W e t hen subset
t h e search recor ds t o t hose o v er lapping wit h t he chosen time inter v al, and clip t hem t o t he
bounds if an y extend be y ond t he inter v al. W e onl y consider search recor ds no long er t han
30 minutes, wit h bo t h ends wit hin core Manhattan. The typical search time during 8am-
9am is 5 m inutes, and it is v er y unlik el y an activ e taxi canno t find a hailer in 30 minutes.
Such search recor ds ma y occur if a driv er w ent off-duty or it w as no t recor ded b y an actual
taxi, so w e suppress t hem t o a v oid lar g e errors in suppl y time es timates. U nder -counted
52
C hapter 3 Opera tions of S treet -hail T axi
search time of routes partiall y wit hin core Manhattan are offset b y t he remaining o v er -
counted activ e time.
8 am 9 am
F igure 3.4: Diag r am of trip subsequence selection. Gr a y region highlights t he inter v al from
8am t o 9am, open on right. Pickups wit hin t he inter v al are counted, sho wn as
black do ts; Search time is t he sum of all inter -trip g aps, clipped at bounds of
t he inter v al, sh o wn as do tted lines wit hin t he highlighted region.
3.3 Suppl y r oute model
W e define suppl y trip as t he pat h of an on-duty taxi betw een consecutiv e drop-off and
pickup, and suppl y route ref ers t o t he sequence of s treet segments t he taxi passes during a
suppl y trip. The t o tal occur ance of each segment in all suppl y routes cons titutes t he suppl y
route dis tribution.
The ideal approach t o es timate taxi suppl y route dis tribution is t o acquire high sam pling
r ate GPS tr a ject ories and project t hem ont o t he road netw or k b y map matching. Ev en f or
tr a ject ories sam pled e v er y f e w minutes, possible routes can be inf erred accur atel y (Zheng
et al., 2012 ). Ho w e v er , t he taxi trip recor ds w e ha v e do no t contain GPS tr a ject or y . In f act,
TL C R ules onl y included On-duty Location P ositioning in December 2012, which demands
positioning of o n-duty taxicabs at a frequency of at leas t e v er y tw o m inutes, s t ored and
maintained b y t he TPEP pro vider f or at leas t six mont hs. Ano t her reason f or t he lack of
taxi tr a ject ories is t hat s t oring high sam pling r ate GPS tr a ject ories across a long time span
is technicall y chanlleging.
53
C hapter 3 Opera tions of S treet -hail T axi
W it h onl y suppl y trip origin and des tination locations a v ailable, one ma y attem p t t o use
shortes t pat h routing t o es timate t he suppl y routes. Alt hough minimizing trip dur ation
is a r at her accur ate assum p tion f or taxi driv ers deliv er y passeng ers, it is in v alid f or driv er
searching beha vior .
A better assum p tion of driv er searching decisions is t hat driv ers maximize t heir pickup
r ate, giv en t hat t he y do no t kno w t he des tination of t heir next passeng er , t hus t he trip
dur ation and net re v enue. Specificall y , if a segment 𝑥 has pickup r ate 𝜇 𝑝𝑥 and suppl y r ate
𝜇 𝑠𝑥 , assuming e v er y pass of a v acant taxi on t his segment has equal probability of picking
up a hailer , a driv er 𝑖 choosing t o search t his segment wit h suppl y r ate 𝜇 𝑠𝑖 𝑥 t hen has an
expected pickup r ate 𝜇 𝑝𝑖 𝑥 = 𝜇 𝑝𝑥 𝜇 𝑠𝑖 𝑥 /𝜇
𝑠𝑥 on t his segment. If t he segmen t has lengt h 𝑙 𝑥 and
taxi search speed is ̃ 𝑣 , t he proportion of search time t he driv er spent on t he segment is t hus
𝑠 𝑖 𝑥 = 𝜇 𝑠𝑖 𝑥 𝑙 𝑥 / ̃ 𝑣 . Using all a v ailable inf or mation in taxi trip recor ds, including suppl y trip
origin and des tination locations 𝑥 1
and 𝑥 2
, and t he corresponding time s tam p 𝑡 1
and 𝑡 2
, t he
mos t lik el y suppl y routes of a r ational taxi driv er w ould satify an op timization problem:
maximize ∑
𝑥∈𝑃
𝜇 𝑝𝑖 𝑥 subject t o ∑
𝑥∈𝑃
𝑛 𝑖 𝑥 𝑙 𝑥 / ̃ 𝑣 = 𝑡 2
− 𝑡 1
𝑃 (𝑡
1
) = 𝑥 1
, 𝑃 (𝑡
2
) = 𝑥 2
𝑛 𝑖 𝑥 ≥ 1, ∀𝑥 ∈ 𝑃 (3.1)
Here 𝑛 𝑖 𝑥 = 𝜇 𝑠𝑖 𝑥 ∗ (𝑡
2
− 𝑡 1
) is t he number of times driv er 𝑖 passes segment 𝑥 on suppl y pat h
𝑃 , which could be g reater t han 1 because t he driv er ma y circle around or sim pl y w ait at
t he c urb.
Because t his op timization is affected b y t he suppl y and pickup dis tributions 𝜇 𝑠𝑥 and
𝜇 𝑝𝑥 , it effectl y f or ms a symmetric g ame among taxi driv ers. Similar t o user equilibrium of
tr affic a ssignment problems, t he equilibrium of taxi suppl y route choice can be f or mulated
54
C hapter 3 Opera tions of S treet -hail T axi
as f ollo w s: giv en t he s tr ategies of all taxi driv ers, no driv er can find a suppl y route wit h a
higher pickup r ate t han t he one already chosen.
This equilibrium could be es timated b y route choice algorit hms, af ter a little modifica-
tion t o t he original prog r am. Because route choice models are based on pla y ers minimzing
additiv e non-neg ativ e edg e cos ts of a pat h on a netw or k , w e ma y ref or mulate t he op timiza-
tion as f ollo w s:
minimize ∑
𝑥∈𝑃
(𝑘 𝑙 𝑥 − 𝜇 𝑝𝑥 /𝜇
𝑠𝑥 )𝑛
𝑖 𝑥 subject t o ∑
𝑥∈𝑃
𝑙 𝑥 𝑛 𝑖 𝑥 = (𝑡
2
− 𝑡 1
) ̃ 𝑣 𝑃 (𝑡
1
) = 𝑥 1
, 𝑃 (𝑡
2
) = 𝑥 2
𝑛 𝑖 𝑥 ≥ 1, ∀𝑥 ∈ 𝑃 (3.2)
Here w e exploit t he equality cons tr aint t o arriv e at a minimization problem; and use a
scaling f act or 𝑘 such t hat 𝑘 𝑙 𝑥 ≥ 1, ∀𝑥 t o guar antee non-neg ativ e edg e cos ts, because e v er y
pickup requires a suppl y , i.e. 𝜇 𝑝𝑥 /𝜇
𝑠𝑥 ≤ 1 . But a limitation of route choice models is t hat
t he y typicall y f orbids multiple passes of a segment, which is r at her possible in taxi search-
ing beha vior . Cy cles, or loops, are allo w ed in some K -shortes t pat h algorit hms (Epps tein,
1998 ), but such char acteris tic is g ener all y considered problematic in o t her route choice
models (Pr at o, 2009 ). Ev en in t he f e w s t ochas tic tr affic assignment algorit hms t hat admit
cy cles (Bell, 1995 ; Akamatsu, 1996 ), t heir solution ma y be i nefficient.
Ins tead, w e op t f or a different w a y t o es timate t his equilibrium. Consider t he drop-off
locations of taxi rides as r andom, t hen at an y moment v acant taxis s tarting t o search f or
riders are dis tributed on t he s treet netw or k accor ding t o drop-off frequency . These driv ers
will tr y t o maximize t heir pickup r ate, com peting ag ains t each o t her and o t her v acant taxis
s till searching. These driv ers do no t kno w t he time of t heir next pickup, so t he y will choose
55
C hapter 3 Opera tions of S treet -hail T axi
t o search on segments nearb y t hat ha v e t he highes t expected pickup per time:
𝜇 𝑝𝑖 𝑥 𝑠 𝑖 𝑥 =
𝜇 𝑝𝑥 𝜇 𝑠𝑖 𝑥 /𝜇
𝑠𝑥 𝜇 𝑠𝑖 𝑥 𝑙 𝑥 / ̃ 𝑣 =
𝜇 𝑝𝑥 ̃ 𝑣 𝜇 𝑠𝑥 𝑙 𝑥 (3.3)
As w e can see, t his v alue is no t driv er -specific, so w e deno te it as 𝑤 𝑥 . If pickup per time 𝑤 𝑥 is no t non-unif or m, driv ers close t o a segment wit h high 𝑤 𝑥 will mo v e t o w ar ds and search
on it. But t his increases t o tal suppl y r ate 𝜇 𝑠𝑥 on t he segment, and despite t o tal pickup r ate
𝜇 𝑝𝑥 on t he segment w ould also increase as a result, it w ould no t be proportional and t hus
𝑤 𝑥 decreases. When t he influx of driv ers t o t his segment reach a point such t hat 𝑤 𝑥 is no
long er locall y maximum, driv ers will t hen mo v e on t o search o t her segments t o increase
t heir pickup per time. A t equilibrium, t he collectiv e search s tr ategy of taxi driv ers will
result in a netw or k wit h unif or m pickup per time on segments being activ el y seached,
while o t her segments ha v e lo w er pickup per time, so t hat no driv er can unilater all y chang e
t heir s tr ategy f or a f as ter expected pickup. This means t he equilibrium suppl y dis tribution
satisfies:
𝑤 𝑥 = 𝑤 ≥ 𝑤 𝑦 , ∀𝑥 , 𝑦 , 𝜇 𝑠𝑥 > 0 (3.4)
N o t e t hat t he cons tant 𝑤 is t he expected pickup per search time at equilibrium, which can
be es timated as t he t o tal pickup divided b y t o tal search time, 𝑤 = ∑
𝑥 𝜇 𝑝𝑥 / ∑
𝑖 𝑠 𝑖 . Consis tent
wit h our con v ention of no tation, 𝑠 𝑖 deno tes t he proportion of time driv er 𝑖 spent searching
in t he same period of time. Our f or mula f or es timating equilibrium suppl y dis tribution
can no w be expressed as:
𝜇 𝑠𝑥 =
𝜇 𝑝𝑥 ̃ 𝑣 ∑
𝑖 𝑠 𝑖 𝑙 𝑥 ∑
𝑥 𝜇 𝑝𝑥 (3.5)
W e assume taxi search speed is cons tant as driv ers f ocus on curbside hailers and do no t
com pete wit h tr affic.
56
C hapter 3 Opera tions of S treet -hail T axi
3.4 Segment -level pic kup model
T o s tudy t he kinetics of s treet-hail taxi, w e propose a class of segment-le v el pickup models.
A s treet segment is a part of s treet tr uncated at inters ections.
1. Hailers arriv e at a one-directional s treet segment 𝑥 of lengt h 𝑙 as a s t ochas tic process
in time-space ℝ
+
× [0, 𝑙] , wit h independent inter -arriv al time dis tribution 𝐴(𝑢) and
unif or m spatial dis tribution. A g roup of hailers tr a v eling t og et her are counted as one.
Demand r ate 𝜇 𝑑 ref ers t o t he occurrence r ate of 𝐴(𝑢) .
2. V acant taxis enter t he segment as a s t ochas tic process in time ℝ
+
, wit h independent
inter -arriv al time dis tribution 𝐵(𝑣 ) . Suppl y r ate 𝜇 𝑠 ref ers t o t he occurrence r ate of
𝐵(𝑣 ) .
3. Hailer patience 𝑇 , or maximum w aiting time, is dis tributed as 𝐶 (𝑡 ) . W e call 𝔼𝑇 hailer
mean patience, and define im patience 𝜇 𝑡 = 1/𝔼𝑇 . W e assume taxis pass t hrough t he
segment much f as ter t han a unit of time ( 𝑡 = 𝑙/ ̃ 𝑣 ≪ 1 , where ̃ 𝑣 is taxi search speed),
and taxi driv ers do no t den y hailers, so if a v acant taxi enters t he segment while at
leas t one hailer is w aiting, t he driv er will pick up a hailer bef ore t he y r un out of
patience.
4. In case multiple hailers are present when a v acant taxi arriv es, eit her of t he f ollo w -
ing pickup disciplines (D) ma y be used: Greedy assum p tion ( 𝐺 ), t he driv er pick s up
t he hailer closes t t o segment entr ance; Courtesy assum p tion ( 𝐶 ), t he hailer who has
w aited f or t he long es t time g ets in t he taxi.
F i g. 3.5 sho w s a diag r am of t he pickup model.
This model es tablishes taxi pickup as ano t her s t ochas tic process in time and space, but
w e are mainl y interes ted in t he pickup r ate 𝜇 𝑝 , which is a function of t he model par am-
eters: 𝜇 𝑝 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) . The pickup r ate function can be sim plified as 𝜎 (𝜌, 𝜅 ) , using t hree in-
57
C hapter 3 Opera tions of S treet -hail T axi
T axi: Poisson(μs)
Hailer: Poisson(μd)
Impatience: μt=1/T
F igure 3.5: Diag r am of t he segment pickup model. Hailers arriv e at a one w a y s treet seg-
ment as a P oisson process wit h r ate 𝜇 𝑑 ; V acant taxis enter t he segment as an
independent P oisson process wit h r ate 𝜇 𝑠 . Hailers quit w aiting if no t pick ed up
wit hin t heir patience, which ma y v ar y across individuals and has an expecta-
tion 𝑇 , t he reciprocal of im patience 𝜇 𝑡 .
dependent dimensionless quantities of t he model: demand fulfillment 𝜎 = 𝜇 𝑝 /𝜇
𝑑 , suppl y -
demand r atio 𝜌 = 𝜇 𝑠 /𝜇
𝑑 , and co v er number 𝜅 = 𝜇 𝑡 /𝜇
𝑑 . Demand fulfillment is t he propor -
tion of taxi demand fulfilled; suppl y -demand r atio is t he number of v acant taxis passed
bef ore a ne w hailer appears; co v er number can be inter preted as t he multiples of hailer
mean patience t o co v er t he expected hailer inter -arriv al time.
In g ener al, t his pickup model is no t a s tandar d queue because alt hough t he pickup dis-
cipline defines a queue of hailers, t here is no dedicated ser v er in t he sys tem. If t he hailer at
queue head quits bef ore a v acant taxi arriv es, t he next hailer at queue head needs t o w ait
f or an extr a amount of time t hat is dis tributed differentl y from t he v acant taxi inter -arriv al
time 𝐵(𝑣 ) . But if 𝐵(𝑣 ) is exponentiall y dis tributed (or memor y less), t he time till pickup f or
t he hailer at queue head will ha v e t he same exponential dis tribution, independent from
t he arriv al times of passed v acant taxis and pre vious hailers, which sim plifies anal ysis.
Deno ting our model as (𝐴(𝑢), 𝐵(𝑣 ), 𝐶 (𝑡 ), 𝐷) , se v er al specifications coincide wit h queueing
models and ha v e anal ytical f or ms of t he pickup r ate function: (𝑀 , 𝑀 , 𝐷, 𝐶 ) (Barrer , 1957b ),
(𝑀 , 𝑀 , 𝐷, 𝐺) (Barrer , 1957a ), (𝑀 , 𝑀 , 𝑀 , 𝐶 ) (Anck er and Gaf arian, 1962 ), and (𝐺𝐼 , 𝑀 , 𝐷, 𝐶 )
(Dale y , 1964 ). Here 𝑀 and 𝐷 deno tes memor y less and deter minis tic dis tributions, and
58
C hapter 3 Opera tions of S treet -hail T axi
𝐺𝐼 deno tes g ener al independent arriv al process. F ig. 3.6 A com pares t he firs t t hree spec-
ifications. Once pickup r ate 𝜇 𝑝 , suppl y r ate 𝜇 𝑠 and hailer im patience 𝜇 𝑡 are deter mined
f or each segment, demand r ate 𝜇 𝑑 can be sol v ed from equation 𝜇 𝑝 = 𝜇 𝑝 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) using
roo t-finding algorit hms such as N e wt on-Raphson or bisection.
Demand fulfillment
Supply-demand ratio
0.1 0.5 1 5 10 50 100
0
0.2
0.4
0.6
0.8
1
Cover Number
0.1
1
10
Model specification
(M, M, M, C)
(M, M, D, C)
(M, M, D, G)
Supply realization
0 0.1 0.2 0.3 0.4 0.5
Demand / hour
10
5
2
A B
F igure 3.6: P erf or mance of s treet-hail taxis. (A) Dimensionless pickup r ate function under
different model specifications and at cons tant co v er numbers. (B) P aret o front of
taxi perf or mance wit h 4-minute ser vice guar antee, at different demand r ates.
P erf or mance of s treet-hail taxi includes hailer w aiting time and taxi v acancy r ate. Bo t h
should be lo w t o reduce cos t of time, unnecessar y cong es tion, and pollution. Inter pret
hailer patience as ser vice guar antee, demand fulfillment as quality of ser vice, and define
suppl y realization 𝜇 𝑝 /𝜇
𝑠 as t he proportion of suppl y matched, t hen model (𝑀 , 𝑀 , 𝐷, 𝐶 )
char acterizes t hese taxi perf or mance measures, see F ig. 3.6 B. The tr ade-off betw een de-
mand fulfillment and suppl y realization depends on t he city planner , but P aret o efficiency
alw a y s im pro v es as demand r ate increases.
59
C hapter 3 Opera tions of S treet -hail T axi
3.4.1 Rela tion with S t and ard Queues
In s tandar d queueing t heor y , cus t omers enter a sys tem of se v er al ser v ers and reques t ser -
vice; if e v er y ser v er is already ser ving a cus t omer , t he o t her cus t omers line in a queue and
w ait f or free ser v er . In K endall’ s no tation (K endall, 1953 ), a particular type of queueing
sys tem is identified as 𝐴/𝐵/𝑠 : cus t omer inter -arriv al times are independentl y dis tributed
as 𝐴(𝑢) ; ser vice time f or a cus t omer is dis tributed as 𝐵(𝑣 ) ; t he number of ser v ers is 𝑠 . If
no t specified, t he queueing discipline def aults t o ”firs t come, firs t ser v ed”, and bo t h t he
capacity of t he queue and t he size of t he population def ault t o infinity .
Cus t omer im patience has also been s tudied in queueing t heor y . Balking is when a cus-
t omer does no t join t he sys tem, v oluntaril y or in v oluntaril y , wit h bounded capacity (Haight,
1957 ) or probabilities conditional on queue size or expected w aiting time (Haight, 1960 ).
R eneging is when a cus t omer lea v e t he sys tem bef ore s tarting or com pleting t heir ser -
vice. (Haight, 1959 ) W e use subscrip t 𝑤 f or cus t omer im patience onl y in w aiting-line, and
use wit h subscrip t 𝑠 f or cus t omer im patience on time in sys tem (sojour n time).
In g ener al, t he segment-le v el pickup model is no t a s tandar d queue, because t here is
no dedicated ser v er in t he sys tem. Ins tead, v acant taxis pass t he segment as a r andom se-
quence, where ser vice time is time t o pick up a hailer , which is effectiv el y zero. If t he hailer
at queue head, as defined b y t he queueing discipline, quits bef ore a v acant taxi arriv es, t he
probability dis tribution of extr a w aiting time f or t he next hailer at queue head will be dif-
f erent from t he dis tribution of v acant taxi inter -arriv al time. But if v acant taxi inter -arriv al
time is exponentiall y dis tributed (memor y less, 𝑀 ), t hen t he time till pickup (ser vice) f or
t he hailer at queue head is t he same exponential dis tribution, independent from arriv al
time of passed v acant taxis and pre vious hailers.
The assum p tions on pickup discipline also corresponds w ell wit h common queueing
disciplines. W e no te t hat t he g reedy assup tion (G) is equiv alent t o Ser vice In Random Or -
der (SIR O), while t he courtesy assum p tion (C) is equiv alent t o F irs t In F irs t Out (FIF O).
60
C hapter 3 Opera tions of S treet -hail T axi
Borro wing from K endall’ s no tation, w e deno te our segment-le v el pickup model as (𝐴, 𝐵, 𝐶 , 𝐷) ,
corresponding t o t he hailer arriv al process, v acant taxi arriv al process, hailer patience, and
pickup discipline respectiv el y . Thus, a (𝐺𝐼 , 𝑀 , 𝐺, 𝐺) model coincides wit h a 𝐺𝐼 /𝑀 /1/𝑆𝐼 𝑅𝑂+
𝐺 𝑠 queue, ref erring t o a g ener al independent (GI) arriv al process of hailers, Mar k o vian/P oisson
(M) arriv al process of v acant taxis, g ener al dis tribution of hailer patience, and Greedy as-
sum p tion on queueing discipline; similar l y , a (𝐺𝐼 , 𝑀 , 𝐺, 𝐶 ) model coincides wit h a 𝐺𝐼 /𝑀 /1/𝐹 𝐼 𝐹 𝑂+
𝐺 𝑠 queue, wit h Courtesy assum p tion o n queueing discipline.
F or models (𝑀 , 𝑀 , 𝐷, 𝐶 ) and (𝑀 , 𝑀 , 𝐷, 𝐺) where 𝐷 ref ers t o a deg ener ate dis tribution (or
deter minis tic number), bo t h hailer and v acant taxi arriv al processes are P oisson, and hailer
patience is a cons tant. These models coincide wit h 𝑀 /𝑀 /1/𝐹 𝐼 𝐹 𝑂 + 𝐷 𝑠 and 𝑀 /𝑀 /1/𝑆𝐼 𝑅𝑂 +
𝐷 𝑠 queues correspondingl y , which are single-ser v er queues wit h Mar k o vian inter -arriv al
time and ser vice time, and wit h deter minis tic cus t omer im patience on time in sys tem. Bar -
rer ( 1957a , b ) firs t s tudied t hese tw o types of queues, and obtained closed expressions f or
t h e r atio of t he a v er ag e r ate at which cus t omers are los t t o t he a v er ag e arriv al r ate. Be-
cause demand fulfillment is com plement t o “los t cus t omer probability” (Barrer , 1957b ) or
“sur viv al r ate” (Barrer , 1957a ), f or model (𝑀 , 𝑀 , 𝐷, 𝐶 ) , w e ha v e:
𝑠(𝑟 , 𝑐 ) =
⎧
{
{
⎨
{
{
⎩
𝑟 𝑒 (𝑟 −1)/𝑐
− 1
𝑟 𝑒 (𝑟 −1)/𝑐
− 1
(𝑟 ≠ 1)
1
𝑐 + 1
(𝑟 = 1)
(3.6)
Then t he pickup r ate func tion can written as:
𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) =
⎧
{
{
{
⎨
{
{
{
⎩
𝜇 𝑠 𝜇 𝑑 𝑒 𝜇 𝑠 /𝜇
𝑡 − 𝑒 𝜇 𝑑 /𝜇
𝑡 𝜇 𝑠 𝑒 𝜇 𝑠 /𝜇
𝑡 − 𝜇 𝑑 𝑒 𝜇 𝑑 /𝜇
𝑡 (𝜇
𝑠 ≠ 𝜇 𝑑 )
𝜇 2
𝑠 𝜇 𝑠 + 𝜇 𝑡 (𝜇
𝑠 = 𝜇 𝑑 )
(3.7)
61
C hapter 3 Opera tions of S treet -hail T axi
Similar l y , f or model (𝑀 , 𝑀 , 𝐷, 𝐺) , w e ha v e:
𝑠(𝑟 , 𝑐 ) = 𝑟 ⎡
⎢
⎣
1 −
⎛
⎜
⎝
1 +
∞
∑
𝑛=1
𝑟 −𝑛
𝑛 ∏
𝑘 =1
(1 − 𝑒 −
𝑟 𝑘 𝑐 )
⎞
⎟
⎠
−1
⎤
⎥
⎦
(3.8)
𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) = 𝜇 𝑠 ⎡
⎢
⎣
1 −
⎛
⎜
⎝
1 +
∞
∑
𝑛=1
(
𝜇 𝑑 𝜇 𝑠 )
𝑛 𝑛 ∏
𝑘 =1
(1 − 𝑒 −
𝜇 𝑠 𝑘 𝜇 𝑡 )
⎞
⎟
⎠
−1
⎤
⎥
⎦
(3.9)
F or model (𝑀 , 𝑀 , 𝑀 , 𝐶 ) , bo t h hailer and v acant taxi arriv al processes are P oisson, and
hailer patience is exponentiall y dis tributed. This model coincides wit h t he 𝑀 /𝑀 /1/𝐹 𝐼 𝐹 𝑂 +
𝑀 𝑠 queue, which is s tudied as t he T ype II beha vior of t he unbounded queue in Anck er and
Gaf a rian ( 1962 ). Because demand fulfillment is “t he probability t hat an arriv al com pletes
ser vice”, f or model (𝑀 , 𝑀 , 𝑀 , 𝐶 ) w e ha v e:
𝑠(𝑟 , 𝑐 ) = 𝑟 [1 − (1 + 𝑒 1/𝑐
𝑐 𝑟 /𝑐
𝛾 (𝑟 /𝑐 + 1, 1/𝑐 ))
−1
] (3.10)
𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) = 𝜇 𝑠 [1 − (1 + 𝑒 𝜇 𝑑 /𝜇
𝑡 (𝜇
𝑑 /𝜇
𝑡 )
−𝜇
𝑠 /𝜇
𝑡 𝛾 (𝜇
𝑠 /𝜇
𝑡 + 1, 𝜇 𝑑 /𝜇
𝑡 ))
−1
] (3.11)
Here 𝛾 (𝑠, 𝑥 ) = ∫
𝑥 0
𝑡 𝑠−1
𝑒 −𝑡
d 𝑡 is t he lo w er incom plete g amma function.
W it h a g ener al probability model f or hailer inter -arriv al time and deter minis tic hailer pa-
tience, model (𝐺𝐼 , 𝑀 , 𝐷, 𝐶 ) corresponds t o queue 𝐺/𝑀 /1 + 𝐷 𝑠 and also has an anal ytical
f or m f or t he pickup r ate function. Dale y ( 1964 ) sol v ed t he s tationar y w aiting-time dis tri-
bution function 𝑊 (𝑥 ) f or 𝑀 /𝐺/1 + 𝐷 𝑠 queues. In his no tation, {𝑣
𝑛 } is t he difference be-
tw een cus t omer patience and actual queueing time, whose limiting dis tribution is 𝑉 (𝑥 ) .
As he also no ted, {𝑣
𝑛 } is t he dual of w aiting time {𝑤
𝑛 } , so t he functional f or m of 𝑉 (𝑥 ) of a
𝐺/𝑀 /1 + 𝐷 𝑠 queue is t he same as 𝑊 (𝑥 ) of an 𝑀 /𝐺/1 + 𝐷 𝑠 queue. Thus, because demand
fulfillment 𝜎 = 1 − 𝑉 (0) , using definition 𝜎 = 𝜇 𝑝 /𝜇
𝑑 and expression of 𝑊 (𝑥 ) , f or model
62
C hapter 3 Opera tions of S treet -hail T axi
(𝐺𝐼 , 𝑀 , 𝐷, 𝐶 ) w e ha v e:
𝜇 𝜏 (𝐴, 𝜇 𝑑 , 𝑇 ) = 𝜇 𝑑 ⎡
⎢
⎣
1 −
⎛
⎜
⎝
∞
∑
𝑛=0
∫
𝑇 0−
[−𝜇
𝑑 (𝑇 − 𝑢)]
𝑛 𝑛!
𝑒 𝜇 𝑑 (𝑇 −𝑢)
d 𝐴 𝑛∗
(𝑢)
⎞
⎟
⎠
−1
⎤
⎥
⎦
(3.12)
Here 𝜇 𝑝 is a function of (𝜇
𝑠 , 𝐴, 𝑇 ) , where 𝐴(𝑥 ) is t he dis tribution of hailer inter -arriv al
time and 𝑇 is hailer patience. 𝐴 𝑛∗
(𝑥 ) is t he 𝑛 -f old con v olution of 𝐴(𝑥 ) wit h itself, wit h
𝐴 0∗
(𝑥 ) = 𝐻 (𝑥 ) , t he Hea viside function.
3.4.2 Model c omp arison
Different models of hailer patience could lead t o different demand es timates. T o com pare
and select a pref erred model specification, w e s tudy t he combinations of t he f ollo wing op-
tions: (1) deter minis tic and exponential dis tribution of hailer patience on a segment ; (2)
im patience and co v er number as t he spatial in v ariant across all segment of t he netw or k;
(3) high and lo w v alues of t he sp atial in v ariant. F or homog eneous im patience, w e pick 10
and 20 per hour ; because im patience is t he reciprocal of hailer mean patience, it means
an a v er ag e hailer w ould w ait f or 6 or 3 minutes bef ore r unning out of patience. F or ho-
mog eneous co v er number , w e pick 1 and 3, which means hailer mean patience is equal
t o one or one t hir d of t he expected arriv al time of t he next hailer . F ig. 3.7 com pares t he
es timated demand dis tribution. Assuming co v er number t o be spatiall y in v ariant is inap-
propriate, as it w ould eit her mak e hailers on high demand segments t oo im patient or t hose
on lo w demand segments t oo patient, of tentimes bo t h. W it h co v er number 1, hailers on a
segment wit h demand r ate 60 per hour ha v e 1 minute patience on a v er ag e, while t hose
on segments wit h demand r ate 1 per hour w ould ha v e 60 minutes of patience on a v er ag e.
This w ould cause underes timates on lo w demand segments, and o v eres timates on high
demand segments. W e ins tead choose im patience t o be t he spatial in v ariant, wit h expo-
nentiall y dis tributed patience across hailers. In our es timation f or NY C, im patience tak es
63
C hapter 3 Opera tions of S treet -hail T axi
Local patience
deterministic
exponential
Spatial invariant
μ
t
= 10 h
μ
t
= 20 h
κ= 1
κ= 3
0.1 0.5 1 5 10 50 100
0.0
0.2
0.4
0.6
0.8
1.0
Cumulative proportion of segments
Demand per hour
F igure 3.7: Cumulativ e dis tribution of demand r ates o v er t he s treet netw or k of core Man-
hattan. Com paring results of different model specification. If hailer patience on
a local segment is exponentiall y dis tributed (dashed lines), demand is higher
t han if it is deter minis tic (solid lines). Demand is also higher wit h high hailer
im patience (blue lines) t han lo w im patience (or ang e lines). If segments ha v e
t he same co v er number (light shades), demand r ates ha v e hea vier tails on bo t h
ends t han if t he y ha v e t he same im patience (dar k shades).
t h e inter mediate v alue, 15 per hour , which means hailer mean patience is 4 minutes. Our
pref e rred model specification is t hus (𝑀 , 𝑀 , 𝑀 , 𝐶 ) wit h 𝜇 𝑡 = 15/ℎ f or all segments.
W e also no te t hat, wit h spatiall y in v ariant im patience, demand fulfillment roughl y f ol-
lo w s an S-cur v e of suppl y r ate, alt hough it also depends on suppl y -pickup r atio, see F ig. 3.8 .
Despite arbitr ar y assum p tions on cus t omer im patience, it canno t be remo v ed from our
model. Because wit h ins tr umentation onl y on t he suppl y side, w e inherentl y lack inf or ma-
tion t o es timate hailer demand.
64
C hapter 3 Opera tions of S treet -hail T axi
F igure 3.8: Demand fulfillment v s. suppl y r ates on s treet segments in core Manhattan, as-
suming cons tant im patience on all segments. Demand fulfillment roughl y f ol-
lo w s an S-cur v e of suppl y r ate, alt hough it is also a function of suppl y -pickup
r atio, which a ppears t o ha v e little influence. As expected, demand fulfillment
decreases if im patience is higher (light shades) or if hailer patience is exponen-
tiall y dis tributed (or ang e) r at her t han deter minis tic (black).
3.4.3 Simula tion Al gorithm
Anal ytical f or m of t he pickup r ate function ma y no t be readil y a v ailable f or a g ener al
segment-le v el pickup model. But w e can resort t o Monte Car lo simulation t o e v aluate it
numericall y , and also s tudy its properties.
The f ollo wing algorit hm can be used t o es timate mean pickup r ate 𝜇 𝑝 f or model (𝐺𝐼 , 𝐺𝐼 , 𝐷, 𝐶 ) :
1. Gener ate hailer arriv al sequence {ℎ
𝑖 } wit hin a dur ation of 𝑇 wit h independent inter -
arriv al time dis tribution 𝐴(𝑢) , where arriv al r ate is 𝜇 𝑑 ;
65
C hapter 3 Opera tions of S treet -hail T axi
2. Gener ate v acant taxi arriv al sequence {𝑓
𝑗 } in a similar w a y , wit h dis tribution 𝐵(𝑣 ) and
arriv al r ate 𝜇 𝑠 .
3. Select point pairs (ℎ
𝑖 , 𝑓 𝑗 ) from product set {ℎ
𝑖 } × {𝑓
𝑗 } t hat f alls in band region 𝐹 =
{(ℎ, 𝑓 )|0 < 𝑓 − ℎ < 1/𝜇
𝑡 } . Deno te t he set as 𝑆 .
4. S tart from 𝑡 = 0 , find ℎ = 𝑚𝑖 𝑛 (ℎ
𝑖 ,𝑓
𝑗 )∈𝑆,ℎ
𝑖 >𝑡
ℎ
𝑖 and 𝑓 = 𝑚𝑖 𝑛 (ℎ,𝑓
𝑗 )∈𝑆
𝑓 𝑗 , until such v alues
do no t exis t.
a) Drop all pairs (ℎ, 𝑓 𝑗 ) wit h 𝑓 𝑗 > 𝑓 from 𝑆 .
b) Drop all pairs (ℎ
𝑖 , 𝑓 ) wit h ℎ
𝑖 > ℎ from 𝑆 .
c) Mar k 𝑡 = ℎ .
5. Es timate 𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) as |𝑆|/𝑇 .
N o te t hat, at t he end, 𝑆 is t he set of actual pickups, identified as pairs of hailer and
v acant taxi arriv al time. F ig. 3.9 sho w s a sk etch of t he simulation. Each r un of t he algorit hm
e v a luates a point of t he pickup r ate function: 𝜇 𝑝 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) , wit h suppl y r ate 𝜇 𝑠 , demand
r ate 𝜇 𝑑 , and hailer im patience 𝜇 𝑡 as in put v ariables. Pickup r ate function e v aluated from
Monte Car lo simulation f or model (𝑀 , 𝑀 , 𝐷, 𝐶 ) is presented in F igure 3.10 , sho wing tw o
dimensionless f or ms.
This algorit hm is used t o s tudy if t he pickup sequences are appro ximatel y P oisson when
bo t h hailer and v acant taxi arriv als are P oisson.
3.4.4 Pr oper ties of pic kup ra te fun ction
The pickup r ate function can be sho wn t o ha v e t he f ollo wing properties:
1. U pper bound: 𝜇 𝜏 ≤ 𝑚𝑖 𝑛(𝜇
𝑠 , 𝜇 𝑑 ) , s trict f or interior points o f ℝ
3
≥0
.
2. Mono t onicity : 𝜕 𝜇 𝜏 /𝜕 𝜇 𝑠 , 𝜕 𝜇 𝜏 /𝜕 𝜇 𝑑 ≥ 0 , 𝜕 𝜇 𝜏 /𝜕 𝜇 𝑡 ≤ 0 , all s trict f or interior points of
ℝ
3
≥0
.
66
C hapter 3 Opera tions of S treet -hail T axi
0 T
Hailer
/
T
Free
agent
F igure 3.9: Sk etch of simulation algorit hm. Ax es sho w hailer and free taxi arriv al time
wit hin a dur ation of 𝑇 . Grid points indicate all hailer -taxi pairs. Shaded area
is t he f easible band where free taxis arriv e bef ore hailers r un out of patience,
which is assumed t o be a cons tant of 1/𝜇
𝑡 . Em phasized do ts are t he initial set
of f easible pairs, wher e t he red do ts are actual tr ansactions.
3. Mono t onicity of partial deriv ativ es: 𝜕 2
𝜇 𝜏 /𝜕 𝜇 2
𝑠 ≤ 0 , 𝜕 2
𝜇 𝜏 /𝜕 𝜇 2
𝑑 ≤ 0 , 𝜕 2
𝜇 𝜏 /𝜕 𝑟 2
≤ 0
where 𝑑 is t he directio n v ect or of (𝜇
𝑠 , 𝜇 𝑑 , 0) , all s trict f or interior points of ℝ
3
≥0
.
4. Asym p t o tics 1: 𝑙𝑖 𝑚 𝜇 𝑡 →0+
𝜇 𝜏 = 𝑚𝑖 𝑛(𝜇
𝑠 , 𝜇 𝑑 )
5. Asym p t o tics 2: 𝑙𝑖 𝑚 𝜇 𝑡 →+∞
𝜇 𝜏 𝜇 𝑡 = 𝜇 𝑠 𝜇 𝑑 6. Asym p t o tics 3: 𝑙𝑖 𝑚 𝜇 𝑠 →+∞
𝜇 𝜏 = 𝜇 𝑑 , 𝑙𝑖 𝑚 𝜇 𝑑 →+∞
𝜇 𝜏 = 𝜇 𝑠 A dditionall y , f or models of type (𝐺𝐼 , 𝐺𝐼 , 𝐷, 𝐶 ) , w e can pro v e t he f ollo wing b y a nal yzing
t he simulation algorit hm:
1. Homog eneity of deg ree 1: 𝜇 𝜏 (𝑘 𝜇 𝑠 , 𝑘 𝜇 𝑑 , 𝑘 𝜇 𝑡 ) = 𝑘 𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 )
2. Duality : 𝜇 (𝐵,𝐴)
𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) = 𝜇 (𝐴,𝐵)
𝜏 (𝜇
𝑑 , 𝜇 𝑠 , 𝜇 𝑡 )
Here supscrip t (𝐵, 𝐴) deno tes t he suppl y and demand inter -arriv al time dis tributions.
67
C hapter 3 Opera tions of S treet -hail T axi
log10(demand/supply)
log10(transaction/supply)
-5
-4
-3
-2
-1
0
-2 -1 0 1 2
log(impatience/supply)
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
log10(impatience/supply)
-2 -1 0 1 2
log(demand/supply)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
A B
F igure 3.10: V ie w s of pickup r ate function 𝔼𝜇 𝑝 (𝜇
𝑓 , 𝜇 ℎ
, 𝜇 𝑡 ) . (U pper) isolines of dimension-
less im patience, on t he dimensionless tr ansaction-demand plane. (Lo w er) iso-
lines of dimension less demand, on t he dimensionless tr ansaction-im patience
plane. N umerical errors g ro w s at extremel y lo w tr ansaction-suppl y r atios,
which w ould no t be encountered in realis tic situations.
Pickup r ate is bounded abo v e b y suppl y and demand intensities because 𝑁 𝜏 ≤ 𝑚𝑖 𝑛(𝑁
𝑓 , 𝑁 ℎ
) .
F or nontrivial situations, bo t h t he probability of no v acant taxi arriving wit hin a hailer’ s
patience and t he probability of no hailer arriv es wit hin a hailer’ s patience are nonzero.
Thus pickup r ate will be s trictl y l ess t han t he suppl y and demand intensities.
It is intuitiv e t hat pickup r ate is non-decreasing in suppl y and demand intensities, and
non-increasing in im patience. F or nontrivial situations where suppl y and demand inten-
sities are positiv e and hailers do no t ha v e infinite patience, increase in suppl y or demand
intensities alw a ys result in higher mean pickup r ate, while increase in im patience alw a ys
result in lo w er mean pickup r ate.
W it h hailer im patience 𝜇 𝑡 fix ed, t he pickup r ate function is a production function where
suppl y r ate and demand r ate are tw o f act ors of production. The la w of diminishing mar ginal
68
C hapter 3 Opera tions of S treet -hail T axi
productivity means t hat second partial deriv ativ es of a production function is neg ativ e. It
also applies t o bundled f act ors of production where f act or com position is fix ed. Thus when
suppl y -demand r atio is fix ed, wit h cons tant hailer im patience, t he second partial deriv a-
tiv e wit h respect t o arriv al r ate is also neg ativ e.
Pickup r ate approaches its upper bound when hailer patience approaches infinity , t his
is pro v ed b y simulation results.
Asym p t o tics 2 means f or an y (𝜇
𝑠 , 𝜇 𝑑 ) , 𝜇 𝜏 = 1/𝜇
𝑡 𝜇 𝑠 𝜇 𝑑 f or 𝜇 𝑡 ≫ 0 , which resembles t he
r ate equation of bimolecular elementar y reactions. This is tr ue because wit h v er y short
hailer patience, taxi pickups are onl y possible when a hailer and a v acant taxi arriv e almos t
simultaneousl y , which has t he same probabilis tic model wit h molecular collision. Rate
equations of elementar y reactions are in f act deriv ed from collision t heor y .
R eg ar dless of hailer patience, when v acant taxi suppl y r ate approaches infinity , t he prob-
ability of a hailer catches a v acant taxi bef ore t he y r uns out of patience con v er g es t o 1. The
con v erse is also tr ue.
T o es timate 𝜇 𝜏 (𝑘 𝜇 𝑠 , 𝑘 𝜇 𝑑 , 𝑘 𝜇 𝑡 ) wit h a giv en realization of arriv al sequences t hat are used
f or es timating 𝜇 𝜏 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) , jus t scale t he arriv al sequences wit h f act or 1/𝑘 . W it h t he ne w
im patience 𝑘 𝜇 𝑡 , t he initial set 𝑆 is identical t o t he original calculation, onl y wit h a scaling
f act or of 1/𝑘 . The res t s ta ys t he same. So t he resulted set 𝑆 is also identical wit h t he original
calculation, ag ain wit h a scaling f act or of 1/𝑘 . The es timate f or t he ne w problem is t hen
|𝑆|/(𝑇 /𝑘 ) , which is 𝑘 times t he original es timate. This pro v es t he deg ree-1 homog eneity of
t he pickup r ate.
T o es timate 𝜇 (𝐴,𝐵)
𝑝 (𝜇
𝑑 , 𝜇 𝑠 , 𝜇 𝑡 ) wit h a giv en realization of arriv al sequences used f or es ti-
mating 𝜇 (𝐵,𝐴)
𝑝 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) , w e jus t need t o shif t t he origin t o (−𝜇
𝑡 , 0) and loop t hrough {𝑓 }
ins tead of {ℎ} . The res t s ta ys t he same. The resulted set 𝑆 is identical wit h t he original cal-
culation, ex cep t t hat all pairs wit h ℎ
𝑖 ∈ (𝑇 − 1/𝜇
𝑡 , 𝑇 ) are lef t out. F or a specific 𝜇 𝑡 , t his part
has negligible influence on t he es timat or |𝑆|/𝑇 as 𝑇 goes t o infinity . Thus, t he es timates
69
C hapter 3 Opera tions of S treet -hail T axi
f or 𝜇 (𝐵,𝐴)
𝑝 (𝜇
𝑠 , 𝜇 𝑑 , 𝜇 𝑡 ) and 𝜇 (𝐴,𝐵)
𝑝 (𝜇
𝑑 , 𝜇 𝑠 , 𝜇 𝑡 ) will con v er g e t o t he same v alue. This pro v es t he
duality of t he pickup r ate.
F or pickup r ate functions wit h homog eneity of deg ree 1, w e can reduce it t o dimension-
less f or ms of tw o v ariables. W it h f e w er deg rees of freedom, it can reduce t he com putational
com plexity when numericall y e v aluating t he function.
In t his dimensionless f or m, se v er al properties of t he r ate function can be ref or mulated
as f ollo w s:
1. Asym p t o tics 1: 𝑙𝑖 𝑚 𝑐→0+
𝑠 = 𝑚𝑖 𝑛(1, 𝜇) .
2. Asym p t o tics 2: 𝑙𝑖 𝑚 𝑐→+∞
𝑠𝑐 = 𝜇 3. Mono t onicity of partial deriv ativ es: 𝜕 2
𝑠/𝜕 𝜇 2
≤ 0 , s trict f or 𝑐 ≠ 0 .
3.5 Suppl y and demand dis tributions
T o es timate taxi suppl y and demand dis tributions, w e firs t identify time inter v als t hat can
be reasonabl y assumed as realizations of t he same r andom field. Because tr ansportation is
essentiall y a social phenomenon, w e partition each y ear int o seasons based on social e v ents.
The obser v ed annual patt er ns of taxi activity in NY C can be categorized int o spring, sum-
mer , f all, and winter seasons, separ ated b y f eder al holida ys. W it hin each season w e ex clude
certain da ys as ex cep tions: public holida ys, cus t om, extreme w eat her , and da ys wit h signif-
icant data issues. Bo t h spring and f all seasons ha v e s table w eekl y pickup patter ns, as mos t
of t he city’ s population are at w or k on w eekda ys. W e choose t he spring season f or its regu-
larity and dur ation, as w e pref er a lar g er sam ple size f or es timation. F rom T uesda y t hrough
Thursda y , taxi pickup patter ns wit hin each da y are almos t identical. If w e pick short time
inter v als of a da y , v ariations in tr ansportation activities become negligible. W e ma y t hen
reg a r d each time inter v al as a clus ter of obser v ations of t he same r andom field, indepen-
dent from each o t her as t he y are dis tantl y placed on t he time axis. W e choose t he AM peak
70
C hapter 3 Opera tions of S treet -hail T axi
from 8am t o 9am T uesda ys t o Thursda ys, as t he y ha v e t he mos t similar taxi and tr ansporta-
tion activities. Giv en a time inter v al, w e need t o choose t he rele v ant sub-sequences of trips
f or each taxi, t o deter mine t he actual pickups in t his inter v al and t he search efforts t hat
lead t o t hese pickups. This procedure is im portant because wit hin a short time inter v al
each taxi does no t mak e man y trips, careless counting ma y t hus cause lar g e error .
W it h a subset of trip recor ds, w e mat ch GPS locations ont o s treet segments. T o contain
t h e size of t he road netw or k wit hout tr uncating much of taxi activity , w e choose a part
of Manhattan where mos t taxi pickups are located, called “core Manhattan”, defined as
t h e Manhattan Island sout h of 130t h S treet. 92.5% of all taxi trips originate from core Man-
hattan, and 84.5% f all com pletel y wit hin t he region. W e extr act NY C road netw or k from
OpenS treetMap (OSM), and create a com pressed g r aph using Open Source R outing Ma-
chine (OSRM) (L ux en and V etter , 2011 ), where edg es are s treet segments as w e defined.
The OSRM com pressed g r aph of core M anhattan has 6001 edg es and 7055 one-directional
segments. GPS recor dings are noisy but reasonabl y accur ate, wit h deg r aded quality in
densel y built area due t o urban can y on effects. Com pared wit h t he typical dis tance of
79 meters betw een s treet center lines in Manhattan, matching GPS locations t o t he near -
es t s treet segment w ould be correct in mos t cases ex cep t in do wnt o wn areas. A bout 2.2%
trip recor ds ha v e missing pickup and drop-off GPS locations, and w e consider t he o v er -
all extent of GPS missing v alues as accep table. T axi pickup dis tribution is spatiall y highl y
heterog eneous, while drop-off dis tribution is more spread out, see F ig. 2.6 . The map of
pickup-dropoff r atio sugg es ts t hat taxi driv ers pref er t o head back t o high demand area
af t er a drop-off at a lo w demand location, consis tent wit h our equilibrium suppl y model.
W e appl y our models t o es timate t he suppl y and demand dis tributions in core Manhat-
tan. Based on taxi trip dis tance and dur ation, t he typical tr affic speed in core Manhattan
during t he 8am-9am peak hour is about 14.5 kilometers per hour (9 miles per hour), which
w e use in suppl y es timation. W e assume taxi search speed is cons tant as driv ers f ocus
71
C hapter 3 Opera tions of S treet -hail T axi
Demand
Supply
Pickup
0dB -33dB
F igure 3.11: T axi pickup, suppl y , and demand dis tributions in core Manhattan, 8am-9am
spring season 2012. Because taxi activities are highl y heterog eneous o v er space,
colors are in log arit hmic scale (dB), relativ e t o t he highes t v alues.
on curbside hailers and do no t com pete wit h tr affic. W e es timate demand wit h our pre-
f erred pickup model: (𝑀 , 𝑀 , 𝑀 , 𝐶 ) wit h 4-minute hailer mean patience. R esults f or spring
season 2012 are sho wn in F ig. 3.11 , along wit h pickup dis tribution f or com parison. T axi
72
C hapter 3 Opera tions of S treet -hail T axi
pickup o v er all concentr ates around Midt o wn, wit h spatial v ariations; taxi suppl y ins tead
is mos tl y along t he numbered a v enues, y et no t unif or m; taxi demand is more spread out
t h an pickup, but t he ho t spo ts are similar t o t hose of pickups. W e com pare pickup model
specifications, and anal yze unfulfilled demand in Section 3.4.2 .
S treet-hail taxi perf or ms v er y w ell in core Manhattan, where about half of t he segments
ha v e at leas t fiv e hailers per hour . A t demand r ate 5/hour , F ig. 3.6 B sho w s t hat pickup
can be guar anteed wit hin 4 minut es f or 95% of t he hailers, while one in ten v acant taxi
passes are successful. Com pare wit h TN Cs, where a v er ag e w ait time is es timated t o be
3-4 minutes in 2017 (Schaller , 2017 ), taxis perf or m better , especiall y in Midt o wn where
demand is t he highes t.
W e com pare taxi demand in t he y ears of 2011-2013, see F ig. 3.12 A . While taxi demand
in 2011 and 2012 a re almos t t he same, it declined about 2% in 2013. T able 3.1 summarizes
ser vice time and pickup, suppl y , and demand r ates in core Manhattan in spring season
2012; results f or 2011 and 2013 are sho wn as percentag e chang e relativ e t o 2012. In t he table,
𝑅 2
ref ers t o t he coefficient of deter mination betw een ser vice time and pickups. CV s tands
f or t he coefficient of v ariation of t he corresponding es timate, com puted using boo ts tr ap
s tandar d error , also sho wn in percentag es. As wit h t he results on high and lo w ser vice
times in 2012 (F ig. 3.12 B), v ariation in demand es timates is higher if suppl y le v el is lo w er .
It is clear from t he table t hat t he 0.6% f e w er trips made in 2011 can be com pletel y accounted
f or b y t he 3.8% less suppl y r ates; while t he 2% reduction in pickups in 2013 w as solel y due
t o t he 2% decline in demand r ates. Effects in bo t h y ears are s tatis ticall y significant.
W it h a fix ed taxi suppl y , a s table econom y , and no ma jor chang e in tr ansportation in-
fr as tr ucture, it should be expected t hat taxi demand in NY C should ha v e s ta y ed t he same
t h rough t hose y ears. The decline in taxi demand in 2013 ma y be caused b y tw o f act ors: t he
entr y of Uber in NY C, and t he T axi and Limousine Commission (TL C) f are r aise, bo t h in
t h e second half of 2012. In particular , Uber announced UberX on 2012-07-04, a ser vice us-
73
C hapter 3 Opera tions of S treet -hail T axi
T able 3.1: T axi activity in core Manhattan, 8am-9am spring seasons
Y ear 2012 2011 2013
Sam ple size 53 43 44
Ser vice t ime 7708.31 hrs/hr -2.32% 0.394%
Pickup r ate 26920.4 pickups/hr -0.628% -1.97%
( 𝑅 2
) (0.512) (0.302) (0.477)
Suppl y r ate 298924 passes/hr -3.79% -0.494%
(CV) (1.29%) (1.70%) (1.57%)
Demand r ate 32124.5 hailers/hr -0.0461% -1.965%
(CV) (0.546%) (0.808%) (0.636%)
ing h ybrid v ehicles and more affor dable t han Uber Black , its black car ser vice. Separ atel y ,
TL C passed r ules effectiv e on 2012-09-04 which increased metered f are b y 25% and also
increased t he flat f are and surchar g e of air port trips, on a v er ag e r aising trip f are b y 17%.
2
Ho w e v er , t he actual cause of decline is be y ond t he scope of t he current chap ter . F rom
ano t her perspectiv e, t he result t hat taxi demand is t he same in 2011 and 2012 reaffir med
our assum p tion t hat urban tr ansportation is in dynamic equilibrium in t he absence of sys-
tematic chang es.
W e no te t hat, t he TL C e-hail (mobile app) pilo t prog r am did no t affect t he s treet-hailing
nature of taxis. TL C s tarted an e-hail pilo t prog r am on 2013-04-26, which w as interr up ted
from 2013-05-01 t o 2013-06-06 due t o litig ation from an appellate judg e.
3
In late 2013 a v er -
ag e dail y e-hail reques ts is under 5000 and fulfillment r ate is about 30%, resulting in onl y
0.3% taxi trips.
4
In Oct ober 2016, onl y 28281 taxi trips w ere originated via e-hail, less t han
mont hl y a v er ag e in late 2013.
5
T axi trips reques ted from t he mobile app are also in t he
trip recor ds.
2
TL C N o tice of Promulg ation of R ules. http://www.nyc.gov/html/tlc/downloads/pdf/
taxi_fare_rules_passed.pdf
3
E-hail pilo t prog r am. http://www.nyc.gov/html/tlc/html/news/initiative_e_hail.
shtml
4
E-hail pilo t prog r am final report. http://www.nyc.gov/html/tlc/downloads/pdf/ehail_
q5_report_final.pdf
5
TL C Annual R eport 2016. http://www.nyc.gov/html/tlc/downloads/pdf/annual_
report_2016.pdf
74
C hapter 3 Opera tions of S treet -hail T axi
31000 31500 32000 32500 33000
0
20
40
60
80
100
Total demand per hour
Bootstrap repetitions
2013 2012
2011
Bootstrap repetitions
31500 32000 32500 33000
0
10
30
50
70
Total demand per hour
High service time
Low service time
-2 -1 0 1 2
-2
-1
0
1
2
R
2
=0.512
0.5 1 1.5 2 2.5 3 3.5
0
Variance-to-mean ratio of pickup counts
A D
C B
1000
800
600
400
200
Number of segments
Service hours, standardized
Pickups, standardized
F igure 3.12: AN O V A and P oisson tes ts, using trips in core Manhattan, 8am-9am spring sea-
sons. (A -B) Sam pling dis tributions of t o tal demand r ate, 1000 boo ts tr ap repe-
titions f or each g roup: (A) b y y ear , 2011-2013; (B) b y t o tal taxi se r vice hours,
partitioning t he 2012 sam ple int o tw o equall y sized g roups sho wn in (C). (D)
His t og r am of v ariance-t o-mean r atio (VMR) of pickup counts on s treet seg-
ments in 2012 (N = 53). Pickup counts on tw o-w a y segments are considered
as uncorrelated and tes ted as one unit. V alues lar g er t han 3.5 are clipped t o 3.5.
Dash line sho w s t he median (1.10). R ed cur v e sho w s t he sam pling dis tribution
of P oisson VMR, v erticall y scaled t o fit plo t.
75
C hapter 3 Opera tions of S treet -hail T axi
3.6 Discussion
3.6.1 Poisson assumption
Here w e tes t if t he arriv als of hailers and v acant taxis can be assumed t o be P oisson pro-
cesses. Alt hough t he arriv als of hailers and v acant taxis are no t directl y obser v ed, if t he y
are in f act tw o independent P oisson processes, our Monte Car lo simulation sho w s t hat
t h e resulting pickups are close t o ano t her P oisson process. Thus w e continue t o tes t if t he
obser v ed pickup counts are P oisson.
Ov er dispersion is a common issue in count data where t he v ariation is lar g er t han a
s tandar d P oisson model w ould sugg es t, which arises when t he arriv als are in clus ters. This
issue has long been discussed in s tatis tical liter ature, wit h man y tes ts proposed f or it, see
f or exam ple Cameron and T riv edi ( 1990 ). F or NY C taxi trip recor ds, Y ang2017a sugg es ts
t hat taxi pickups are highl y o v er dispersed, wit h v ariances on t he or der of 10000 times
lar g er t han t he a v er ag es. W e calculate t he v ariance-t o-mean r atio (VMR) of pickup counts
on s treet segments in core Manhattan, 8am-9am spring season 2012, sho wn in F ig. 3.12 D.
W it h v ariance-mean relationship specified as 𝜎 2
= 𝛼𝜇 , t he null h ypo t hesis 𝐻 0
∶ 𝛼 = 1 and
t h e alter nativ e h ypo t hesis 𝐻 1
∶ 𝛼 > 1 , t he null is rejected at size 5% if t he VMR ex ceeds
1.34455, and at size 0.1% if its ex ceeds 1.75. F or t he s treet segments in core Manhattan,
t he median VMR is 1.10, wit h 24.8% of t he segments wit h VMR lar g er t han 1.34455, and
8.06% of t he segments wit h VMR lar g er t han 1.75. Thus t he P oisson assum p tion is consis-
tent wit h obser v ations on mos t of t he segments, and w ould s till be appropriate on mos t of
t he remaining segments. S treet segments wit h v er y high pickup r ates ha v e higher VMR,
which can be caused b y o ccasional e v ents t hat dr a w lar g e cro wds increasing taxi activity .
On segments wit h taxi s tands, typicall y at ma jor tr ansportation hubs, v acant taxis line up
and w ait f or cus t omers, which challeng es our model assum p tion. These segments can be
seen t o ha v e infinite suppl y r ates as long as t he taxi line is no t em p ty , and t hus demands
76
C hapter 3 Opera tions of S treet -hail T axi
are alw a ys fulfilled. Our model natur all y handles t his situation as t he es timated equilib-
rium suppl y r ate is proportional t o pickup r ate, and high suppl y r ate is associated wit h
high demand fulfillment (see F ig. 3.8 ), pro viding appropriate demand es timates e v en if
t h e model assum p tions are challeng ed. Our result on o v er dispersion s tands in contr as t t o
o t her liter ature sugg es ted, which highlights t he im portance of time sam pling and spatial
unit selection.
3.6.2 S t ability of demand es tima tes
Since t he es timated taxi demand dis tribution has ne v er been directl y measured, w e v ali-
date it b y tes ting its s tability at different suppl y le v els. T o tal pickup is positiv el y correlated
wit h taxi ser vice hours in t he same time inter v al, see F ig. 3.12 C. The 𝑅 2
is close t o 0.5, be-
cause bo t h suppl y and demand le v els contribute t o t he v ariance of pickup counts; 𝑅 2
has
similar v alues in o t her y ears, see T able 3.1 . Here w e use ser vice hours t o measure suppl y
le v el, r at her t han taxi counts or search time, because no t all taxis pro vide t he same amount
of ser vice time t hat is in core Manhattan, while search time is conf ounded b y taxi counts.
Specificall y , tw o com peting f act ors affect t he correlation betw een search time and pickups:
assuming t he a v er ag e trip dur ation is s table, a fix ed number of activ e taxis means a fix ed
sum of search and trip time, search time is t hus neg ativ el y correlated wit h pickups; wit h
more activ e taxis and a fix ed demand, pickups and search time bo t h increase, t hus posi-
tiv el y correlated. Assuming demand dis tribution is t he same in all obser v ations, t he de-
mand dis tribution es timate is s table if it i s uncorrelated wit h suppl y le v el. In o t her w or ds,
demand es timates do no t chang e b y clus tering obser v ations of similar suppl y le v els. W e
partition t he original sam ple int o tw o equall y sized subsam ples b y ser vice hours, and es ti-
mate t he demand dis tribution separ atel y wit h 1000 boo ts tr ap resam ples, results sho wn in
F ig. 3.12 B. The a v er ag e demand es timates are v er y close, and t he difference is no t s tatis ti-
call y significant. It means t hat t he difference in pickups betw een t he t w o subsam ples are
77
C hapter 3 Opera tions of S treet -hail T axi
com pletel y explained b y t he difference in suppl y le v els, and t he demand es timate is t he
same, consis tent wit h our assum p tion.
3.6.3 Applic ability
T axicab tr ansportation has long been a go v er nment regulated segment of urban tr ansporta-
tion, so f or cities t hat ha v e been collecting taxi GPS tr a ject or y data, our model can be read-
il y applied f or t he es timation of taxi demand. If f or technical or his t orical reasons onl y trip
origin-des tination locations are a v ailable, our model pro vides a sim ple met hod t o es timate
equilibrium suppl y route dis tribution. The kno w ledg e of taxi suppl y and demand can help
regulat ors and ser vice pro viders better unders tand pre vious taxi oper ation and im pro v e
current ser vice. A cademics can also exploit t hese es timates f or furt her anal yses, as such
v ariables ha v e no t been pre viousl y o bser v ed.
T r ansportation netw or k com panies (TN C) w or ldwide ha v e been cutting int o tr aditional
taxi ser vices, creating a fr agmented mar k et of ride-hiring in each city . Alt hough t hese com-
panies can and do collect demand inf or mation t hrough app activ ation logs, t he y ha v e in-
centiv e no t t o share it wit h o t her parties. This mak es it har der t o es timate t he com plete
demand dis tribution from a single source of data, but our model s till applies t o t he remain-
ing demand field t hat seek s s treet-side ser vice. And b y com paring es timated taxi demand
dis tributions bef ore and af ter TN C entr y , w e can ha v e a much detailed unders tanding of
TN Cs ’ im pact on taxicab t r ansportation.
3.6.4 O ther issues
Demand concentr ation, or “mar k et t hickness”, affects t o tal rent: A t t he same t o tal demand
and t o tal suppl y le v el, a dis tributed demand field can lead t o lo w er rent (and a v er ag e pro-
ductivity) t han a concentr ated demand field.
Alter nativ e specifications of t he pickup model can be expored using t he Monte Car lo
78
C hapter 3 Opera tions of S treet -hail T axi
simulation. T o account f or o v er -dispersion, P oisson mixture models ma y be used f or sup-
pl y and demand arriv al processes. F or exam ple, P oisson wit h r ate par ameter from g amma
dis tribution, which results in neg ativ e binomial counts; and P oisson wit h v ariable clus ter
size.
Demand es timation ma y need special treatment at certain locations. T axi s tand is a place
where taxicabs are aut horized, eit her b y NY C Do T or a tr ansportation ter minal oper at or ,
t o line up and w ait f or cus t omers. F eed line is t he line of T axicabs t hat f eeds int o t he spe-
cific pick -up location t o pick up a passeng er . As used at certain tr ansportation ter minals,
taxicabs in t he f eed line designated as a long haul line mus t onl y accep t cus t omers who are
reques ting trips of at leas t a certain dis tance or time. Those in t he f eed line designated as a
short haul line mus t onl y accep t cus t omers who are reques ting trips of less t han a certain
dis tance or time. If taxis line up at taxi s tands (e.g. P ort A ut hority Bus T er minal) or w aits b y
t h e curb, t his segment can be treated as if wit h infinite taxi suppl y r ate, and pickup equals
demand. So when pickup r ate is high, suppl y r ate is almos t surel y infinite, and demand
equals pickup.
79
C h apter 4
Equilibrium of T axi Transpor t a tion
U rban tr ansportation has periodic beha vior per da y , w eek and season. Such regularity can
be unders t ood as t he outcome of individual decision making in response t o tr ansporta-
tion ser vice and demand. Giv en specific en vironment conditions such as tr affic speed and
tr ansportation ser vice dis tribution and f are pricing, t he v alue maximization of t he popu-
lation leads t o an economic equilibrium. W e f or malize tr ansportation decision making of
t h e population as a non-cooper ativ e g ame, and pro vide a sufficient condition f or its N ash
equilibrium. Giv en t he tr ansportation decision of t he population, t he N ash equilibrium is
sol v ed f or taxi driv ers. F urt her more, w e pro vide an analogy of t his equilibrium t o t her mo-
dynamic equilibrium f or a macroscopic inter pretation.
T axi driv ers are bo t h r ide ser vice pr o viders and indepe ndent contr act ors. F or t he s treet-
hail taxi indus tr y , each taxi in ser vice can be seen as a multi-mar k et fir m, e v er y s treet
segment is a dis tinct mar k et, and fir ms allocate ser vice time across t he s treet netw or k. W e
g ener alize t he model int o a g ame of multi-mar k et com petition among fir ms of equal ca-
pacity , and pro v e t hat t he g ame has pure-s tr ategy N ash equilibrium (PSNE), which is (1)
symmetric, (2) essentiall y unique in t hat mar ginal pla y er pa y offs are unif or m across all in-
v es ted mar k ets, and (3) globall y asym p t o ticall y s table under g r adient adjus tment process
and imitativ e lear ning. The a gg reg ate s tr ategy at equilibrium maximizes a “po tential func-
80
C hapter 4 Equilibrium of T axi Transpor t a tion
tion”, and it differs from t he social op timal s tr ategy f or mos t f or ms of production functions.
W e v alidate t hat taxi driv ers ’ beha vior conf or m t o t his equilibrium under ex og enous tr af-
fic speeds and taxi demand. Consis tent wit h t he equilibrium, mar ginal segment income is
cons tant o v er time-of-da y in each shif t. W it h t he launch of S treet Hail Liv er y (g reen cab) in
late 2013, which increases s treet-hail v ehicles out of core Manhattan, w e obser v e a decrease
in y e llo w c ab pickups be y ond Eas t 96t h S treet and W es t 110t h S treet.
4.1 Micr osc opic decision makin g: ec on omic equilibir um
Each taxi in ser vice can be seen as a multi-mar k et fir m, where e v er y s treet segment is
a dis tinct mar k et, and t he fir m allocates its ser vice time among v arious s treet segments.
Com petition among taxis c ould lead t o specific choices of driv er s tr ategies, called economic
equilibrium.
The tr ansportation decision of a taxi driv er can be sim pl y expressed as: taxi driv ers max-
imize t heir income b y choosing t heir driving s tr ategy . W e ignore t he exit decision of taxi
driv ers, and assume t hat individuals who driv e a taxi can ear n at leas t as much income
as t heir cos t, i.e. t heir alter nativ e income. When t his condition does no t hold, r ational in-
dividuals w ould no t be driving a taxi. W e sho w in t he f ollo wing t hat driv er’ s objectiv e
function is s tr ategicall y equiv alent t o trip re v enue, and f or malize driv er’ s decision as an
op t imization problem.
Income s tr ucture of a taxi driv er differs b y t he property r ights of t he taxi in use. Owner -
driv ers are Medallion o wners who also driv e t heir taxis, so t he y ha v e no lease t o pa y .
Driv ers of driv er -o wned v ehicle (DO V) lease a Medallion from fleets, ag ents, or Medal-
lion o wners, and eit her o wn or finance t he purchase of t he v ehicle, at different lease cos ts.
Ot her driv ers lease bo t h t he Medallion and t he v ehicle. In an y kind of such leases, t he
driv er pa ys a fix ed amount of mone y eit her per shif t which las ts 12 hours, or per w eek
81
C hapter 4 Equilibrium of T axi Transpor t a tion
in long er -ter m leases.
1
The lease ma y op tionall y include g asoline surchar g e, also a fix ed
amount, since 2012-09-30.
2
T axi lease type can be inf erred from d riv er names on t he taxi’ s
r ate car d: if a taxi has named driv ers, its o wner typicall y uses long-ter m lease; if it has un-
specified driv er , its o wner typicall y uses shif t lease. T able 4.1 sho w s t he number of NY C
taxis in 2005 b y t heir manag er and driv er types, deriv ed from Schaller ( 2006 ).
T able 4.1: NY C taxis b y manag er -driv er type, 2005
Owner -driv er N amed driv er U nspecified
Owner 3730 1210 -
Fleet - 1481 635
A g ent - 1435 4305
T axi driv ers also pa y f or fuel usag e, which depends on v ehicle model, v ehicle speed and
acceler ation, air tem per ature, and air conditioning. As of v ehicle model, af ter t he 2008-
05-02 TL C auction, 275 of t he 13237 Medallions are res tricted t o alter nativ e fuel v ehicles,
but man y unres tricted Medallion o wners v oluntaril y con v erted t o clean-fuel v ehicles
3
(see
T able 4.2 ). F or g asoline/h ybrid light passeng er v ehicles oper ating at urban tr affic speed
(16-40 km/h, or 10-25 m ph), fuel consum p tion per hour is almos t cons tant, see S. C. Da vis,
Dieg el, and Boundy ( 2017 ). This means t hat fuel cos t per ser vice time can be seen as a
cons tant f or each taxicab reg ar dless of speed — w e do no t consider taxis par k ed b y t he
curb wit h engine off activ el y in ser vice. Ev en wit hout t his obser v ation, fuel cos t per ser vice
time w ould s till be appro ximatel y cons tant f or a driv er in one shif t, as long as t he driv er
has consis tent driving speeds and acceler ation patter ns.
A taxi driv er ear ns t he remaining f are and tips af ter pa ying f or lease, fuel, or bo t h. F or -
mall y , t he hour l y income 𝑢 𝑖 of driv er 𝑖 deriv es from hour l y trip re v enue 𝜋 𝑖 , minus hour l y
1
TL C R ules §58-21: Leasing a T axicab or Medallion.
2
TL C lease cap r ules chang e. http://www.nyc.gov/html/tlc/downloads/pdf/lease_cap_
rules_passed.pdf
3
TL C 2008-2013 Annual R eports. http://www.nyc.gov/html/tlc/html/archive/annual.
shtml
82
C hapter 4 Equilibrium of T axi Transpor t a tion
T able 4.2: NY C taxis b y v ehicle fuel type
End of y ear Gasoline Hybrid-electric Diesel CN G
*
2007 12422 728 0 -
2008 11394 1843 0 -
2009 10177 3043 17 -
2010 9029 4185 19 4
2011 7540 5681 14 2
2012 6455 6769 10 3
2013 5320 7905 9 3
*
CN G: com pressed natur al g as
fuel cos t 𝑓 𝑖 , minus amortized hour l y lease pa yment 𝑟 𝑖 :
𝑢 𝑖 = 𝜋 𝑖 − 𝑓 𝑖 − 𝑟 𝑖 (4.1)
The amortized hour l y lease pa yment b y t he driv er is 𝑟 𝑖 = 𝑅 𝑖 /𝑇
𝑖 , where 𝑇 𝑖 deno tes driv er
t o tal ser vice time during t he lease ter m, and 𝑅 𝑖 deno tes lease pa yment, i.e. rent of t he
Medallion taxicab. Depending on t he lease, 𝑓 𝑖 or 𝑟 𝑖 ma y be zero. Since 𝑓 𝑖 and 𝑟 𝑖 are con-
s tant f or driv er 𝑖 in an y giv en shif t, t he y do no t affect t he driv er’ s driving s tr ategy . Thus,
driv er’ s objectiv e is s tr ategicall y equiv alent t o trip re v enue 𝜋 𝑖 . W e no te t hat alt hough v e-
hicle maintenance is ano t her cos t t o driv ers who o wn t he v ehicle, it is no t rele v ant t o t he
driv er s tr ategy of our interes t.
T o define taxi driv ers ’ driving s tr ategy , w e firs t anal yze taxi tr ansportation. T axis in ser -
vice are eit her v acant or occupied: when v acant, driv ers search t he s treets f or hailers; when
occupied, driv ers tak e t he passeng ers t o t heir des tination. T axi driv ers can freel y choose
ho w t he y spend t heir search time o v er t he s treet netw or k. Once t he y find hailers, driv ers
will s t op searching and pick t hem up.
4
T axi f are r ate is set b y t he city go v er nment, which
ma y be metered or has a flat r ate, depending on t he des tination. U nder flat r ate, driv ers
4
In real lif e, no t all taxi driv ers pick up e v er y hailer t he y meet. The y ma y discriminate hailers based on
t he des tination, r ace, or o t her f act ors, due t o profitability , security , or end-of-shif t concer ns. See NY C 311
recor ds f or com plaints about taxis ser vice denial.
83
C hapter 4 Equilibrium of T axi Transpor t a tion
are bes t off taking t he f as tes t pat h. Metered r ates char g e b y dis tance or dur ation, based on
a speed t hreshold, which are typicall y set such t hat driv ers ha v e no incentiv e t o driv e slo w .
Alt hough driv ers do ha v e an incentiv e t o tak e routes long er t han t he f as tes t pat h, passen-
g ers typicall y are mo tiv ated t o super vise trip dur ation. In case of driv er fr aud, det ouring
is no t a common s tr ategy (Balaf outas, K erschbamer , and Sutter , 2015 ). Thus, w e assume
t h at taxi driv er’ s deliv er y s tr ategy is t o tak e passeng ers t o t heir des tination via t he f as tes t
pat h, so trip dur ation be tw een tw o specific locations onl y depend on tr affic speed. W e can
see t hat t he onl y s tr ategic element f or taxi driv ers is ho w t he y allocate t heir search time.
N o w w e f or malize driv ers ’ driving s tr ategy . Let 𝑁 be t he set of taxi driv ers currentl y in
ser vice. Let 𝐺 = (𝑉 , 𝐸) be t he road netw or k wit hin t he urban area being s tudied, where 𝑉 is t he set of intersections and dead ends, and 𝐸 is t he set of s treet segments. S treet segment
𝑥 ∈ 𝐸 has lengt h 𝑙 𝑥 , wit h tr affic speed 𝑣 𝑥 and taxi search speed ̃ 𝑣 𝑥 . Define demand r ate 𝜇 𝑑𝑥𝑦 as t he frequency of hailers s tart hailing on segment 𝑥 who are going t o segment 𝑦 ; such
a g roup of hailers ha v e im patience 𝜇 𝑡𝑥𝑦 = 1/𝔼𝑇
𝑥𝑦 , t he reciprocal of hailer mean patience.
W it hin a short time inter v al, en vironment condition ℰ = ( v , 𝜇 𝑑 , 𝜇 𝑡 ) can be considered as
cons tant, where v is t he v ect or of tr affic speeds, and 𝜇 𝑑 and 𝜇 𝑡 are matrices of hailer demand
and im patience. S tr ategy f or driv er 𝑖 can be defined as t he spatial dis tribution of suppl y
r ates 𝜇 𝑠𝑖 , where 𝜇 𝑠𝑖 𝑥 = (𝜇
𝑠𝑖 )
𝑥 is t he frequency at which driv er 𝑖 enters segment 𝑥 as a v acant
taxi. Equiv alentl y , driv er s tr ategy can be defined as t he dis tribution of driv er’ s search time
per un it time:
𝑡 𝑠𝑖 𝑥 𝑡 =
𝑙 𝑥 ̃ 𝑣 𝑥 𝜇 𝑠𝑖 𝑥 (4.2)
This sho w s t hat on each segment, driv er search time is linear l y related t o driv er suppl y
r ate. Define pickup r ate 𝜇 𝑝𝑖 𝑥𝑦 as t he frequency at which driv er 𝑖 pick s up passeng ers on
𝑥 going t o 𝑦 . These attributes natur all y agg reg ates on each segment: 𝜇 𝑝𝑥 = ∑
𝑖 ∑
𝑦 𝜇 𝑝𝑖 𝑥𝑦 ,
𝜇 𝑠𝑥 = ∑
𝑖 𝜇 𝑠𝑖 𝑥 , 𝜇 𝑑𝑥 = ∑
𝑦 𝜇 𝑑𝑥𝑦 , and 𝜇 𝑡𝑥 = 1/𝔼𝑇
𝑥 . Pickup r ate can t hus be expressed as a
84
C hapter 4 Equilibrium of T axi Transpor t a tion
function of suppl y r ate, demand r ate and hailer im patience: 𝜇 𝑝𝑥 (𝜇
𝑠𝑥 , 𝜇 𝑑𝑥 , 𝜇 𝑡𝑥 ) . R. Zhang
and Ghanem ( 2018 ) proposed a class of pickup models and pro v ed t hat t he pickup r ate
functions are increasing, s trictl y conca v e, and arbitr aril y differentiable, wit h respect t o sup-
pl y r ate; f or t hree representativ e models, anal ytical f or ms of t he pickup r ate functions are
also pro vided.
W e no w relate driv er s tr ategy wit h driv er re v enue. Let Π
𝑥𝑦 be t he re v enue of a single trip
from 𝑥 t o 𝑦 , which onl y depends on tr affic speeds v . W e can write hour l y re v enue originated
on 𝑥 as 𝜋 𝑥 = ∑
𝑦 Π
𝑥𝑦 𝜇 𝑝𝑥𝑦 and a v er ag e re v enue of a trip originated on 𝑥 as Π
𝑥 = 𝜋 𝑥 /𝜇
𝑝𝑥 .
Assume patience and des tination are appro ximatel y uncorrelated f or hailers wit h t he same
origin, which means ∀𝑥 , 𝑦 ∈ 𝐸, 𝜇 𝑡𝑥 ≈ 𝜇 𝑡𝑥𝑦 . Then hailers on t he same segment ha v e an equal
chance of being pick ed up reg ar dless of t heir des tination:
∀𝑥 ∈ 𝐸, 𝜇 𝑝𝑥𝑦 ∝ 𝜇 𝑑𝑥𝑦 , ∀𝑦 ∈ 𝐸 Thus, t he a v er ag e re v enue f or a trip originated on 𝑥 onl y depends on tr affic speeds and de-
mand r ates: Π
𝑥 ( v , 𝜇 𝑑𝑥 ) = ∑
𝑦 Π
𝑥𝑦 𝜇 𝑑𝑥𝑦 /𝜇
𝑑𝑥 . Since driv ers are assumed no t t o discriminate
hailers:
∀𝑖 ∈ 𝑁 , ∀𝑥 ∈ 𝐸, 𝜇 𝑝𝑖 𝑥𝑦 ∝ 𝜇 𝑝𝑥𝑦 , ∀𝑦 ∈ 𝐸 Driv er re v enue originated on a segment 𝜋 𝑖 𝑥 = ∑
𝑦 Π
𝑥𝑦 𝜇 𝑝𝑖 𝑥𝑦 can t hus be written as 𝜋 𝑖 𝑥 =
∑
𝑦 Π
𝑥𝑦 𝜇 𝑝𝑥𝑦 𝜇 𝑝𝑖 𝑥 /𝜇
𝑝𝑥 = Π
𝑥 𝜇 𝑝𝑖 𝑥 . Since each pass of a v acant taxi has an equal chance of
picking up a hailer reg ar dless of t he driv er :
∀𝑥 ∈ 𝐸, 𝜇 𝑝𝑖 𝑥 ∝ 𝜇 𝑠𝑖 𝑥 , ∀𝑖 ∈ 𝑁 W e ha v e 𝜋 𝑖 𝑥 = Π
𝑥 𝜇 𝑝𝑖 𝑥 = Π
𝑥 𝜇 𝑝𝑥 𝜇 𝑠𝑖 𝑥 /𝜇
𝑠𝑥 . Driv er hour l y trip re v enue can t hus be expressed
85
C hapter 4 Equilibrium of T axi Transpor t a tion
wit h explicit function de pendency as:
𝜋 𝑖 = ∑
𝑥∈𝐸
𝜋 𝑖 𝑥 = ∑
𝑥∈𝐸
Π
𝑥 ( v , 𝜇 𝑑𝑥 )𝜇
𝑝𝑥 (𝜇
𝑠𝑥 , 𝜇 𝑑𝑥 , 𝜇 𝑡𝑥 )
𝜇 𝑠𝑖 𝑥 𝜇 𝑠𝑥 (4.3)
A more anal yticall y con v enient definition of driv er s tr ategy is driv er’ s allocation of ser -
vice time. Ser vice time 𝑡 𝑖 𝑥 = 𝑡 𝑠𝑖 𝑥 + 𝑡 𝑝𝑖 𝑥 is t he t o tal time driv er 𝑖 spends searching and
deliv ering trips originated on 𝑥 during a period of time 𝑡 . The r ationale of using ser vice
time dis tribution as driv er s tr ategy ins tead of suppl y r ate or search time is t hat: ser vice
time is a conser v ed quantity and identical f or all driv ers; mean while, ser vice time is mono-
t onic in suppl y r ate and preser v es properties of t he pickup r ate function. Let 𝑡 𝑥𝑦 be t he
trip dur ation from 𝑥 t o 𝑦 , which onl y depends on tr affic speeds v . The a v er ag e dur ation
of a trip originated on 𝑥 is 𝑡 𝑥 ( v , 𝜇 𝑑𝑥 ) = ∑
𝑦 𝑡 𝑥𝑦 𝜇 𝑑𝑥𝑦 /𝜇
𝑑𝑥 = ∑
𝑦 𝑡 𝑥𝑦 𝜇 𝑝𝑥𝑦 /𝜇
𝑝𝑥 , wit h reasoning
similar t o a v er ag e trip re v enue Π
𝑥 . The proportion of time driv er 𝑖 spends deliv ering trips
originated on 𝑥 is t hus 𝑡 𝑝𝑖 𝑥 /𝑡 = ∑
𝑦 𝑡 𝑥𝑦 𝜇 𝑝𝑖 𝑥𝑦 = ∑
𝑦 𝑡 𝑥𝑦 𝜇 𝑝𝑥𝑦 𝜇 𝑝𝑖 𝑥 /𝜇
𝑝𝑥 = 𝑡 𝑥 𝜇 𝑝𝑖 𝑥 = 𝑡 𝑥 𝜇 𝑝𝑥 𝜇 𝑠𝑖 𝑥 /𝜇
𝑠𝑥 ,
wit h reasoning similar t o 𝜋 𝑖 𝑥 . T og et her wit h Equation 4.2 , t he proportion of ser vice time
driv er 𝑖 allocates on 𝑥 can t hus be written as:
𝑠 𝑖 𝑥 =
𝑡 𝑠𝑖 𝑥 + 𝑡 𝑝𝑖 𝑥 𝑡 = (
𝑙 𝑥 ̃ 𝑣 𝑥 + 𝑡 𝑥 𝜇 𝑝𝑥 𝜇 𝑠𝑥 ) 𝜇 𝑠𝑖 𝑥 (4.4)
This sho w s t hat on each segment, driv er ser vice time is also linear l y related t o driv er suppl y
r ate: ∀𝑥 ∈ 𝐸, 𝑠 𝑖 𝑥 ∝ 𝜇 𝑠𝑖 𝑥 , ∀𝑖 ∈ 𝑁 . F rom Equation 4.4 , ser vice time on a segment 𝑠 𝑥 =
𝜇 𝑠𝑥 𝑙 𝑥 / ̃ 𝑣 𝑥 + 𝜇 𝑝𝑥 𝑡 𝑥 . W it h pickup r ate function 𝜇 𝑝𝑥 (𝜇
𝑠𝑥 , 𝜇 𝑑𝑥 , 𝜇 𝑡𝑥 ) and cons tant en vironment
condition ℰ , pickup r ate is im plicitl y a function of ser vice time: 𝜇 𝑝𝑥 (𝑠
𝑥 , ℰ ) . Each t axi driv er
mus t allocate all t he ser vice time among t he s treet segments: ∑
𝑥 𝑡 𝑖 𝑥 = 𝑡 , or equiv alentl y
∑
𝑥 𝑠 𝑖 𝑥 = 1 . The driving s tr ategy of taxi driv er 𝑖 is t hus s
𝑖 ∈ 𝑆 𝑖 , where t he s tr ategy space
𝑆 𝑖 = Δ
|𝐸|−1
, a sim plex of dimension one less t han t he number of segments. N o w w e can
86
C hapter 4 Equilibrium of T axi Transpor t a tion
f or mall y write t he op timization problem of a taxi driv er :
maximize ∑
𝑥∈𝐸
Π
𝑥 ( v , 𝜇 𝑑𝑥 )𝜇
𝑝𝑥 (𝑠
𝑥 , ℰ )
𝑠 𝑖 𝑥 𝑠 𝑥 subject t o s
𝑖 ≥ 0
s
𝑖 ⋅ 1 = 1
(4.5)
N o w w e pro v e t hat pickup r ate 𝜇 𝑝𝑥 (𝑠
𝑥 , ℰ ) is also increasing, s trictl y conca v e, and arbitr aril y
differentiable wit h respect t o 𝑠 𝑥 . W it h cons tant en vironment condition ℰ , t he im plicit func-
tion can be abs tr acted t o 𝑧 = 𝑎𝑥 + 𝑏𝑦 , where 𝑧 = 𝑠 𝑥 , 𝑥 = 𝜇 𝑠𝑥 , 𝑦 = 𝜇 𝑝𝑥 , 𝑎 = 𝑙 𝑥 / ̃ 𝑣 𝑥 , and 𝑏 = 𝑡 𝑥 ;
𝑦 (𝑥 ) is increasing, s trictl y conca v e, and arbitr aril y differentiable, while 𝑎, 𝑏 > 0 are con-
s tants. Our proposition is t hus equiv alent t o: 𝑦 (𝑧) is also increasing, s trictl y conca v e, and
arbitr aril y differentiable. Differentiablity is sim pl y preser v ed b y t he linear relation. Since
𝑧(𝑥 ) = 𝑎𝑥 + 𝑏𝑦 (𝑥 ) is increasing, its in v erse 𝑥 (𝑧) is t hus also increasing; b y com position,
𝑦 (𝑧) = 𝑦 (𝑥 (𝑧)) is also increasing. By im plicit differentiation, d 𝑦 / d 𝑧 = 𝑦 ′
(𝑥 )/(𝑎 + 𝑏𝑦 ′
(𝑥 )) ,
and t hus d
2
𝑦 / d 𝑧 2
= 𝑎𝑦 ″
(𝑥 )/(𝑎 + 𝑏𝑦 ′
(𝑥 ))
3
. Since 𝑦 ′
(𝑥 ) > 0 and 𝑦 ″
(𝑥 ) < 0 , 𝑦 ″
(𝑧) < 0 , which
means 𝑦 (𝑧) is also s trictl y conca v e.
Despite t he v arious alter nativ es w e proposed as f or mal driv er s tr ategy , here w e point
out ho w taxi driv ers w ould im plement such a s tr ategy . Picture a taxi driv er 𝑖 who is f amil-
iar wit h t he tr affic of t he city , and hailer and taxi dis tributions t hroughout a da y . T o ear n
more mone y , t he driv er has a plan on ho w much time t o spend searching different places
f or hailers; t he plan v aries f or different time of da y . A t t he beginning of 𝑖 ’ s shif t, t he driv er
heads t o t he region where t he plan allocates t he mos t search time. Af ter deliv ering t he
firs t pickup, t he driv er is lik el y t o be in a region wit h less planned search time. T o a v oid
o v er -searching t he current region, 𝑖 driv es back t o t he pref erred region. If 𝑖 goes t hrough
t he pref erred region wit hout a pickup, t he driv er w ould circle around and continue t he
search, as long as t he t o tal search time wit hin t he region is no t t oo long com pared wit h
87
C hapter 4 Equilibrium of T axi Transpor t a tion
t h e plan. The driv er does no t alw a ys search or immediatel y go back t o t he region wit h t he
highes t pla nned search time, but w ould balance t he allocation of realized search time t o
appro ximate t he plan. But when 𝑖 drops off at a location wit h v er y little planned search
time, t he driv er w ould directl y head t o a place nearb y where t he plan giv es more search
time, since a single pass w ould typicall y suffice f or t he drop-off location. Because t he t o tal
search time is limited f or an y giv en shif t, t he driv er w ould no t be able t o perf ectl y im-
plement t he s tr ategy in one shif t. But agg reg ated o v er time, t he dis tribution of realized
search time could reasonabl y appro ximate an intended s tr ategy . In later sections, w e tak e
t he dis tribution of realized search time as a driv er’ s s tr ategy .
4.2 Sol ution c on cept : N ash equilibir um
W it h decision problems f or malized f or t he individuals in an urban tr ansportation sys-
tem, each depending on t he choices of t he individual and t he population, w e can sol v e
f or t he tr ansportation decision of t he population as a g ame t heor y problem. N ash equi-
librium (N ash, 1951 ) is t he mos t widel y used solution concep t in g ame t heor y f or non-
cooper ativ e g ames. In g ame t heor y , a non-cooper ativ e g ame is one in which pla y ers mak e
decisions independentl y , wit h no contr act enf orceable b y t hir d parties; a set of pla y er s tr ate-
gies is a N ash equilibrium if no pla y er can be better off b y unilater all y changing s tr ategy .
In t his section w e f or malize t he g ame of multi-mar k et com petition among fir ms of equal
capacity , and pro v e t hat t he g ame has pure-s tr ategy N ash equilibrium (PSNE), which is
symmetric and essentiall y unique in t hat mar ginal pla y er pa y offs are unif or m across all
in v es ted mar k ets.
W e use subscrip t 𝑥 t o deno te a mar k et, or product ; subscrip t 𝑖 f or a fir m, or pla y er ; sub-
scrip t −𝑖 f or opponents of fir m 𝑖 . Boldf ace deno tes a v ect or ; single subscrip t indicates sum-
mation. Conditions in parent heses are op tional.
88
C hapter 4 Equilibrium of T axi Transpor t a tion
Game setup of multi-mar k et oligopol y . F or fir ms 𝑖 ∈ 𝑁 , |𝑁 | = 𝑛 , each dis tributing a unit
of resources o v er mar k ets 𝑥 ∈ 𝐸 , |𝐸| = 𝑚 :
1. T o tal pa y off in a mar k et 𝑢 𝑥 (𝑠
𝑥 ) , 𝑠 𝑥 ≥ 0 , 𝑢 𝑥 (0) = 0 , is (increasing) non-decreasing,
differentiable, and (s trictl y) conca v e;
2. P a y off per in v es tment in a mar k et 𝑝 𝑥 (𝑠
𝑥 ) = 𝑢 𝑥 /𝑠
𝑥 , 𝑠 𝑥 > 0 , is (decreasing) non-increasing;
no t necessaril y con v ex;
3. Pla y er pa y off in a mar k et 𝑢 𝑖 𝑥 (𝑠
𝑖 𝑥 ; 𝑠 −𝑖 𝑥 ) = 𝑝 𝑥 (𝑠
𝑥 )𝑠
𝑖 𝑥 , 𝑠 𝑖 𝑥 ∈ [0, 1] , 𝑠 −𝑖 𝑥 = ∑
𝑗 ≠𝑖
𝑠 𝑗 𝑥 ∈
[0, 𝑛 − 1] ;
4. Pla y er pa y off 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) = ∑
𝑥 𝑢 𝑖 𝑥 (𝑠
𝑖 𝑥 ; 𝑠 −𝑖 𝑥 ) , s
𝑖 ∈ 𝑆 𝑖 = Δ
𝑚−1
, s
−𝑖
= ∑
𝑗 ≠𝑖
s
𝑗 ∈ 𝑆 −𝑖
=
(𝑛 − 1)Δ
𝑚−1
; Here Δ
𝑚−1
= { v ∈ ℝ
𝑚 ∣ v ≥ 0, v ⋅ 1 = 1} is t he (𝑚 − 1) -dimensional
sim plex.
5. Mar ginal pla y er pa y off in a mar k et at equilibrium 𝜙 𝑥 (𝑠
𝑥 ) = 𝑝 𝑥 (𝑠
𝑥 ) + 𝑝 ′
𝑥 (𝑠
𝑥 )𝑠
𝑥 /𝑛 , or
equiv alentl y 𝜙 𝑥 (𝑠
𝑥 ) = 𝑢 ′
𝑥 (𝑠
𝑥 )/𝑛 + (1 − 1/𝑛)𝑢
𝑥 (𝑠
𝑥 )/𝑠
𝑥 , is (positiv e) non-neg ativ e, (de-
creasing) non-increasing;
6. P o tential function Φ( s ) = ∑
𝑥 ∫
𝑠 𝑥 0
𝜙 𝑥 (𝑡 ) d 𝑡 , s ∈ 𝑛Δ
𝑚−1
, which is equiv alent t o Φ( s ) =
∑
𝑥 [𝑢
𝑥 (𝑠
𝑥 )/𝑛 + (1 − 1/𝑛) ∫
𝑠 𝑥 0
𝑢 𝑥 (𝑡 )/𝑡 d 𝑡 ] ;
Multi-mar k et oligopol y is similar t o Cour no t oligopol y (Cour no t, 1838 ), but differs in
significant w a ys. In Cour no t oligopol y , each pla y er chooses a production le v el of t he same
product, whose mar ginal retur n decreases wit h t o tal production; while t he multi-mar k et
oligopol y can be seen as a multi-product Cour no t g ame, where all pla y ers ha v e t he same
t o tal productivity . F or mall y , Cour no t oligopol y can be written as: 𝐺 𝑐 = {𝑁 , 𝑄, u } , where
pla y er s tr ategy 𝑞 𝑖 ∈ 𝑄 𝑖 = ℝ
≥0
, and pla y er pa y off function 𝑢 𝑖 (𝑞
𝑖 , 𝑞 −𝑖
) = 𝑝(𝑞)𝑞
𝑖 − 𝑐 𝑞 𝑖 ; price
𝑝(𝑞) is a decreasing function on t o tal productivity 𝑞 = ∑
𝑖 𝑞 𝑖 , and mar ginal cos t 𝑐 is as-
sumed t o be cons tant. The multi-mar k et oligopol y ins tead has 𝑚 products, and each pla y er
89
C hapter 4 Equilibrium of T axi Transpor t a tion
dis tributes one unit of resource 𝑠 among t he products, ear ning pa y off from all products in-
v es ted.
T o pro v e t hat multi-mar k et fir ms of t he same capacity ha v e a unique and symmetric
PSNE, w e f ollo w a lis t of propositions sho wn belo w . Bef ore g etting int o t he details, w e
point out t he k e ys t o t he proof: con v ex g ame guar antees PSNE exis ts; equal capacity leads
t o symmetr y ; and mono t onic mar ginal pa y offs pro vide a unique solution.
Propositions:
1. Φ( s ) is (s trictl y) conca v e.
2. 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) is (s trictl y) conca v e , ∀𝑖 , ∀ s
−𝑖
∈ 𝑆 −𝑖
.
3. Multi-mar k et oligopol y is a con v ex g ame.
4. Multi-mar k et oligopol y has PSNE, (all s trict).
5. Multi-mar k et oligopol y can onl y ha v e symmetric P SNE.
6. Multi-mar k et oligopol y ha v e a (unique) esse ntiall y unique PSNE, in t hat mar ginal
pla y er pa y offs are unif or m across all in v es ted mar k ets.
7. The equilibrium of multi-mar k et oligopol y is globall y asym p t o ticall y s table under
g r adient adjus tment process.
Let 𝑃 𝑥 (𝑠
𝑥 ) = ∫
𝑠 𝑥 0
𝑝 𝑥 (𝑡 ) d 𝑡 . Since 𝑃 𝑥 (𝑠
𝑥 ) is a differentiable real function wit h a con v ex
domain, it is (s trictl y) conca v e if and onl y if it is globall y (s trictl y) dominated b y its linear
expansions: ∀𝑠
0
> 0, ∀𝑠
𝑥 ≥ 0, 𝑠 𝑥 ≠ 𝑠 0
,
𝑃 𝑥 (𝑠
𝑥 ) − [𝑃
𝑥 (𝑠
0
) + 𝑝 𝑥 (𝑠
0
)(𝑠
𝑥 − 𝑠 0
)]
= ∫
𝑠 𝑥 𝑠 0
𝑝 𝑥 (𝑡 ) d 𝑡 − 𝑝 𝑥 (𝑠
0
)(𝑠
𝑥 − 𝑠 0
)
= ∫
𝑠 𝑥 𝑠 0
𝑝 𝑥 (𝑡 ) − 𝑝 𝑥 (𝑠
0
) d 𝑡 ≤ 0
90
C hapter 4 Equilibrium of T axi Transpor t a tion
This is tr ue because 𝑝 𝑥 (𝑠
𝑥 ) is (decreasing) non-increasing. Because Φ( s ) is a positiv e linear
tr ansf or mation of 𝑃 𝑥 (𝑠
𝑥 ) and 𝑢 𝑥 (𝑠
𝑥 ) which is also (s trictl y) conca v e, it im plies t hat Φ( s )
is (s trictl y) conca v e on t he non-neg ativ e cone ℝ
𝑚 ≥0
. Because sim plex 𝑛Δ
𝑚−1
is a con v ex
subset of t he non-neg ativ e cone ℝ
𝑚 ≥0
, it im plies t hat Φ( s ) is (s trictl y) conca v e on t he sim plex
𝑛Δ
𝑚−1
. This pro v es Proposition 1.
Because sim plex 𝑆 𝑖 is a con v ex subset of t he non-neg ativ e cone ℝ
𝑚 ≥0
, if 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) is
(s trictl y) conca v e on ℝ
𝑚 ≥0
, ∀𝑖 , ∀ s
−𝑖
∈ 𝑆 −𝑖
, t hen 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) is also (s trictl y) conca v e on 𝑆 𝑖 ,
∀𝑖 , ∀ s
−𝑖
∈ 𝑆 −𝑖
. It suffices t o pro v e t he f or mer s tatement wit hout cons tr aints on opponent
s tr ategies: 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) is (s trictl y) conca v e on ℝ
𝑚 ≥0
, ∀𝑖 , ∀ s
−𝑖
∈ ℝ
𝑚 ≥0
. Because 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
) is a
positiv e linear tr ansf or mation of 𝑢 𝑖 𝑥 (𝑠
𝑖 𝑥 ; 𝑠 −𝑖 𝑥 ) , 𝑥 ∈ 𝐸 , it suffices if 𝑢 𝑖 𝑥 (𝑠
𝑖 𝑥 ; 𝑠 −𝑖 𝑥 ) is (s trictl y)
conca v e on ℝ
≥0
, ∀𝑥 , ∀𝑖 , ∀𝑠
−𝑖 𝑥 ≥ 0 . T o sim plify no tations, t his is equiv alent t o 𝑢 𝑖 𝑥 (𝑠; 𝑐 ) =
𝑝 𝑥 (𝑠 + 𝑐 )𝑠 (s trictl y) conca v e on ℝ
≥0
, ∀𝑥 , ∀𝑐 ≥ 0 . This can be pro v ed b y definition, and w e
do no t include t he proof here because it is s tr aightf or w ar d but tedious. The k e y t o t his
proof is t hat 𝑢 𝑥 (𝑠
𝑥 ) is (s trictl y) conca v e and 𝑝 𝑥 (𝑠
𝑥 ) is (decreasing) non-increasing; eit her of
t he op tional conditions can guar antee s trict conca vity . This pro v es Proposition 2.
A con v ex g ame is a g ame where each pla y er has a con v ex s tr ategy space and a conca v e
pa y off function 𝑢 𝑖 (𝑠
𝑖 ; 𝑠 −𝑖
) f or all opponent s tr ategies. In t his g ame, pla y er s tr ategy space is
t he same sim plex 𝑆 𝑖 = Δ
𝑚−1
f or all pla y ers, which is con v ex. T og et her wit h Proposition 2,
t his is pro v es Proposition 3.
A con v ex g ame has PSNE if it has a com pact s tr ategy space and continuous pa y off func-
tions, see Nikaido and Isoda ( 1955). Because t he product space of sim plices is com pact,
t his g ame has a com pact s tr ategy space 𝑆 ≡ ∏
𝑖 𝑆 𝑖 = ∏
𝑖 Δ
𝑚−1
. Because 𝑢 𝑥 (𝑠
𝑥 ) is continu-
ous ∀𝑥 , pla y er pa y off 𝑢 𝑖 ( s ) is t hus continuous ∀𝑖 . This g ame t hus has PSNE. If 𝑢 𝑖 ( s
𝑖 ; s
−𝑖
)
is s trictl y conca v e, all PSNEs are s trict. This pro v es Proposition 4.
Giv en a PSNE s
∗
, f or all pla y er 𝑖 , equilibrium s tr ategy s
∗
𝑖 sol v es t he con v ex op timization
91
C hapter 4 Equilibrium of T axi Transpor t a tion
problem:
maximize 𝑢 𝑖 ( s
𝑖 ; s
∗
−𝑖
)
subject t o s
𝑖 ≥ 0
s
𝑖 ⋅ 1 = 1
(4.6)
Since t his con v ex op timization problem is s trictl y f easible, b y Slater’ s t heorem, it has s trong
duality . Since t he objectiv e function 𝑢 𝑖 ( s
𝑖 ; s
∗
−𝑖
) is differentiable, t he Kar ush-K uhn- T uck er
(KKT) t heorem s tates t hat op timal points of t he op timization problem is t he same wit h t he
solutions of t he KKT conditions:
∇ 𝑢 𝑖 + 𝜆 𝑖 − 𝜈 𝑖 1 = 0 (saddle point)
s
𝑖 ≥ 0 (primal cons tr aint 1)
𝜆 𝑖 ≥ 0 (dual cons tr aint)
s
𝑖 ∘ 𝜆 𝑖 = 0 (com plementar y slackness)
s
𝑖 ⋅ 1 = 1 (primal cons tr aint 2)
(4.7)
Here oper at or ∘ deno tes t he Hadamar d product: (𝑥 ∘ 𝑦 )
𝑖 = 𝑥 𝑖 𝑦 𝑖 . Giv en t he saddle point
conditions 𝜕 𝑢 𝑖 /𝜕 𝑠 𝑖 𝑥 + 𝜆 𝑖 𝑥 − 𝜈 𝑖 = 0, ∀𝑥 , t he dual cons tr aint im plies t hat t he mar ginal pa y off
f or pla y er 𝑖 in mar k et 𝑥 is bounded abo v e: 𝜕 𝑢 𝑖 /𝜕 𝑠 𝑖 𝑥 ≤ 𝜈 𝑖 , ∀𝑥 . If pla y er 𝑖 in v es ts in mar k et 𝑥 ,
𝑠 𝑖 𝑥 > 0 , b y com plementar y slackness t he upper bound is tight, which means t he mar ginal
pa y offs f or pla y er 𝑖 are unif or m in all mar k ets 𝑖 in v es ts. T og et her , mar ginal pla y er pa y offs
at equilibrium ha v e relation:
𝜕 𝑢 𝑖 𝜕 𝑠 𝑖 𝑦 ≤
𝜕 𝑢 𝑖 𝜕 𝑠 𝑖 𝑥 = 𝜈 𝑖 , ∀𝑖 , ∀𝑥 , 𝑦 , 𝑠 ∗
𝑖 𝑥 > 𝑠 ∗
𝑖 𝑦 ≥ 0 (4.8)
Since 𝜕 𝑢 𝑖 /𝜕 𝑠 𝑖 𝑥 = 𝑝 𝑥 (𝑠
𝑥 )+𝑝
′
𝑥 (𝑠
𝑥 )𝑠
𝑖 𝑥 , and 𝑝 ′
𝑥 < 0 , t his is equiv alent t o 𝑝 𝑥 (𝑠
∗
𝑥 ) ≤ 𝜈 𝑖 +|𝑝
′
𝑥 (𝑠
∗
𝑥 )|𝑠
∗
𝑖 𝑥 , ∀𝑥 ,
wit h equality if 𝑠 ∗
𝑖 𝑥 > 0 . If pla y er 𝑖 in v es ts more in mar k et 𝑥 t han pla y er 𝑗 does, 𝑠 ∗
𝑖 𝑥 > 𝑠 ∗
𝑗 𝑥 ≥ 0 ,
92
C hapter 4 Equilibrium of T axi Transpor t a tion
t h is im plies 𝜈 𝑖 + |𝑝
′
𝑥 (𝑠
∗
𝑥 )|𝑠
∗
𝑖 𝑥 ≤ 𝜈 𝑗 + |𝑝
′
𝑥 (𝑠
∗
𝑥 )|𝑠
∗
𝑗 𝑥 . But because t he pla y ers ha v e t he same capacity ,
pla y er 𝑖 mus t ha v e in v es ted less in some mar k et 𝑦 t han pla y er 𝑗 does: 𝑠 ∗
𝑗 𝑦 > 𝑠 ∗
𝑖 𝑦 ≥ 0 , which
im plies 𝜈 𝑗 + |𝑝
′
𝑦 (𝑠
∗
𝑦 )|𝑠
∗
𝑗 𝑦 ≤ 𝜈 𝑖 + |𝑝
′
𝑦 (𝑠
∗
𝑦 )|𝑠
∗
𝑖 𝑦 . T og et her , t hese inequalities im pl y |𝑝
′
𝑥 (𝑠
∗
𝑥 )|(𝑠
∗
𝑖 𝑥 −
𝑠 ∗
𝑗 𝑥 ) + |𝑝
′
𝑦 (𝑠
∗
𝑦 )|(𝑠
∗
𝑗 𝑦 − 𝑠 ∗
𝑖 𝑦 ) ≤ 0 . This contr adicts our assum p tion on pla y er resource allocation,
t hus all pla y ers mus t ha v e t he same s tr ategy in equilibrium. This pro v es Proposition 5.
F rom Proposition 4 and 5, multi-mar k et fir ms ha v e PSNE, which are symmetric. F or a
symmetric PSNE s
∗
, pla y er s tr ategy s
∗
𝑖 = s
∗
/𝑛 , and mar ginal pla y er pa y offs in in v es ted mar -
k ets are t he same f or all pla y ers: 𝜈 𝑖 = 𝜈 , ∀𝑖 . N o w t he relation among equilibrium mar ginal
pla y er pa y offs can be re written as: 𝑝 𝑥 (𝑠
∗
𝑥 ) + 𝑝 ′
𝑥 (𝑠
∗
𝑥 )𝑠
∗
𝑥 /𝑛 ≤ 𝜈 , ∀𝑥 , wit h equality in in v es ted
mar k ets, 𝑠 ∗
𝑥 > 0 . Because 𝜙 𝑥 (𝑠
𝑥 ) = 𝑝 𝑥 (𝑠
𝑥 ) + 𝑝 ′
𝑥 (𝑠
𝑥 )𝑠
𝑥 /𝑛 , t his is equiv alent t o
𝜙 𝑥 (𝑠
∗
𝑥 ) ≤ 𝜈 , ∀𝑥 (4.9)
wit h equality in in v es ted mar k ets. Since 𝑢 𝑥 (𝑠
𝑥 ) is a uni-v ariate differentiable (s trictl y) con-
ca v e function, 𝑢 ′
𝑥 (𝑠
𝑥 ) is (decreasing) non-increasing. Because 𝑝 𝑥 (𝑠
𝑥 ) is also (decreasing)
non-increasing, 𝜙 𝑥 (𝑠
𝑥 ) = 𝑢 ′
𝑥 (𝑠
𝑥 )/𝑛 + (1 − 1/𝑛)𝑝
𝑥 (𝑠
𝑥 ) is (decreasing) non-increasing. Define
in v erse function 𝜙 −1
𝑥 ∶ ℝ
≥0
→ ℝ
≥0
, so t hat 𝜙 −1
𝑥 (𝜈 ) = 0 f or 𝜈 > 𝜙 −1
𝑥 (0) . The function is
non-increasing (decreasing f or 𝜈 ≤ 𝜙 −1
𝑥 (0) ) and t he equilibrium satisfies:
𝑠 ∗
𝑥 = 𝜙 −1
𝑥 (𝜈 ), ∀𝑥 (4.10)
Since t o tal in v es tment equals t he number of pla y ers, ∑
𝑥 𝑠 𝑥 = 𝑛 , mar ginal pla y er pa y off in
in v es ted mar k ets 𝜈 is deter mined b y :
∑
𝑥 𝜙 −1
𝑥 (𝜈 ) = 𝑛 (4.11)
Because t he lef t-hand side of Equation 4.11 is decreasing f or 𝜈 ≤ 𝑚𝑎𝑥 𝑥 𝜙 −1
𝑥 (0) where t he
93
C hapter 4 Equilibrium of T axi Transpor t a tion
lef t -hand side is positiv e, t he equation giv es a unique solution 𝜈 . Thus Equation 4.10 giv es
a (unique) essentiall y unique s
∗
. F igure 4.1 sho w s t his process g r aphicall y . This pro v es
Proposition 6.
F igure 4.1: Deter mination of equilibrium. Mar ginal pla y er pa y off 𝜈 at equilibrium can be
deter mined from ∑
𝑥 𝑠 𝑥 (𝜈 ) = 𝑠 . Equilibrium allocation in each mar k et can t hen
be deter mined b y 𝑠 ∗
𝑥 = 𝑠 𝑥 (𝜈 ) .
The g r adient a djus tment process (Arro w and Hur wicz, 1960 ) is a heuris tic lear ning r ule
where pla y ers adjus t t heir s tr ategies accor ding t o t he local g r adient of t heir pa y off func-
tions, projected ont o t he tang ent cone of pla y er s tr ategy space. F or mall y , g r adient adjus t-
ment process is a dynamical sys tem:
d s
𝑖 d 𝑡 = 𝑃 𝑇 (𝑠
𝑖 )
∇
𝑖 𝑢 𝑖 ( s ), ∀𝑖 (4.12)
Here ∇
𝑖 deno tes t he g r adient wit h respect t o pla y er s tr ategy 𝑠 𝑖 , 𝑇 (𝑠
𝑖 ) is t he tang ent cone of
pla y er s tr ategy space 𝑆 𝑖 at point 𝑠 𝑖 , and 𝑃 is t he projection oper at or . F or all interior points
of t he pla y er s tr ategy space, 𝑃 𝑇 (𝑠
𝑖 )
is sim pl y t he centering matrix, 𝑀 1
= 𝐼 − 11
T
/𝑚 . T o
pro v e t hat t he dynamical sys tem is globall y asym p t o ticall y s table, w e sho w t hat 𝑉 ( s ) =
Φ( s
∗
) − Φ( s ) is a global L y apuno v function: a function t hat is positiv e-definite, contin-
uousl y differentiable, and has neg ativ e-definite time deriv ativ e. F rom Proposition 1 and
94
C hapter 4 Equilibrium of T axi Transpor t a tion
KKT t heorem, t he maximal points of t he po tential function Φ( s ) is deter mined t he same
w a y as Equation 4.9 . That is, t he maximal set of t he po tential function is identical t o t he
PSNE of multi-mar k et oligopol y . This means 𝑉 ( s ) > 0 at non-equilibrium points, so 𝑉 ( s )
is positiv e-definite. 𝑉 ( s ) is clea r l y continuousl y differentiable, and its time deriv ativ e
d 𝑉 ( s )
d 𝑡 = −∇ Φ( s ) ⋅
d s
d 𝑡 = −
𝑚 ∑
𝑥=1
𝑛 ∑
𝑖 =1
⎛
⎜
⎜
⎝
𝜕 𝑢 𝑖 𝑥 𝜕 𝑠 𝑖 𝑥 −
1
𝑚 𝑚 ∑
𝑦 =1
𝜕 𝑢 𝑖 𝑦 𝜕 𝑠 𝑖 𝑦 ⎞
⎟
⎟
⎠
𝜙 𝑥 = −𝑛
𝑚 ∑
𝑥=1
⎛
⎜
⎜
⎝
𝜙 𝑥 −
1
𝑚 𝑚 ∑
𝑦 =1
𝜙 𝑦 ⎞
⎟
⎟
⎠
𝜙 𝑥 = −𝑚𝑛 ( 𝜙 2
− 𝜙 2
)
Here 𝜙 = ∑
𝑚 𝑥=1
𝜙 𝑥 /𝑚 and 𝜙 2
= ∑
𝑚 𝑥=1
𝜙 2
𝑥 /𝑚 . Thus, 𝜙 2
− 𝜙 2
≥ 0 , wit h equality if and onl y
if 𝜙 𝑥 are all equal. F rom Equation 4.9 , w e can see t hat d 𝑉 / d 𝑡 ≤ 0 , wit h equality onl y at
equilibrium points s
∗
. W e ha v e t hus sho wn t hat 𝑉 ( s ) is a global L y apuno v function of t he
dynamical sys tem, which immediatel y im plies Proposition 7.
The s tability result in Proposition 7 is onl y intended t o sho w t hat under a sim ple and
plausible lear ning r ule, global asym p t o tic s tability of N ash equilibrium is possible in multi-
mar k et oligopol y so t hat t he equilibrium can be em piricall y obser v ed. The g r adient adjus t-
ment process adop ted in t his paper is no t meant t o be t he exact lear ning r ule used in real
lif e, which is har d t o deter mine. But com pared wit h Ba y esian or bes t-response lear ning
r ule s, it is less demanding on t he pla y ers as it does no t require com plete inf or mation of
t he g ame or long-ter m memor y of t he pla y ers. And e v en if some pla y ers adop t alter nativ e,
non-economic lear ning r ules, t he s tability of t he equilibrium ma y w ell be preser v ed. F or
exam p le, ne w driv ers ma y sim pl y choose imitativ e lear ning (R o t h and Ere v , 1995 ; F uden-
ber g and Le vine, 2009 ), or in o t her w or ds “f ollo w t he older driv ers”. In t his case t he N ash
equilibrium is s till t he s table f ocus as all pla y ers adop t t he same s tr ategy and t he r ational
95
C hapter 4 Equilibrium of T axi Transpor t a tion
pa y off-im p ro ving pla y ers adjus t t o t he equilibrium. By imitativ e lear ning, ne w driv ers sa v e
t h e possibl y long process of s tr ategy adjus tment and quickl y con v er g e t o t he equilibrium
s tr ategy . This allo w s t he equilibrium remain s table under an e v ol ving set of driv ers.
W e no te t hat t he pa y off in multi-mar k et oligopol y is no t s trictl y diagonall y conca v e,
so t he uniqueness and s tability results canno t f ollo w R osen ( 1965 ). But t he eig en v alues
of t he Jacobian ∇ ( d s / d 𝑡 ) are alw a ys neg ativ e, so local asym p t o tic s tability at t he equilib-
rium is guar anteed under g r adient dynamics wit h individual-specific adjus tment speeds.
W e also no te t hat unlik e t he Cour no t g ame, multi-mar k et oligopol y is no t an agg reg ate
g ame defined in Selten ( 1970 ) or later g ener alizations
5
, because pla y er s tr ategies are multi-
dimensional. Thus it does no t inherit t he s tability under discrete-time bes t-response dy -
namics. Multi-mar k et oligopol y is also no t a po tential g ame
6
and t hus does no t inherit
t h e g ener al dynamic s tability properties in Monderer and Shaple y ( 1996 ). Ins tead, w e pro-
vided a “po tential function” t hat is a global L y apuno v function f or t he g r adient dynamics.
4.3 Ma cr osc opic interpret a tion: thermod yn amic equilibir um
In t his section, w e inter pret t he N ash equilibrium of taxi driv ers as a t her modynamic
equilibrium. This es tablishes a macroscopic equilibrium where agg reg ate beha vior is per -
ceiv ed as tr ansport phenomenon built up from individual choices. W e firs t introduce t he
s tate v ariables and dynamic relations of t he t her modynamic sys tem wit h respect t o urban
tr ansportation. Later , w e com pare t he proposed t her modynamic po tential wit h t o tal taxi
re v e nue, and explain t heir t heir difference.
The r ationality t o build a bo tt om-up macroscopic equilibrium concep t is t hat, it is no t
f easible t o obser v e t he microscopic s tate of a tr ansportation sys tem, but regularity in mi-
5
A g ame is agg reg ativ e if e v er y pla y er’ s pa y off is a function of t he pla y er’ s o wn s tr ategy and an agg reg ate of
all pla y ers ’ s tr ategies.
6
A po tential g ame is a g ame where all pa y offs depend on one real-v alued function, called t he po tential func-
tion.
96
C hapter 4 Equilibrium of T axi Transpor t a tion
cros tates can be lear ned on a coarser scale b y t he population from t heir experiences. In
t h e case of taxi tr ansportation, alt hough taxi driv ers ha v e no kno w ledg e of t he locations or
des tinations of hailers, t he y can lear n from experience t he agg reg ate spatial dis tribution
of hailers at different time of da y . So does t his lear ning process appl y t o hailers, who also
ha v e no kno w ledg e of free taxis ’ locations but ha v e a sense of t he suppl y r ate on t he current
s treet segment.
Initiall y a ne w driv er has no kno w ledg e of t he sys tem, so t he cruising s tr at egy 𝑠 𝑖 𝑥 could
be arbitr ar y . Giv en hailer demand wit h im patience {𝜇
𝑑𝑥𝑦 , 𝜇 𝑡𝑥𝑦 } and tr affic v , bo t h seen as
fix ed at a specific time of da y , t he driv er will lear n t he demand and tr affic dis tribution
o v e r time. The dynamics of taxi driv ers im pl y t hat, activ e driv ers will adjus t t he spatial
dis tribution of t heir virtual ser vice time 𝑠 𝑖 𝑥 so t hat all s treet segments being cr uised ha v e
equal mar ginal income 𝜕 𝜋 𝑖 𝑥 /𝜕 𝑠 𝑖 𝑥 . W e ha v e sho wn t hat f or an arbitr ar y number of activ e
taxis 𝑛 , t here are N ash equilibria which giv e t he same agg reg ate allocation t hat maximizes
t he po tential function Φ(𝑠) . Thus, holding t he demand and tr affic conditions, an equilib-
rium will e v entuall y be reached o v er a long time, and t he dis tribution of agg reg ate virtual
ser v ice time o v er s treet segments will become s tationar y .
F or an urban sys tem inter acting wit h its surroundings t o approach dynamic equilib-
rium, se v er al conditions need t o hold on t he built en vironment, t he population, and t he
surroundings. Since t he tr ansportation infr as tr ucture e v ol v es on a much long er time scale
t ha n population tr a v el beha vior , it can be seen as cons tant in a matter of da ys. The pop-
ulation wit hin t his area could be g ener all y divided int o residents and visit ors: residents
s ta y wit hin t he area f or an extended period; visit ors enter and lea v e t he area f or a short
dur ation. When population com position s ta ys cons tant at a specified time scale, t he urban
tr ansportation sys tem will approach a dynamic equilibrium.
R eg ar d t o tal ser vice time 𝑠 , which equals t he number of driv ers in ser vice, as t o tal en-
er gy of t he taxi tr ansportation sys tem. R eg ar d t he po tential function Φ of multi-mar k et
97
C hapter 4 Equilibrium of T axi Transpor t a tion
oligopol y as entrop y . And reg ar d t he reciprocal of equilibrium mar ginal driv er re v enue,
𝜓 = 1/𝜙 , as tem per ature. 𝑠 , 𝜓 , and Φ are all s tate v ariables of t he taxi sys tem at equilibrium
giv en en vironment condition ℰ .
Being a s tate v ariable and intensiv e property , 𝜓 is t he driving f orce of t he tr ansport of
ser vice time 𝑠 o v er t he s treet segments. As w e ha v e pro v ed ear lier , t he g r adient dynamics of
multi-mar k et oligopol y alw a ys increases t he po tential function Φ( s ) , which is maximized
at equilibrium. When tw o taxi sys tems at equilibrium are put int o contact wit h an interf ace
per meable t o t he tr ansf er of taxi ser vice time, 𝑠 will flo w from t he sys tem wit h higher 𝜓 t o
t he one wit h lo w er 𝜓 . A t equilibrium, 𝜓 is homog eneous across all searched segments. In
summar y , w e can mak e t he f ollo wing s tatements of t her modynamics:
Zeroth Law T w o taxi sys tems in contact ha v e t he same equilibrium mar ginal driv er re v -
enue. Equiv alentl y ,
𝜓 1
= 𝜓 2
First Law T axi tr ansportation is t he tr ansf er process of t o tal ser vice time 𝑠 , which is a con-
ser v ed quantity . Equiv alentl y ,
d 𝑠 = ∑
𝑥∈𝐸
d 𝑠 𝑥 Second Law U nder fix ed taxi demand and tr affic s tate, a closed taxi sys tem maximizes its
entrop y Φ . Equiv alentl y ,
d Φ ≥
𝛿 𝑠 𝜓 The contact equilibrium defines equiv alent classes of taxi equilibrium, which are s trictl y
t o tall y or dered b y s tate v ariable 𝜓 . The manif old of taxi equilibrium is t hus one-dimensional,
par ameterized b y 𝜓 , and an y o t her s tate v ariable mus t depend on it. This means t hat s tate
space (Φ, 𝑠, 𝜓 ) ∣ ℰ has onl y one deg ree of freedom, and t his dependency is t he cons titu-
tiv e relation of t he taxi sys tem giv en en vironment condition ℰ . W riting t he cons titutiv e
98
C hapter 4 Equilibrium of T axi Transpor t a tion
relation explicitl y as 𝜓 (𝑠) ∣ ℰ , or equiv alentl y 𝜙(𝑠) ∣ ℰ , our discussion in Section 4.5.2
has sho wn ho w t his cons titutiv e relation can be measured from obser v ational data under
certain conditions. R earr anging t he exact differential of 𝑠(Φ) ∣ ℰ giv es t he fundamental
t h er modynamic relation of taxi equilibrium:
d 𝑠 = 𝜓 d Φ (4.13)
Our discussion in Section 4.5.4 can be seen as an exam ple of contact equilibrium, where
t he ne w taxi sys tem (g reen cab) is g eog r aphicall y res tricted t o pickup outside core Man-
hattan. The increased taxi suppl y out of core Manhattan driv es do wn 𝜙 and t hus r aises
tem per ature 𝜓 , f orcing some y ello w cabs int o core Manhattan. The ne w equilibrium is
reached when tem per ature 𝜓 across t he boundar y are t he same.
4.4 Efficien cy : the pr oblem of social c os t
W e no tice t hat in multi-mar k et oligopol y t he t o tal pa y off 𝑢( s ) = ∑
𝑖 ∈𝑁
𝑢 𝑖 ≠ Φ( s ) , which
means t o tal pa y off is g ener all y no t maximized in N ash equilibrium, t hus no t sociall y op-
timal. In f act, if t o tal pa y off is maximized, t hen 𝜕 𝑢 𝑥 /𝜕 𝑠 𝑥 ≥ 𝜕 𝑢 𝑦 /𝜕 𝑠 𝑦 , ∀𝑥 , 𝑦 ∈ 𝐸, 𝑠 𝑥 > 0 ,
which means mar ginal pa y off are t he same f or all in v es ted mar k ets. Com pare wit h Equa-
tion 4.9 and t he definition of 𝜙 𝑥 (𝑠
𝑥 ) , a w eighted a v er ag e of mar ginal and a v er ag e pa y off
is balanced ins tead. W it h 𝑛 ≫ 1 in t he case of NY C taxi sys tem, w e ha v e 𝜙 ≈ 𝑢 𝑥 /𝑠
𝑥 . So at
equilibrium t he a v er ag e segment income per ser vice time are effectiv el y t he same f or all
searched segments.
This is similar t o t he Cour no t g ame. The t o tal pa y off in t he Cour no t g ame is 𝑢(𝑞) =
∑
𝑖 ∈𝑁
𝑢 𝑖 = 𝑝(𝑞)𝑞 − 𝑐 𝑞 . Assuming 𝑝(𝑞) differentiable, t he social op timum is 𝑢 ∗
= (𝑝(𝑞
∗
) − 𝑐 )𝑞
∗
,
where 𝑞 ∗
satisfies 𝑝 ′
(𝑞
∗
)𝑞
∗
+ 𝑝(𝑞
∗
) = 𝑐 . The N ash equilibrium is 𝑞 𝑖 = 𝑞 †
/𝑛, ∀𝑖 ∈ 𝑁 , where
𝑞 †
satisfies 𝑝 ′
(𝑞
†
)𝑞
†
/𝑛 + 𝑝(𝑞
†
) = 𝑐 . This mak es 𝑞 †
> 𝑞 ∗
and 𝑢(𝑞
†
) < 𝑢(𝑞
∗
) , so t he N ash
99
C hapter 4 Equilibrium of T axi Transpor t a tion
equilibrium is no t social op timal, and decreases furt her as t he number of pla y er increases.
Ho w e v er , t he N ash equilibrium of multi-mar k et oligopol y is sociall y op timal if mar k et
pa y offs are po w er functions of t he same or der : 𝑢 𝑥 (𝑠
𝑥 ) = 𝑎 𝑥 𝑠 𝑝 𝑥 , 𝑎 𝑥 > 0, 𝑝 ∈ (0, 1) . In t his case
t h e t o tal pa y off 𝑢 = ∑
𝑥∈𝐸
𝑎 𝑥 𝑠 𝑝 𝑥 and pla y er pa y off 𝑢 𝑖 = ∑
𝑥∈𝐸
𝑎 𝑥 𝑠 𝑝−1
𝑥 𝑠 𝑖 𝑥 . A t social equilibrium,
𝜕 𝑢 𝑥 /𝜕 𝑠 𝑥 = 𝑎 𝑥 𝑝𝑠 𝑝−1
𝑥 is a cons tant f or all mar k ets 𝑥 ∈ 𝐸 . Since ∑
𝑥∈𝐸
𝑠 𝑥 = ∑
𝑖 ∈𝑁
∑
𝑥∈𝐸
𝑠 𝑖 𝑥 = 𝑛 ,
social op timal s tr ategy is 𝑠 ∗
𝑥 = 𝑛𝑎 1/(1−𝑝)
𝑥 / ∑
𝑦 ∈𝐸
𝑎 1/(1−𝑝)
𝑦 , ∀𝑥 ∈ 𝐸 . A t N ash equilibrium, f or
all pla y ers 𝑖 ∈ 𝑁 , let 𝑢 𝑖 𝑥 = 𝑢 𝑥 𝑠 𝑖 𝑥 /𝑠
𝑥 , t hen 𝜕 𝑢 𝑖 𝑥 /𝜕 𝑠 𝑖 𝑥 = 𝑎 𝑥 ((𝑝 − 1)𝑠
𝑝−2
𝑥 𝑠 𝑖 𝑥 + 𝑠 𝑝−1
𝑥 ) is a con-
s tant f or all mar k ets 𝑥 ∈ 𝐸 . This means ∑
𝑖 ∈𝐸
𝜕 𝑢 𝑖 𝑥 /𝜕 𝑠 𝑖 𝑥 = (𝑝 − 1 + 𝑛)𝑎
𝑥 𝑠 𝑝−1
𝑥 is a cons tant f or all
mar k ets 𝑥 ∈ 𝐸 , which giv es t he same agg reg ate s tr ategy 𝑠 †
𝑥 = 𝑛𝑎 1/(1−𝑝)
𝑥 / ∑
𝑦 ∈𝐸
𝑎 1/(1−𝑝)
𝑦 , ∀𝑥 ∈
𝐸 , so t he N ash equilibrium is social op timal. Use t he condition ag ain, w e find N ash equi-
librium 𝑠 †
𝑖 𝑥 = 𝑠 †
𝑥 /𝑛, ∀𝑖 ∈ 𝑁 , 𝑥 ∈ 𝐸 .
This phenomenon of difference betw een cooper ativ e and com petitiv e decisions has been
s tudied f or a long time under different names. The concep t of economic inefficiency ref ers
t o a situation where t o tal income, or social w ealt h, is no t maximized, see Mill ( 1859 ) and
Sidgwick ( 1883 ). The problem of social cos t is t he div er g ence betw een priv ate and social
cos ts or v alue, see t he discussion betw een Pigou ( 1920 ) and Knight ( 1924 ). This discussion
br a nch int o t he concep t of exter nal effect, originated b y Meade ( 1952 ). Independentl y , Gor -
don ( 1954 ) proposed rent dissipation, where maximum rent is no t realized at equilibrium.
Mar k et f ailure is ano t her ter minology of t he same phenomenon, see Bat or ( 1958 ) f or exam-
ple. Coase ( 1960 ) dismissed t he discussion of social cos t, calling t he reduced social income
as tr ansaction cos t. Exter nality e v ol v ed out of exter nal effect, whose proponents typicall y
call f or go v er nment regulation, see O. A . Da vis and Whins t on ( 1962 ). Ins titution cos t is a
g ener alization of tr ansaction cos t, see Cheung ( 1998 ). A recent de v elopment in algorit hmic
g ame t heor y uses tw o ter ms f or t his inefficiency of equilibria: price of anarch y (K outsou-
pias and P apadimitriou, 1999 ; R oughg ar den, 2002 ), and price of s tability .
Despite t he v arious ter minologies, t he essence of t he problem is t he same: when individ-
100
C hapter 4 Equilibrium of T axi Transpor t a tion
uals do no t ha v e incentiv e in maximizing t he t o tal pa y off, equilibrium natur all y will differ
from t he op timum set, which b y definition results in less t o tal pa y off. Here I propose t he
main tak ea w a y f or t he case of multi-mar k et oligopol y :
Theorem If a property is heterog eneous in productivity , t he o wner canno t obtain t he op-
timal rent b y leasing t o multiple ten ants wit hout contr acting on t heir allocation of
effort.
4.5 Empiric al resul ts
4.5.1 Sp a tial equilibrium
T o v alidate t hat taxi driv ers f ollo w t he t heoretical equilibrium, w e proceed in tw o parts.
F irs t , t he s tr ategy profile at equilibrium is symmetric, which means t hat all driv ers use
t h e same s tr ategy . Second, giv en driv ers use t he same s tr ategy , unif or m mar ginal driv er
re v e nue across s treet segments means t hat 𝜙 𝑥 is t he same on all segments.
Alt hough driv er s tr ategy , t he spatial dis tribution of ser vice time, is no t directl y obser v ed,
it is proportional t o driv er pickup probability on each segment. If all driv ers use t he same
s tr ategy , t he pickup probability dis tribution across segments of each driv er shall be t he
same as t hat of t he o v er all dis tribution. Then each driv er’ s actual pickups shall be a sam-
ple of t he corresponding categorical r andom v ariable. Since t here are t housands of s treet
segments, pickup recor ds of each driv er is no t enough t o tes t t he probability model. W e
partition t he segments int o 10 equi-probable g roups, so pickup counts in t hese g roups
shall be a multinomial r andom v ariable wit h t he same probability f or each g roup. Driv ers ’
pickup counts in t hese g roups can be tes ted b y a corrected log lik elihood r atio of multino-
mial dis tributions (Smit h et al., 1981 ). F or each driv er , t he pickup counts are nor malized
int o a probability v ect or x . And w e consider t he de viation from t he equi-probable v ect or ,
x
′
= x − 1 /10 , lar g e if its 𝐿1 -nor m ex ceeds 0.3. Onl y a small fr action of driv ers ha v e s ta-
101
C hapter 4 Equilibrium of T axi Transpor t a tion
tis ticall y significant lar g e de viations, see F ig. 4.2 A . The t hreshold f or lar g e de viation is
arbitr ar y , but t he result sho w s t hat mos t driv ers use similar s tr ategies.
F igure 4.2: V alidation of equilibrium, using trip recor ds in Spring 2011 and Spring 2012.
(A) Size and s tatis tical significance of driv er de viation from a v er ag e s tr ategy in
T ue- Thu PM peak s, 6pm-10pm. 3.66% of all driv ers ha v e s tatis ticall y significant
( 𝑝 > 0.05 ) lar g e de viations ( || x
′
||
1
> 0.3 ). (B) Correlation betw een search time
and income on s treet segments ( 𝑅 2
= 0.85 ), bo t h in log scale and s tandar dized,
f or Mon-F ri 6pm-7pm. If t he tw o quantities are proportional, mar ginal income
on s treet segments are unif or m.
T o sho w t hat mar ginal driv er re v enue on all s treet segments are equilibr ated, w e no te
t h at 𝜙 𝑥 ≈ 𝑢 𝑥 /𝑠
𝑥 , because at an y moment t he number of taxi driv ers in ser vice in Manhattan
is in t he t housands. So it suffices t o sho w t hat re v enue originated on each segment 𝑢 𝑥 is
proportional t o t o tal driv er ser vice time attributable t o t he segment 𝑠 𝑥 , which is t he sum
of search time 𝑡 𝑠𝑥 and trip time 𝑡 𝑝𝑥 per unit time. Because t he ma jority of taxi trips are
metered, which is calculated from trip dis tance and time in slo w tr affic, driv er re v enue
from each trip is highl y correlated t o trip dur ation reg ar dless of driv er s tr ategy , especiall y
when tr affic speeds are hold s tationar y . T o a v oid t he influence of t his f act, consider trip
time is a linear function of trip re v enue, t hen 𝑢 𝑥 ∝ 𝑠 𝑥 is equiv alent t o 𝑢 𝑥 ∝ 𝑡 𝑠𝑥 , and w e tr y
102
C hapter 4 Equilibrium of T axi Transpor t a tion
t o sho w t he latter . Because search routes are no t recor ded in t he trip recor ds, w e tak e trip
recor ds betw een 6pm and 7pm on w eekda ys in spring, and es timate taxi routes betw een
trips b y shortes t dis tance routing. W e consider t his approach accep table be cause during
t h e selected hours, tr affic is roughl y at a unif or m cong es ted speed while a v er ag e taxi search
time is t he shortes t, so route de viation from t he shortes t pat h is unlik el y . The correlation
betw een re v enue and es timated search time on s treet segments are reasonabl y high, wit h
𝑅 2
= 0.85 , see F ig. 4.2 B. Because shortes t pat h routing pro vides a single route f or trips
wit h t he same origin and des tination, es timated search time ma y be concentr ated t o a f e w
s treet segments, which w eak ens t he actual correlation.
4.5.2 D yn amic equilibrium
As en vironment condition ℰ v aries o v er times of a da y , taxi equilibrium will also v ar y . If
taxi driv ers are free t o choose when t o w or k and are indifferent about w or king at different
times of a da y , taxi suppl y will adjus t so t hat at equilibrium t he a v er ag e driv er income
is t he same t hroughout a da y . T o v erify t his, w e examine t he tr a ject or y of a v er ag e driv er
re v e nue and number of driv ers t hroughout a typical w eekda y , sho wn in F ig. 4.3 . A v er ag e
driv er re v enues during 8am-4pm and 6pm-3am center around $35/hour and $30/hour
respectiv el y , and are cons tant in t he sense t hat its o v er all v ariation is about t he same as its
short-ter m v ariation. The difference betw een a v er ag e driv er re v enue f or t hese tw o periods
can be explained b y tw o f act ors. F irs t, t he t o tal number of taxis is limited and no t all is
a v ailable f or t he night shif t, so no t all driv ers who w ould lik e t o w or k at night can g et a
taxi. Second, t he lease r ate f or da y shif ts is less t han t hose of night shif ts, so t he difference in
a v er ag e driv er income betw een t he tw o periods is less t han t hat of a v er ag e driv er re v enue.
During 4pm-6pm mos t double-shif ted taxis chang e driv ers, which means suppl y decisions
during t his period is no t up t o t he driv ers, so t he a v er ag e driv er re v enue is no t cons tant.
During 3a m-6am v er y f e w driv ers are at w or k , and t he high a v er ag e driv er re v enue jus tifies
103
C hapter 4 Equilibrium of T axi Transpor t a tion
5 10 15 17 19 24 5
25
30
35
40
45
50
Average driver revenue, $/hour
Hour
Average number of taxis
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Average driver revenue, $/hour
Number of drivers
0 2000 4000 6000 8000 10000
25
30
35
40
45
50
F igure 4.3: N umber of driv ers and a v er ag e driv er income t hroughout a typical W ednesda y
in spring, 2011-2012. (U pper) T ime series. (Lo w er) T r a ject or y . Each do t repre-
sents one minute, a v er ag ed o v er all obser v ations and colored b y t he hour . T ext
labels mar k hours o f a da y , from 0 t o 23, positioned at t he middle of t he hour .
t h e cos t of w or king when mos t people pref er t o be sleeping. During 6am-8am mos t da y
shif t driv ers s tart w or king, and alt hough t he a v er ag e driv er re v enue is no t cons tant, it
104
C hapter 4 Equilibrium of T axi Transpor t a tion
s tabilizes as more driv ers become activ e.
In contr as t t o t he equilibr ation of a v er ag e driv er income o v er time, giv en en vironment
condition ℰ , equilibrium mar ginal segment re v enue is a decreasing function of t he number
of driv ers: 𝜙(𝑠) ∣ ℰ . This relation is har d t o measure wit hout controlled experiment, but
it is reflected in t he obser v ational data if t he number of driv ers is f orced t o chang e much
f as t er t han t he en vironment does, such as during shif t tr ansition. N o te t hat equilibrium
mar ginal segment re v enue and a v er ag e driv er re v enue are appro ximatel y t he same: 𝜙 ≈
∑
𝑥 𝑢 𝑥 / ∑
𝑥 𝑠 𝑥 , because 𝜙 𝑥 ≈ 𝑢 𝑥 /𝑠
𝑥 . R eusing F ig. 4.3 , t he do wn w ar d trend in 5pm-6pm
reflects 𝜙(𝑠) f or t hat time of da y , when people lea v e w or k and taxis retur n f or t he night
shif t.
4.5.3 Driver learnin g
It is natur al t o ask if driv ers lear n t o use t he same s tr ategy resulting in spatiall y unif or m
mar ginal re v enue. W e use driv ers ’ firs t appear ance in trip recor ds t o measure t heir o v er -
all experience, and t he number of trips driv ers made during a chosen time slo t t o measure
t h eir experience wit h t he specific situation. F ig. 4.4 sho w s t hat s tr ategy de viation decreases
wit h driv er experience. A v er ag e driv er de viation con v er g es wit hin about one y ear of driv -
ing, while decreases mono t onicall y wit h situation-specific experience.
4.5.4 Policy imp a ct on equilibrium
Chang e in taxi regulation affects t he equilibrium. On 2013-08-08, NY C TL C launched S treet
Hail Liv er y , kno wn as g reen cabs, which are allo w ed t o pick up s treet-hail passeng ers out-
side core Manhattan, defined as sou t h of W es t 110t h S treet and Eas t 96t h S treet. This g r ad-
uall y increased suppl y of s treet-hail ser vice be y ond core Manhattan, decreasing mar ginal
driv er re v enue on segments t herein. Equilibrium demands t hat mar ginal driv er re v enue
on segments wit hin core Manhattan should also decrease t o t he same le v el, which im plies
105
C hapter 4 Equilibrium of T axi Transpor t a tion
F igure 4.4: Driv er lear ns equilibrium. Using t he same trip recor ds as F ig. 2A . (U pper) A v -
er ag e driv er de viation decreases wit h t heir y ears of driving. Driv ers s tarted be-
f ore data collection are clus tered near 2009. R ed cur v e sho w s local reg ression.
Dashed line sho w s a v er ag e de viation of driv ers s tarted betw een mid-2009 and
2011. (Lo w er) A v er ag e driv er de viation decreases wit h number of trips made.
more suppl y of y ello w cabs in core Manhattan where t he y ha v e ex clusiv e rights t o ser vice.
W e com pare t he time-series of pickup percentag e in t he region bor dering core Manhattan
in 2012 and 2013, see F ig. 4.5 . Ex cluding irregularity due t o Hurricane Sandy and holi-
da ys, t he percentag e is s table in t he later mont hs of bo t h y ears, reflecting a robus t decline
in y ello w cab suppl y be y ond core Manhattan.
4.6 Discussion
4.6.1 A thermod yn amic model of urb an transpor t a tion
As w e’ v e sho wn a t her modynamic inter pretation of taxi driv er beha vior , one ma y be tem p ted
t o build a g ener al t her modynamics model f or urban tr ansportation. Here I’ll comment on
t h e f easibility of such a model.
T o adop t t he ener gy concep t of t her modynamics, w e ma y assign a tr a v el ener gy t o each
individual, analogous t o chemical ener gy of molecules. Mos t of t he time individuals s ta y
106
C hapter 4 Equilibrium of T axi Transpor t a tion
0 50 100 150
1.5
2.0
2.5
3.0
Percent of pickups bordering core Manhattan
Days since July 1
2012
2013
F igure 4.5: Equilibrium shif t af ter g reen cab launch. Solid cur v es are 7-da y rolling pickup
probability in t he region bor dering core Manhat tan, wit h 90% propability in-
ter v al. This probability slightl y reduced af ter 2012 f are r aise (red line), g reatl y
increased during Hurricane Sandy (shaded area), and moder atel y increased
during Thank sgiving (v ertical lines) and Chris tmas.
at t heir current locations, which is considered t heir base s tate and ha v e zero tr a v el ener gy .
Once t he y need t o tr a v el, t heir tr a v el ener gies become g reater t han zero and are at ex cited
s tates. Individuals wit h tr a v el needs ma y retur n t o t heir base s tates t hrough an y of t he
tr ansportation modes. If w e g roup individuals b y t heir tr ansportation mode choice, t he
dynamics of urban tr ansportation can be modeled on a s tate diag r am sho wn in F igure 4.6 .
In t his model, at an y moment, each individual in an urban area is at one of t he specified
s tates, where s tate tr ansf er is ins tantaneous. The tr a v el ener gy of an urban sys tem is t he
t o tal tr a v el ener gy of t he population wit hin t his urban area, a t her modynamic po tential
analogous t o Gibbs free ener gy (Gibbs, 1876 ), det er mined b y its population com position
and t he tr a v el po tentials of each g roup.
In Meier ( 1968 ), t he metropolis is seen as a tr ansaction-maximizing sys tem where popu-
lation density s timulates tr ansactions betw een individual act ors. As sho wn here, t he rent
maximization of taxi driv ers lead t o t he maximization of t o tal rent of t he city’ s taxi indus-
107
C hapter 4 Equilibrium of T axi Transpor t a tion
Staying
D B T H
t
F igure 4.6: S tate Diag r am of U rban T r ansportation. Individuals ma y tr ansf er from base
s tate (s ta ying) t o high ener gy s tates, and back t o t he base s tate. D, decide t o
driv e; B, decide t o bik e; T , decide t o tak e public tr ansit ; H, decide t o hail a taxi;
t, tr ansition s tate.
tr y . This analogy promises a g ener alized model of t he whole urban tr ansportation sys tem
and e v en o t her aspects of urban sys tems.
108
C h apter 5
Efficien cy of NY C T axi Indus tr y
In t his chap ter , w e s tudy t he s tr ucture of N e w Y or k City taxi indus tr y . W e propose a g ame
model t o cap ture t he rele v ant tr ansportation ins titutions, and design an efficient mecha-
nism f or taxi tr ansportation, measured b y social v alue. W e also address some issues of
im plementing t he efficient mechanism.
5.1 NY C c ar indus tries
TL C regulates six car indus tries in NY C:
1. T axicab: T axicab is a go v er nment-regulated indus tr y wit h licensed driv ers non-cooper ativ el y
seeking f or profit.
2. F or -hire v ehicles (FHV): Public and TL C-regulated FHVs are no t com peting in t he
same mar k et wit h taxis.
a) Liv er y : Liv eries ha v e similar ser vice le v el wit h y ello w cabs, but are prearr ang ed
b y phone onl y ;
b) Black car : Black cars ser v es mos tl y cor por ate c lients;
c) L uxur y limousine: L uxur y limousines ser v e t he luxur y mar k et.
109
C hapter 5 Efficien cy of NY C T axi Indus tr y
3. P ar atr ansit v ehicle (ambulette): Healt hcare f acility commute f or t he disabled.
1
4. Commuter v an: F or passeng ers along fix ed routes .
2
Bo t h y ello w cabs and g reen cabs are ref erred t o as taxicabs b y TL C. P ar atr ansit and com-
muter v ans h a v e negligible ser vice. Priv ate car ser vices, dominated b y Uber , slo w l y pick s
up de spite TL C sanction.
5.1.1 T axic abs
T axis mak e up about 45% of all v ehicles (tr affic v olume) in Eas t and W es t Midt o wn (taxi
anal y sis zones); taxis and black cars t og et her mak e about 60% of t r affic in t he same area.
Through-mo ving taxis on 7t h A v e (Sout hbound) are 84% occupied, while cross-t o wn (on
S t reets) taxi occupancy is 55%.
3
NY C DO T es timated a v er ag e m ph of tr affic speeds w eek -
da ys 7 am - 8 pm in Sep-Oct 2009 using taxi trips wit h o v er 80% mileag e in indicated
directions: (F ield Sur v e y in W es t Midt o wn co v ers 23r d-59t h S t, 1.8 mile; 5t h-11t h A v e, 1
mile.)
T able 5.1: T r affic spee ds in 2009 Sep-Oct, w eekda ys 7am-8pm
R egion nort h sout h eas t w es t in km/h
Eas t Midt o wn (e as t of 5t h A v e) 9.0 9.0 7.0 5.5 14.4, 14.4; 11.2, 8.8
W es t Midt o wn (5t h -9t h A v e) 8.0 7.4 5.5 6.5 12.8, 11.8; 8.8, 10.4
F ield Sur v e y in W e s t Midt o wn† 9.4 8.9 6.2 7.0 15, 14.2; 9.9, 11.2
Buses (6t h A v e a nd 7t h A v e) 5.9 4.7 - - 9.5, 7.5; -, -
Medallion taxi are s treet hailed. E-hail (mobile app) pilo t prog r am s tarted in 2013, but
e v en in late 2013 onl y 0.3% y ello w trips are reques ted from t he mobile app.
1
P ar atr ansit (200 pro viders, 2k v ehicles). http://www.nyc.gov/html/tlc/html/industry/
paratransit_base.shtml
2
Commuter V an A ut hority . (500 v ehicles) http://www.nyc.gov/html/tlc/html/industry/
commuter_van_authority.shtml
3
NY C DO T 2010 Broadw a y R eport. http://www.nyc.gov/html/dot/downloads/pdf/
broadway_report_final2010_web2.pdf
110
C hapter 5 Efficien cy of NY C T axi Indus tr y
TL C pro vides inf og r aphics
4
on t he TPEP sys tem
5
, and on percentag e of all y ello w taxis
on t he road and occupied during a w eek
6
; and ho w passeng ers arriv e and depart from JFK
and L G A
7
. A t t he PM r ush hour , f e w er taxis are on t he road as taxis chang e driv ers f or t he
e v ening shif t ; near l y tw o-t hir ds of t he taxis lef t on t he road betw een 4-6pm are occupied.
TL C irregular l y releases reports f or t he public, such as its T axicab F act Book s.
8
Of t he
13237 taxis, taxis in ser vice is at 7k hour l y a v er ag e, 10k in peak hours: Monda y (s till higher
t h an Sunda y) AM shif ts, 72%, PM shif ts, 77%; T uesda y t hrough Thur sda y AM shif ts, 80-
82%, PM shif ts, 81-85%; F rida y AM shif ts, 79%, PM shif ts, 85% (ends later); Satur da y AM
shif t s, 71%, PM shif ts, 82% (ends later); Sunda y bo t h shif ts, 67%. Mini-fleet medallions
mus t oper ate tw o shif ts per da y , typicall y around 6:30-7:30AM and 5:00-6:00PM; a typi-
cal shif t is 9.5 hours; Man y independent medallion o wners choose t o oper ate tw o shif ts
b y leasing out an yw a y ; Onl y around 10% of all medallions oper ate f or one dail y shif t on
a consis tent basis. On w eekda ys, number of activ e taxis peak s around 8pm, at 11k; bo t-
t oms out around 4am, at 2k; Y ello w taxi dail y trips during Dec 2008 - N o v 2013 is about
485K/da y . T op da ys include December 11, 2009, a F rida y ; F ebr uar y 12, 2011 and F ebr uar y
11 2012, Satur da ys bef ore V alentine’ s Da y . A v er ag e dail y taxi usag e is typicall y highes t in
t h e spring mont hs (F eb, Mar , Apr) and lo w es t in t he summer mont hs (Jul, A ug, Sep). Da ys
wit h f e w er t han 350,000 trips can be explained b y eit her holida ys or ma jor w eat her e v ents:
N e w Y ear’ s Da y , Memorial Da y , Independence Da y , Labor Da y , Thank sgiving, Chris t-
mas; Blizzar ds, 2011 Hurricane Irene, 2012 Hurricane Sandy . As of y ello w taxi pickup and
dropoff trends b y boro, Manhattan has 90.3% pick -ups, mos tl y belo w 96t h S treet), JFK and
L G A (3.5%), Brookl yn (3.1%), Queens (1.5%), Bronx (0.9%), and S taten Island (0.8%). The
Brookl yn share of pick -ups reaches its peak s o v er night, usuall y betw een 10PM and 5AM;
4
http://nyctaxi.tumblr.com/
5
http://nyctaxi.tumblr.com/image/80606190306
6
http://nyctaxi.tumblr.com/image/79177508825
7
http://nyctaxi.tumblr.com/image/82004161268
8
2014 T axicab F act Book. http://www.nyc.gov/html/tlc/downloads/pdf/2014_taxicab_
fact_book.pdf
111
C hapter 5 Efficien cy of NY C T axi Indus tr y
drop-offs in Brookl yn peak in ear l y mor nings betw een 2am and 5am (about 18% of all trips
on Satur da ys at 4:45AM).The Queens share of pick -ups reaches its peak s betw een 4:30am
and 6am, lik el y due t o t he f act t hat mos t taxi g ar ag es are located in N ort hw es ter n Queens;
drop-off in Queens peak s at similar times wit h Brookl yn. A t t he air ports, dail y peak s occur
in t he AM around 5:30am and in t he e v ening around 4:30pm (4% t o 7% of all pickups).
Hour l y re v enue r ang es from $44 (6pm-10pm) t o $26 (3am), based on 2013 TPEP data. N et
hour l y re v enue (deducting es timated amortized hour l y v ehicle lease pa yments and g as
expenses) r ang es from $31 (6pm-10pm w eekda ys) t o lo w $15 (3am W ednesda y). In com-
parison, bus driv ers ’ a v er ag e hour l y income is about $21, ex cluding em plo y er -sponsored
benefits, accor ding t o Bureau of Labor S tatis tics. As of t he demog r aphics of t he 50k Medal-
lion driv ers, 45.6% are from Bangladesh, P akis tan and India; Ov er 10,250 driv ers from
Bangladesh; 5,850 from P akis tan; and 2660 from US and associated territ ories. 43% liv e
in Queens, 23% in Brookl yn, 13% in Bronx. 99% are male, 536 are f emale. The demog r aph-
ics of y ello w cab passeng ers ( 236m/y , 1.35/trip) are much closer socio-economicall y t o
Manhattanites, y ound and affluent.
A ccor ding t o t he 2006 T axicab F act Book , liv e miles (miles wit h a passeng er) percentag e
s tables around 61% during 2002-2006; so d riv ers don ’ t cr uise long dis tances. P asseng ers
said t hat driv ers do no t w ant t o dead-head back from an outer -borough des tination, t he y
w ant t o a v oid becoming s tuck in r ush hour bridg e or tunnel tr affic, or t he y belie v e t hat a
trip up t o wn will be more profitable t han a passeng er’ s desired trip do wnt o wn. When pas-
seng ers are plentiful, (at leas t some) driv ers decide t o be more choosy about which t rips t o
tak e, and as a result, a lar g er number of passeng ers are refused ser vice. 39% of individual
o w ner -driv en cabs w ere also leased f or a second shif t in 2005, up from about 10% in 1992.
TL C mandated t hat r adios be mo v ed from medallion t o non-medallion cars. The tr ansi-
tion of r adios out of y ello w cabs w as com pleted b y March 1987. (Separ ation of hailing and
prearr ang ement mar k ets.) Lease manag ers shif t t o w ar d long-ter m leasing in t he 2000s. A c-
112
C hapter 5 Efficien cy of NY C T axi Indus tr y
counting f or bo t h cash income and t he v alue of t hese benefits, lease driv ers ear ned less in
1986 t han did commission driv ers in 1981, af ter adjus ting f or inflation; W it h incomes f alling
and t hen s tagnant, taxi driving became a tr ansient job filled b y an e v er -changing mix of
immig r ants from o v er 80 count ries. The City g ained S tate Legislativ e appro v al t o auction
400 ne w medallions as a mone y -r aising measure in t he ear l y 1990s. (Since t he go v er nment
controls medallion licensing right, a city’ s taxi indus tr y is t he priv ate property of its go v -
er n ment. Issuing medallion is t hus a fiscal measure.) The 400 ne w medallions w ere issued
t h rough t hree set s of auctions in 1996 and 1997. A second set of auctions issued 900 ne w
medallions from 2004 t o 2006. (Ma y or Bloomber g issued ano t her 150 medallions b y 2008:
11787 + 400 + 900 + 150 = 13237) The e v olution of NY C FHV indus tr y : taxi firs t emer g ed;
liv eries appeared when demand reco v ers tw o decades af ter WWII; black car differentiated
from individual medallions due t o mandated separ ation of r atio prearr anging de vice from
medallion taxicabs in 1980s. (S treet-hail liv er y emer g ed as a leg alization-regulation deal
f or ”gypsy cab” liv eries.)
A ccor ding t o t he 2016 T axicab F act Book , emer ging car ser vices lik e Uber and L yf t are
treated as black cars and ref erred t o as app-based FHV com panies, t o dis tinguish from
tr aditional FHV com panies. There mobile apps are called E-Dispatch apps, t o dis tinguish
from TL C’ s E-Hail apps f or medallion and SHL. SHL shif ts are much more spread out t han
medallions, and t hus don ’ t ha v e t he 4pm drop in v ehicles in ser vice and pickups. SHL in
ser vice is about 3k t hroughout an y da y , and occupancy r ate is about 40% of medallion ’ s.
T r aditional FHV (mos tl y liv eries) ha v e w eekda y dail y peak s in t he mor ning r ush hours (5-
8am). Interes tingl y , air port pick -up percentag e and tem por al patter n are almos t identical
across medallions, app-based FHV and tr aditional FHVs. The liv eries seems t o depend
on ser vice reques ts from outer Boros (42% in Bronx, 17% in bo t h Brookl yn and Queens,
20% in Manhattan, 3% in air ports), as also ar gued in Schaller ( 2007 , Section 7.3) and NY C
T axi F act Book 2006, pag e 24. Thus taxi and liv er y should be seen as tw o com plementar y
113
C hapter 5 Efficien cy of NY C T axi Indus tr y
sys tems where mos t trips of t he NY C FHV indus tr y f all int o.
5.1.2 S treet Hail Liver y
Green Cab is a combination of taxi and liv er y , t hus t he alter nativ e name ”S treet Hail Liv -
er y ”.
9
Green cabs are allo w ed t o pick up s treet-hail (and e-hail) passeng ers in Boro Zones:
outside Core Manhattan (sout h of W es t 110t h S treet and Eas t 96t h S treet) and t he air ports,
r ates set b y TL C. Prearr ang ed trips are allo w ed from Boro Zones and air ports, r ates set b y
base.
On 2011-01-19, Michael Bloomber g announced a plan t o create “a ne w categor y of liv er y
cars t hat can mak e on-s treet pickups outside of Manhattan”.
10
S tate legislature passed an
initial v ersion of t he S treet Hail Liv er y La w in 2011, and in 2011 and 2012 it f aced man y
leg a l challeng es.
11
The firs t Boro T axi hit t he s treets on 2013-08-08; LPEP trip data has
been published on TL C w ebsite since. By 2013-11-12, o v er 1,000 Boro T axis w ere on t he
road. There is a fix ed number of SHL pemits.
A ccor ding t o t he 2013 Boro mar k et s tudy
12
The N umber of Boro taxis in ser vice increases
while trips per taxi k eep s table. Boro T axi pickups per block concentr ate in N ort her n Man-
hattan (Broadw a y/Columbia U , 125t h S t ; Mount Sinai Hospital) and As t oria (S tein w a y ,
31s t S t) (near tr ansit hubs), due t o exis ting FHVs affiliating wit h Boro T axi bases nearb y .
Almos t a t hir d of Boro T axi driv ers ha v e been licensed as FHV or y ello w taxi driv ers f or 10
or more y ears. T axi ser vice has a symbio tic relationship wit h r apid tr ansit, mos t ob vious
at outer boroughs.
Betw een 2013-10-31 and 2013-11-19, TL C conducted field obser v ations at 17 ho tspo ts of
9
Bef ore final launch, Green Cabs ha v e also be called ”fiv e borough taxi plan” (5B..) and Hail A ccessible Inter -
Borough License (HAIL). Back g round on t he Boro T axi prog r am. http://www.nyc.gov/html/tlc/
html/passenger/shl_passenger_background.shtml
10
2011 S tate of t he City A ddress. https://www.mikebloomberg.com/news/
progress- at- work- 2011- state- of- the- city- address/
11
NY Ses sion La w N o. 602 (2011), N o. 9 (2012). Dock et#102472-2012, #102783-2012, #102553-2012.
12
http://www.nyc.gov/html/tlc/downloads/pdf/boro_taxi_market_study.pdf
114
C hapter 5 Efficien cy of NY C T axi Indus tr y
illeg a l s treet hails, see T able 5.2 . A cron yms in t he table: IO, illeg al offers; IA , illeg al accep ted;
BO, boro offers; B A , boro accep ted. Ov er all, a v ailable Boro T axi (or leg al taxi) ser vice is
much lo w er t han illeg al ones (including liv er y) at mos t locations TL C obser v ed.
T able 5.2: 2013 S treet Hail F ield S tudy R esults, 1-Hour Obser v ations
S tart T ime IO IA BO B A Location R egion
2013-11-12 15:30 15 4 2 0 125t h and Lexingt on U pper Manhattan
2013-11-19 16:30 16 1 3 1 131s t and 7t h U pper Manhattan
2013-10-31 18:00 10 3 3 1 Broadw a y and Gr and Elmhurs t
2013-11-01 17:00 9 1 7 1 R oose v elt and Main S t. Flushing
2013-11-04 08:00 6 2 3 0 61s t and R oose v elt W oodside
2013-11-05 09:00 12 3 0 0 Lefferts and Liberty Queens
2013-11-05 16:30 20 6 2 0 Jamaica LIRR Queens
2013-11-04 08:00 5 2 0 0 1500 Sheepshead Ba y Rd. Brookl yn
2013-11-04 10:00 12 4 1 0 N os tr and and Flatbush Brookl yn
2013-11-04 17:00 3 1 0 0 S tillw ell and Mer maid Brookl yn
2013-11-05 08:00 4 1 0 0 Flatbush and A v e. V Brookl yn
2013-11-07 17:00 28 6 1 0 Broadw a y and Junction Brookl yn
2013-11-13 09:00 13 1 6 1 N os tr and and F ult on Brookl yn
2013-11-06 16:30 10 0 2 0 Exterior and 225t h Bronx
2013-11-07 17:00 20 4 4 0 E. F or dham and W ebs ter Bronx
2013-11-09 10:30 15 4 3 0 149t h and Morris Bronx
2013-11-12 18:00 1 0 0 0 W es tches ter and S t. P aul Bronx
5.1.3 F or -Hire Vehicles
F or - hire v ehicles are arr ang ed t hrough a DSP or a TL C-licensed base and perf or med b y
TL C-licensed driv ers in TL C-licensed v ehicles. Dispatch ser vice pro vider (DSP) is a type
of TL C-licensed entity t hat w or k s wit h TL C-licensed bases t o connects passeng er wit h a
FHV .
F or -Hire- V ehicles (FHV) f all int o t hree classes, all open entr y . Liv eries are also kno wn
as Community Cars or Car Ser vices. P asseng ers (r adio) call a local dispatcher and ar -
r ang e t o be pick ed up at a specific place, t he dispatcher pro vides a f are quo te (us ing a
zone/neighbor hood pricing sys tem, which is less precise t han taximeter); if passeng er ac-
115
C hapter 5 Efficien cy of NY C T axi Indus tr y
cep ts t he quo te, t he y’ll g et a car number t o look f or . There are 500 liv er y bases and 25k
v ehicles
13
;500k passeng ers per da y , which is on par wit h Y ello w cabs ( 650k/da y), but are
ex cluded from s treet hailing. Black cars ha v e f are set b y contr acts wit h clients, mos tl y cor -
por ate, and 90% non-cash basis. There are 80 black cars bases and 10k v ehicles, g ener all y
Lincoln T o wn Car (a model line of full-size luxur y sedans). Business-account trips w ere
concentr ated in t he e v ening (7pm and af ter), as businesses pro vided w or k ers wit h free
tr ansportation home. L uxur y limousines are chartered ser vices, in v ol ving 200 com panies
and 7k v ehicles.
TL C beg an collecting FHV trip recor ds electronicall y in 2015, including liv er y , app-
based black cars, and luxur y limousines. Data are lis ted on TL C w ebsite t og et her wit h
y ello w and g reen taxi data.
14
T w o attributes are collected per trip: datetime and taxi zone
ID of t he pickup, associated wit h base number . P er -base w eekl y agg reg ate data is on NY C
OpenData.
15
5.2 Or g aniza tion of NY C t axi indus tr y
T axicab tr ansportation is a regulated indus tr y in mos t cities. In NY C, t he TL C controls t he
issuance of Medallion licenses and sets t he f are r ate. The TL C also caps taxi lease price, as
Medallion o wners usuall y lease out t heir taxicabs t o non-o wner taxi driv ers under fix ed-
rent contr acts, typicall y t hrough taxi fleets or ag ents.
A sim plified hier arch y of NY C taxicab indus tr y or g anization:
1. The T axi and Limousine Commission;
2. Medallion o wner , fleet/ag ent, brok er ; tr ade assoc iation; secondar y mar k etplace;
13
https://data.cityofnewyork.us/Transportation/CURRENT- BASES/eccv- 9dzr
14
http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml
15
https://data.cityofnewyork.us/Transportation/FHV- Base- Aggregate- Weekly- Report/
2v9c- 2k7f
116
C hapter 5 Efficien cy of NY C T axi Indus tr y
3. T axi driv er ; labor union/g roup;
4. T axi passeng er ;
NY C once had a chance t o monopolize its taxicab oper ation, t hus eliminating t he second
hier arch y : in 1930, t hen-Ma y or James W alk er had announced his intention of selling t he
right t o oper ate all of t he City’ s cabs t o a single entity . F or exam ple, R eport of t he Ma y or’ s
Commission on T axicabs (1930-09-23, F r ank P . W alsh as Chair man) recommended cer -
tificate of public con v enience and necessity f or ne w cabs and e v entuall y fr anchising taxi
ser vice t o single pro vider . Ho w e v er , W alk er resigned in 1932 af ter it came out t hat t hat
he had tak en bonds from a back er of a lar g e taxi fleet t hat s t ood t o g ain from t he a w ar d
of a monopol y fr anchise. See Hodg es ( 2007 , p47, 49) and also R ogoff ( 1980 , p462, 465-67,
470-72, 89, 94-95)
Fleets are r un as a multitude of priv atel y held cor por ations, setting up a separ ate cor -
por ation wit h e v er y tw o or t hree medallions and mortg aging t hem f or t he maximum pos-
sible amount.( ibid. , p156) ”Mini-fleets” are tw o taxicabs and tw o partners, each driving
one cab, usuall y one shif t per da y ; canno t join union. The individual oper at or chooses t he
bes t times t o k eep his taxicab in oper ation. The mini-fleet oper at or , lik e individual o wn-
ers, driv es onl y at t he bes t times.( ibid. , p158) Individual oper at ors can much more easil y
oper ate outside t he tax sys tem b y under -reporting ear nings (”skimming”). Some indus-
tr y participants es timate t hat as much as 50% of t he individual oper at or’ s income is no t
reported f or tax pur poses.
5.2.1 T axi and Limousine C ommittee
The NT C T axi and Limousine Commission (TL C) is headed b y nine commissioners, all
appointed b y t he Ma y or including t he chair man, where fiv e representing t he Boroughs
are recommended b y t he City Council.
117
C hapter 5 Efficien cy of NY C T axi Indus tr y
T able 5.3: R egulation T imeline
T ime Ev ent
1925 NY C City Council task ed NYPD’ s Hack Bureau t o enf orce its regulation
o v er NY C taxicab indus tr y .
1937-03-01 Haas A ct es tablished Medallion NY C Or dinances v ol. I 545
1965 T axicab Driv ers U nion (TDU) f or med, or g anizing 82 fleets. R ogoff 1980
1966 Fleets sold Medallions as ”mini-fleets” t o bail out loans as bank s lo w ered
credits. R ogoff 1980, p156
1967 City or dered all taxicabs painted y ello w f or dis tinction.
1971 Fleet Medallion prices hit recor d lo w since 1952.
1971-03-02 NY C TL C w as created t o regulate t he taxi indus tr y (and f or -hire v ehi-
cles). NY C Local La w N o. 12 (1971)
1979 TL C per mitted Medallion/taxicab leasing; commission (share tenancy)
g r aduall y replaced b y leasing.
1982 TL C allo w ed t hat tw o-w a y r adios be mo v ed from Medallion t o non-
Medallion cars; black cars t ook o v er .
1985 TL C mandated taxicabs remo v e tw o-w a y r adios b y 1987-03-15.
mid-1980s Minifleet o wners f or med fleets. Oper at ors f or med leasing ag ents.
1987 TL C g ained clear jurisdiction o v er f or -hire v ehicles; ”gypsy cabs” be-
come liv er y . NY C Local La w N o. 76 (1986)
1990-01-01 TL C’ s o wner -mus t-driv e r ule of tr ansf erred individual Medallions w ent
in effect.
1995 S tate legislature per mitted sale of 400 Medallions. 1995 NY S La w s ch.359
1996 TL C lease cap w as firs t enacted; f are r aise;
2003 S tate and city per mitted sale of 900 Medallions. 2003 NY S La w s ch.63,
P art I; NY C Local La w N o.51 (2003)
2004-Ma y An across-t he-boar d f are increase rose t he metered f are b y about 26 per -
cent ; lease cap r aised;
2006 S tate and city per mitted sale of 150 Medallions 2006 NY S La w s ch.535;
NY C Local La w N o.18 (2006); s t opped/slo w r ate w as r aised;
2011 Go v er nor aut horized TL C t o issue 18000 HAIL licenses, along wit h 2000
accessible Medallions (400 immediatel y); liv er y becomes s treet-hail in
non-core area. NY S La w N o.602 (2011), N o.9 (2012)
2012-09-04 F are r ate r aise
5.2.2 Br oker and Lender
Brok er arr ang e v ehicle sales, and lenders finance medallion purchases. Brok er is a TL C-
licensed individual or business who acts as an ag ent f or ano t her person or business in
118
C hapter 5 Efficien cy of NY C T axi Indus tr y
T able 5.4: TL C Chair manship
S tart End N ame N ominating Ma y or
1971 1973 Michael J. Lazar Lindsa y
1974 1977 Moses K o v e Beame
1978 1986 Ja y L. T uroff Beame; K och
1986 1988 Char les Gor man Gilbert K och
1988 1991 Jack S. L usk K och
1991 1995 F idel F . Del V alle Dinkins
1995 1996 Chris t opher R. L ynn Giuliani
1996 2000 Diane McGr at h-McK echnie Giuliani
2001 2010 Matt he w W . Daus Giuliani; Bloomber g
2010 2013 Da vid Y assky Bloomber g
2014 N A Meer a Joshi de Blasio
nego tiating eit her t he tr ansf er of an y interes t in a Medallion, or a loan t o be secured b y a
Medallion or a T axicab.
16
Medallion F inancial Cor p ( N ASD A Q:MFIN ) finances t he purchase of medallions in N e w
Y or k and o t her cities. The common s t ock of Medallion F inancial Cor p. beg an publicl y tr ad-
ing on t he N ASD A Q N ational Mar k et on 1996-05-23 under t he symbol T AXI . It consis ts
of Medallion Bank , Medallion Lending, Mezzanine Lending, and in v es t ors.
17
Medallion
Bank i s no t an in v es tment com pan y , and t heref ore is no t consolidated wit h t he Com pan y ,
but ins tead is treated as a portf olio in v es tment.
Ot her lenders are credit unions, including Lomt o FCU , Melrose Credit U nion, Montauk
Credit U nion, and Prog ressiv e Credit U nion.
5.2.3 Trade Associa tions
T r ade associations ha v e activ e roles in NY C taxi indus tr y , including Metropolitan T axi
Boar d of T r ade (MTBO T), Greater N e w Y or k T axi Association (GNYT A), T axicab Ser vice
Association (TS A), Committee F or T axi Saf ety , and T axicab, Limousine and P ar atr ansit As-
16
TL C R ules §51-03
17
Medallion F inancial Cor p. http://www.medallion.com
119
C hapter 5 Efficien cy of NY C T axi Indus tr y
sociation (TLP A).
Metropolitan T axi Boar d of T r ade (MTBO T), a tr ade association f or 33 fleet taxicab op-
er a t ors managing appro ximatel y 3500 of NY C medallion v ehicles (near half of mini-fleet
Medallions). Its president R on Sher man is also t he f ounder of CMT ; S tanle y M. F riedman
w as t he lobb yis t. MTBO T is in v ol v ed in t he R eport of Leasing C ommunications (1978-
05-12 and 1979-10-23). It also sued t he City multiple times: in December 2007, ag ains t
Bloomber g’ s PlaNY C t hat leads t o TL C’ s T axicab Specifications amendment demanding
minimum miles per g allon on ne w taxicabs
18
; on 2012-05-07, ag ains t Bloomber g’ s 5 Boro
prog r am (S treet Hail Liv er y)
19
.
Greater N e w Y or k T axi Association (GNYT A) has 7 member fleets and appro ximatel y
1500 y ello w medallion taxis.
20
T axicab Ser vice Association (TS A) represents credit unions
financing medallions.
21
NY S trial judg e r uled t he S treet Hail Liv er y La w violates NY S con-
s titution.
22
Committee F or T axi Saf ety is an interes t g roup of NY C Medallion leasing ag ents
managing appro ximatel y 20% of t he taxicabs and o v er 5000 driv ers.
23
The T axicab, Limou-
sine and P ar atr ansit Association (TLP A) is a tr ade association wit h o v er 1100 member busi-
nesses t hat pro vide local passeng er tr ansportation ser vice f or -hire w or ldwide.
24
The TLP A
launched ”Who ’ s Driving Y ou” cam paign t o expose t he regulat or y issues t he association
belie v es Uber , L yf t, and o t her tr ansit apps are violating.
25
18
Dock et# 08 Civ . 7837, 09-2901-cv and 10-618. http://harvardlawreview.org/?p=1655
19
Dock et#102472-2012
20
W ebsite archiv e. https://web.archive.org/web/www.gnyta.org . It is in v ol v ed in
Dock et#102783-2012, which w as on 2012-05-24.
21
TS A lobb ying his t or y on NY C Lobb yis t Search. http://prtl- drprd- web.nyc.gov/
lobbyistsearch/search?client=Taxicab+Service+Association
22
Dock et #102553-2012, on 2012-08-17
23
W ebsite, http://committeefortaxisafety.com/ ; T witter , @CommT axiSaf e ty
24
TLP A w ebsite, http://www.tlpa.org/ .
25
”Who ’ s Driving Y ou” cam paign, http://www.whosdrivingyou.org/ .
120
C hapter 5 Efficien cy of NY C T axi Indus tr y
5.2.4 Labor Union
N e w Y or k T axi W or k ers Alliance (NYTW A) is a labor union of NY C taxi driv ers.
26
NYTW A
is affiliated wit h N ational T axi W or k ers Alliance (NTW A) since 2011, which is affiliated
wit h t he American F eder ation of Labor and Cong ress of Indus trial Or g anizations (AFL-
CIO) and t he Inter national T r ansport W or k ers ’ F eder ation (ITF). T axi driv ers are indepen-
dent contr act ors, no t pro tected under t he N ational Labor R elations A ct. The NYTW A can
coor dinate pro tes ts and s trik es, but has no collectiv e bar g aining rights.
27
In 2007, it ap-
pealed ag ains t TPEP ,
28
. In 2009, it coerced t he reduction of MT A tax from $1 t o $0.50. In
2011, Enf orcement units f or Lease Caps and Illeg al Pick -ups w as es tablished in TL C, and
Driv ers ’ Bill of Rights w as mandated. In 2012, it cam paigned f or f are r aise and ag ains t
lease o v erchar g e.
29
The 17% f are r aise in 2012 w as also credited t o w ar d NYTW A .
30
5.2.5 Online Gr oups and Marketpla ces
Y ello w Smart, Inc. o wns a f e w under g round mar k ets, including NY CityCab and Driv er -
Zoo.
NY CityCab pro vides NY C Medallion, SHL and FHV inf o.
31
Medallions f or Sale
32
has
lis ting wit h date, s tatus, price (typicall y $800k), contact and descrip tion f or o v er 220 f or -
sale Medallions (independent, minifleet), dating back t o 2009-04-29. Hack driv er partner
33
has lis ting wit h date, w/o medallion, shif t reques ted, location, contact and descrip tion f or
26
NYTW A . http://www.nytwa.org/
27
There’ s no future f or taxis. ( https://www .t heguar dian.com/us-ne w s/2017/oct/20/ne w -y or k -y ello w -cab-
taxi-medallion-v alue-cos t)
28
http://cityroom.blogs.nytimes.com/2007/09/26/do- taxi- drivers- have- a- right- to- privacy/
29
”Raise t he F are/F reeze t he Leases”, https://web.archive.org/web/20121014111356/http:
//www.nytwa.org/campaigns/raisefarefreezeleases ; ”S t op Gar ag e/Brok er Ov er -
char g es”, http://web.archive.org/web/20121001000123/http://www.nytwa.org:
80/campaigns/stopovercharges
30
https://cityroom.blogs.nytimes.com/2012/07/12/taxi- fares- in- new- york- to- rise- by- 17/
31
NY CityCab w ebsite. http://nycitycab.com/
32
http://nycitycab.com/Business/TaxiMedallionList.aspx
33
http://nycitycab.com/Business/Partnerslist.aspx
121
C hapter 5 Efficien cy of NY C T axi Indus tr y
shif t partnership, 20873 recor ds dating back t o 04/01/2007.
A ccor ding t o NY C T axi Guide
34
: Ear l y Mor ning (7 AM T O 9 AM) mos t passeng ers are
w or k ers heading t o w ar d midt o wn a nd Do wnt o wn, t heref ore taxicabs tends t o pick up on
t h e surrounding neighbor hoods and drop off on Midt o wn and lo w er Manhattan; Midt o wn
is t he easy spo t t o find a cab; Eas t V illag e and W es t V illag e are less affected. N eighbor hoods
lik e U pper W es t side and U pper Eas t side are mos t har d area t o find one. More chance t o
find em p ty taxis heading nort h. A v enues lik e Ams ter dam, Centr al P ar k W es t, Madison,
P ar k A v e, 3r d A v e a re good spo ts t o find a cab. Ot her good locations include schools af ter
drop-off, g as s tations. In t he e v ening (4 pm t o 6 pm), off-duty taxis are lik el y going back
t o g ar ag es t o switch shif t, as t he y f ace s tiff fines f or been late on retur n time; t hese cabs
might pic k up a passeng er if going t he sam e dir ection, and t he driv er can add up a f e w
dollars. T axi driv ers mus t close windo w s and lock doors f or pro tection, and t he y usuall y
ask t he passeng er’ s des tination bef ore unlocking t he doors. Medallion light and off-duty
light s tatus: (on, off), On Duty and ready f or pick up; (off, off), Has a passeng er ; (on, on), Off
Duty ; (off, on), Off Duty but has a passeng er . In r ush hours and especiall y in t he e v ening
y ou see all kind of black cars and limos do illeg al Pick ups. On a v er ag e a driv er does around
26 t o 30 trip a da y . Ot her inf o include taxi school, brok er , meter shop, g ar ag e (ag ents and
fleets).
Driv erZoo is a lis ting source f or a ll taxi driv ers all o v er t he s tates, find T axis f or sale,
medallions and licenses, T axi equipments.
35
It has resources f or leasing a Y ello w T axi v er -
sus leasing Black car using E-Hail
36
; a v oiding tick ets, lo w er y our expenses, tips t o increase
y our dail y tip, fighting s tress
37
; and com pare cos t and re v enue breakdo wn of TN C and
taxi under 8 scenarios
38
.
34
http://nycitycab.com/NYC%20Taxi%20Guide.aspx
35
Driv erZoo w ebsite. http://www.driverzoo.com/
36
NY C: Y ello w T axi v s E-hail, Ho w a driv er mak es a choice. http://www.driverzoo.com/
YellowTaxivsE- Hail
37
T axi drivi ng tips f or a happ y da y . http://www.driverzoo.com/DriverTips
38
NY C Y ello w T axi v s E-hail Uber X, Driv er Cos t and R e v enue. http://www.driverzoo.com/
122
C hapter 5 Efficien cy of NY C T axi Indus tr y
A f e w priv ate blogs are also dedicated t o N e w Y or k City Y ello w Cab T axis, ne w s, los t
and f ound messag e, adv ertising.
39
GPS tr acking de vice does no t violate t he F ourt h Amend-
ment rights of unreasonable search and seizure; taxi driv ers do no t ha v e a pro tected pri-
v acy interes t in t he v ehicles t he y driv e and t hat taxicabs are no t tr ul y priv ate v ehicles.
40
.
Cab Driv er Hassan El-N ahal w as among t he driv ers who w ere accused of o v erchar ging
passeng ers in 2010 and he sued t he city and TL C in 2013 s tating it violated his F ourt h
Amendment pro tection. In 2010, t he GPS de vices sho w ed t hat 13,315 of 21,819 driv ers had
o v erchar g ed cus t omers.
5.3 NY C t axi regula tion
The NY C taxicab indus tr y w as originall y regulated b y NYPD’ s Hack Bureau since 1925. In
1971, NY C TL C w as created t o regulate t he taxi and f or -hire v ehicle indus tries.
TL C r ules
41
is T itle 35 of t he R ules of t he City of N e w Y or k
42
: T axi and Limousine Com-
mission. The TL C R ules R e vie w Project re vised TL C r ules and regulations t o mak e t hem
easier t o unders tand and more consis tent across t he six TL C-regulated indus tries. Old
r u les ref ers t o Chap ters 1 t o 14, effectiv e bef ore 2011-04-01. N e w r ules s tart from Chap ter
51, effectiv e on 2011-04-01.
43
As of 2011-07-03, t he adminis tr ativ e tribunal (adjudications
function; some sa y ”kang aroo court”) of TL C has been effectiv el y tr ansf erred t o t he Office
of A dminis tr ativ e T rials and Hearings (O A TH). O A TH is independent of t he ag encies t hat
write tick ets and is dedicated t o enhancing t he prof essionalism of t he City’ s adminis tr ativ e
judiciar y .
RevenueandCost
39
Y ello w CabNY CT a xi. https://www.yellowcabnyctaxi.com/
40
https://www.yellowcabnyctaxi.com/blog/appeals- court- rules- city- can- monitor- taxis- movements- with- gps
41
TL C r ules. http://www.nyc.gov/html/tlc/html/rules/rules.shtml
42
R CNY . http://rules.cityofnewyork.us/codified- rules
43
Indus tr y N o tice #11-12. http://www.tlc- mag.com/archive/pre_2013_site/tlc_news_
shell_june11.html
123
C hapter 5 Efficien cy of NY C T axi Indus tr y
5.3.1 Licensin g
Medallion is t he TL C-issued license t o leg all y oper ate a v ehicle as a taxicab in NY C. The
license is ph ysicall y presented as a piece of metal attached on t he hood of a (y ello w bodied)
v ehicle. The g reen cab co unter part of Medallion is called S treet Hail Liv er y P er mit.
Haas A ct 1937 es tablished t he Medallion sys tem (Schaller , 2006 , T able 3): it controls
Medallion issuance, and maintains a ”60/40” r atio of mini-fleet (58%) t o independent
(42%) Medallions. T o add additional licenses, TL C needs appro v al of t he City Council and
also t he S tate legislature, because auctioning medallions in v ol v es selling t hem “f or more
t h an adminis tr ativ e cos ts” wit h “t he ex cess ... considered a tax”.
44
T able 5.5 lis ts Medallion issuance o v er time. In t he table, U/A/W/M/I ref ers t o unre-
s tricted, alter nativ e fuel, wheelchair accessible, mini-fleet, and independent Medallions
respectiv el y . FY ref ers t o NY C fiscal y ear , ending on June 30. On 2011-12-23, NY go v er nor
Andre w Cuomo signed legislation aut horizing t he TL C t o issue 18000 HAIL licenses (close
t o t he current number of liv eries), and auction an additional 2000 accessible Medallions,
while onl y 400 w ere allo w ed bef ore t he appro v al of t he Disabled A ccessibility Plan.
45
All t he 13237 Medallions in effect during 2009-2013 are sho wn in F ig. 5.1 . N o te t hat
Medallions 4G95-6 o wned b y “ TE C ORP” w ere long out of business and should ha v e ex-
pired in 1999.
T ypes of Medallion property rights. Mini-fleet Medallion o wnership requires t hat all
mini-fleet m edallions mus t b e o wned i n g ro ups o f at leas t tw o individuals, and be oper ated
f or a minimum of tw o 9-hour shif ts dail y .
46
Independent Medallion o wnership is an indi-
vidual or business (partnership or cor por ation) who can o wn onl y one medallion and ma y
no t be a shareholder or o wner of ano t her ; tr ansf er of o wnership are res tricted t o ano t her
44
NY C Chart er §2303(b)(4) (2000). See also Dock et #102553-2012 and #102472-2012.
45
NY Ses sion La w N o. 602 (2011), N o. 9 (2012)
46
TL C R ules §51
124
C hapter 5 Efficien cy of NY C T axi Indus tr y
T able 5.5: Medallion issuance o v er time
T ime Since T o tal UM UI AM AI WM WI N o te
1907 65 - - - - - - F rench-im port.
1912 2,800 - - - - - - Quick g ro wt h of taxi.
1923 15,000 - - - - - - Fleets f or med/entered.
1931 21,000 - - - - - - Ov ersuppl y , cong es tion,
f are-cutting, inadequate
insur ance.
1933 15,500 - - - - - - Demand dropped in Great
Depression.
1934 14,000 - - - - - -
1937 13,595 - - - - - - Haas A ct. N o issuance in
59 y ears.
WWII 7,500 - - - - - -
1947 11,414 - - - - - - Medallion g ained v alue,
tr aded at $1500 each.
1964 11,787 - - - - - - N umber s tagnated.
Ma y 1996 11,920 80 53 FY1996
Oct 1996 12,053 80 53 FY1997
Sep 1997 12,187 80 54 FY1998: 400 b y Giuliani
2004-04-16 12,361 174
2004-04-23 12,487 126 FY2004: 300
2004-10-15 12,533 18 1 25 2
2004-10-18 12,649 116
2004-10-22 12,779 130 FY2005: 292 of 300
2006-06-16 12,833 54
2006-06-22 13,087 124 130 FY2006: 300+8
2007-11-01 13,150 63
2008-05-02 13,237 (2) 86 1 FY2008: 150+2
2013-11-14 13,437 200
2014-02-26 13,605 168
2014-03-25 13,637 32 FY2014: 350 of 400 final-
ized, Bloomber g.
2014 end 13,635 - - - - - -
2015 end 13,587 -50
independent taxicab o wner and mus t be appro v ed b y t he TL C.
47
Owner of independent
medallion mus t ha v e hack license. Owner -mus t-driv e (OMD) demands t hat if purchased
47
TL C R ules, Chap 1, ”independent taxicab o wner” and ”o wner”.
125
C hapter 5 Efficien cy of NY C T axi Indus tr y
F igure 5.1: 13237 Medallions during t he 5 y ears recor ded in trip data. Medallion res tric-
tions: indie, independent Medallion; omd, o wnner -mus t-driv e; some Medal-
lions mus t use alter nativ e fuel or wheelchair accessible v ehicles. Mini-fleet
Medallions are typicall y o wned b y fleets or oper ated b y ag ents.
t h rough a tr ansf er af ter 1990-01-07, including a spouse who acquires t he medallion b y
inheritance, t he individual or one partner or shareholder mus t oper ate t he taxicab t hem-
sel v e s f or at leas t 210 9-hour shif ts in e v er y calendar y ear (shorter shif ts do no t count).
48
This is intended t o f orce balancing fleet consolidation. Effectiv e since Jul y 2011, t his re-
quirement w as reduced t o 180 9-hour shif ts e v er y calendar y ear ; o wners 62 y ears or older
who ha v e driv en f or at leas t 10 y ears shall driv e 150 7-hour shif ts per y ear ; duties can be
divided among up t o 4 o wner -driv ers, pro vided t hat each o wns at leas t 10% interes t of t he
medallion; wit h a $5000 penalty , o wners can designate an independent medallion driv er ;
t h e inheriting spouse is no t required t o driv e if t he deceased spouse w as no t required t o
driv e because he or she acquired t he medallion bef ore 1990. Independent Medallion Driv er
(IMD; effectiv e 2011-07) is a driv er who is t he title o wner of t he taxicab v ehicle or t he lessee
of t he taxicab v ehicle wit h a conditional purchase ag reement, and driv es t he taxicab an
a v er a g e of at leas t 120 hours per mont h. A driv er can be t he IMD f or onl y one indepen-
48
TL C R ules §1-09(b)
126
C hapter 5 Efficien cy of NY C T axi Indus tr y
dent taxicab. A ccor ding t o t he pre vious r ules, independent Medallions no t acquired from
tr ansf ers af ter 1990-01-07 are no t subject t o t his r ule, but t he number can onl y diminish
o v e r time.
Details on o wner -mus t-driv e r ules. S tudies ha v e sho wn t hat o wner -driv en taxicabs ha v e
f e w er accidents, f e w er violations of r ules, and higher v ehicle inspection pass r ates.During
t h e time fr ame from 1991 t o t he period when t he GPS w as enacted prior t o 2009, t his r ule
w as ne v er enf orced. Since 2009, TL C enf orces t he r ule using TPEP and im poses a fine and
license suspension on violat ors. U nder t he original r ule, a long-time o wner -driv er who
wishes t o retire or t o reduce his or her w or k schedule mus t eit her sell t he medallion t o
a v oid violating t he o wner -mus t-driv e r ules.
49
TL C has allo w ed o v er 175 of t he pos t-1990
individual medallions t o be oper ated b y leasing ag ents or fleets, which are unlik el y t o be
o w ner -driv en (Schaller , 2006 ). In 2009, t hose char g ed wit h noncom pliance who pled guilty
receiv ed t he minimum penalty ($100); in 2010, t he fine schedule w as settled t o be: $2500
f or less t han 50 shif ts per calendar y ear ; $1500 f or 51-100 shif ts; $500 f or 101-210 shif ts. The
2011-07 re vision
50
r aised penalties t o betw een $1000 and $10000 based on shif ts missed,
and adds penalties f or ag ents. The 2015-01-29 re vision chang ed driving requirements from
shif t s t o cumulativ e hours, and reduced penalty . On 2016-02-25, TL C repealed t he o wner
mus t driv e r ules.
An Ownership V erification Letter is a s tatement sho wing people appro v ed b y t he TL C t o
o w n and oper ate t he Medallion. F or cor por ations, t he Ownership V erification Letter will
lis t t he names of t he appro v ed officers and shareholders and t he amount of shares each
o w ns.
Medallion (and SB V license) expires e v er y tw o y ears b y April 30, unless t he f ollo wing
49
An Open Letter b y t he League of Individual Medallion Owners.
Published on 2014-06-22. https://indytaxinyc.wordpress.com/
an- open- letter- to- mayor- deblasio- and- the- tlc/
50
OMD R ule R e visions. http://www.nyc.gov/html/tlc/downloads/pdf/omd_revisions_
042111.pdf
127
C hapter 5 Efficien cy of NY C T axi Indus tr y
rene w al f ees are paid b y t hat time, along wit h insur ance documents: $1,100 license rene w al
f ee ($550 x2); $540 ($270 x2) f or six Saf ety and Emissions inspections; $10 f or a replacement
tin (Does no t appl y t o SB V licenses). One mus t place t he Medallion and t he original Rate
Car d in s t or ag e if y our v ehicle is no t oper ational f or a period of 10 da ys or more which
canno t ex ceed 60 da ys. Medallion license ma y be re v ok ed an y time a v ehicle is no t driv en
as a taxi f or 60 consecutiv e da ys. T em por ar y Medallion ma y be issued f or los t or s t olen
Medallion, which expires in 30 da ys.
Price of Medallion. Betw een 2004 (wit h a f are increase) and 2012, t he a v er ag e annual
price of independent medallions increased 260% (214% inflation-adjus ted), mini-fleet medal-
lions 321% (265%). In 2013, t he a v er ag e price of a n independent medallion w as appro xi-
matel y $967,000 (47% more t han 2011), and one mini-fleet medallion (sold in pairs) appro x-
imatel y $1,150,000 (28% more t han 2011). A v er ag e price of t he 200 mini-fleet wheelchair
accessible medallions auctioned on 2013-11-14: $2,270,000 per pair . Difference in a v er ag e
prices can be explained t hat man y independent medallions require t he o wner t o driv e t he
taxi; lar g e fleet com panies can more easil y lease a taxi f or tw o shif ts e v er y da y . Medallion
sale prices can be f ound in TL C mont hl y tr ansf er reports and unofficial lis tings
51
.
T able 5.6: Gro wt h Rate of Annual A v er ag e Medallion Prices
Y ear Independent Mini-fleet
2004 22% 22%
2005 22% 21%
2006 14% 27%
2007 11% 19%
There are f our class types of TL C driv er license: (1) Medallion Driv er License (aka hack
license), which can also oper ate g reen cab since its introduction in late 2013; (2) F or -Hire
V ehicle Driv er License; (3) Commuter V an Driv er License; (4) P ar atr ansit Driv er License.
52
51
U nofficial lis tings. http://nycitycab.com/Business/TaxiMedallionList.aspx
52
License Applications, R ene w als and Summonses sys tem. https://www1.nyc.gov/lars/
128
C hapter 5 Efficien cy of NY C T axi Indus tr y
A driv er ma y hold all f our class types at one time. But if a driv er holds a FHV license, t he y
can onl y driv e f or -hire v ehicle, no t y ello w or g reen taxicab. F or all types of TL C driv er
licenses, application f ee is $252, rene w al f ee is $168. A driv er shall no t oper ate a taxicab f or
more t han 12 consecutiv e hours.
53
Hack is t he license f or a driv er t o leg all y oper ate a Medallion v ehicle. Hack licenses
expire e v er y 2 y ears; s tarting Jan 2016, 3-y ear licenses are also issued. The application
f or Hack license requires: DMV Driv er’ s license, 6 hours DMV -certified def ensiv e driv -
ing class wit hin 6 mont hs; TL C-licensed taxi school ($105 f or 24h; $325 f or 80h) which
exams on NY C g eog r aph y , map reading, and TL C r ules and regulations ($25); wheelchair
accessibility v ehicle (W A V) tr aining; and $252 License F ee pa y able t o NY C TL C, $75 F ing er -
printing F ee pa y able t o TL C/DCJS (Division of Criminal Jus tice Ser vices), $26 Dr ug T es t
F ee pa y able t o LabCor p.
T axicab (Medallion taxicab, licensed taxicab) is a mo t or v ehicle, y ello w in color , bearing
a Medallion indicating t hat it is licensed b y t he Commission t o carr y up t o fiv e passeng ers
f or hire and aut horized t o accep t hails from persons in t he s treet.
54
T axicab candidate is a v ehicle being considered f or use as a T axicab Model. TL C has a
lis t of v ehicle models appro v ed f or use a s NY C taxicab which chang es o v er time. Current
requirements differ f or U nres tricted, Alter nativ e F uel, and A ccessible Medallions. In 2006,
F or d Cro wn V ict oria com prises 92% of t he y ello w taxi fleet. A ccor ding t o 2014 taxicab
f act book , 60% of Medallion v ehicles are h ybrid-electric v ehicles and 2% are wheelchair -
accessible (W A V). Hybrid v ehicles in use are mos tl y F or d Escape (SUV); T o y o ta Camr y ,
T o y o ta Prius (Sedan). Bloomber g pushed a ” T axi of T omorro w” prog r am t hat w ould ha v e
pick ed Nissan NV200 t o be t he ex clusiv e model f or Medallion v ehicles f or t he ten y ears
s tarting Oct ober 2013, which g ets scr aped as taxi fleets sued and cos t t he city go v er nment
$80 million t o Nissan f or breach of t he $1 billion contr act.
53
TL C R ules §1-51
54
TL C R ules §51-03
129
C hapter 5 Efficien cy of NY C T axi Indus tr y
Being used as a taxicab, a v ehicle needs t o go t hrough a sequence of prepar ation: TL C
certifies t he v ehicle; DMV regis ters t he v ehicle (v ehicle identification number , VIN) and is-
sues a Medallion plate (eit her identical t o t he Medallion or appended wit h a TL C-assigned
sub-plate letter); DoF (Department of F inance) issues tax s tam p (placed on t he lo w er right
hand cor ner of t he v ehicle’ s front windshield); TL C regis ters t he v ehicle; Hack -up. T o hack
up a v ehicle, a TL C aut horized meter shop paints, attaches decals (signs), ins talls roof light,
meters, and partitions
55
. Then TL C’ s inspection f acility at W oodside ins talls t he medallion
and check s t hat all equipment is w or king wit hin TL C regulations.
A f e w documents are required f or an y tr ansaction at TL C. W or k ers ’ Com pensation, ei-
t h er Certificate or Ex em p tion F or m, deals wit h when driv ers shall g et injured while per -
f or ming duties as a taxicab driv er . V ehicle insur ance includes F or -hire P asseng er V ehicle
Insur ance Certificate (FH-1) and Insur ance Declar ation P ag e or Certificate of Liability .
TL C since 1989 demands e v er y Medallion v ehicle t o be inspected 3 times a y ear (e v er y 4
mont hs) at its Saf ety and Emissions inspection f acility at 24-55 B.Q.E W es t, W oodside, NY
11377. Each of t he cab’ s 18 different sensors is re vie w ed in a f our -s tag e inspection process.
F or exam ple, if t he meter r uns t oo slo w l y or quickl y , it mus t be recalibr ate’ d bef ore t he
v ehicle is allo w ed back out on t he s treets. A typical inspection tak es 15-20 minutes, and
t h e a v er ag e w ait time f or an inspection is about 55 minutes in 2014, o v er an hour in 2012,
and o v er 2 hours in y ears prior . A v ehicle inspection report (VIR) is issued at t he end of
inspection. Besides TL C inspection, a Meter Mile R un (MMR) tes t shall be done one time
each y ear at a TL C licensed T aximeter shop t o obtain a meter certification.
Scheduled v ehicle retirement f or v ehicles hack ed-up prior t o 2015-04-20.
56
Double-shif ted
v ehicles ha v e 36-mont h scheduled retirement, ex cep t f or v ehicles driv en b y at leas t one
Long- T e r m Driv er or aut horized S tand-By V ehicles. All o t her v ehicles ha v e 60-mont h sched-
55
P artitions are mandated since 1994 as a saf ety precaution. http://www.nytimes.com/1994/01/
21/nyregion/taxi- panel- requires- bullet- resistant- partitions.html
56
TL C R ules §67-18
130
C hapter 5 Efficien cy of NY C T axi Indus tr y
uled retirem ent. The a v er ag e ag e of Medallion v ehicles in ser vice is 3.3 y ears, and a v er ag e
ser vice lif e is about 5 y ears bef ore it f ails t he inspection and no t w ort h t he repair or passes
t h e scheduled retirement date.
There are t hree models of taxi oper ation, illus tr ated in T able 5.7 . F or driv er -o wned v ehi-
cle (DO V), t he driv er leases a medallion and eit her o wns or leases t he car . V ehicle o wner
means t he individual or business entity in whose name t he v ehicle is regis tered and t he
v ehicle license issued.
57
Mini-fleets of ten contr act wit h a fleet f or t he dail y s t or ag e and
dispatch of t heir taxicabs. Fleets and ag ents oper ate essentiall y in t he same w a y .
T able 5.7: Models of taxi oper ation
medallion v ehicle hack license
license driv er
medallion o wner driv er -o wned v ehicle
o wner oper at or
Manag ement of taxicabs. A g ent is a TL C-licensed individual or business entity who op-
er a tes or f acilitates t he oper ation of one or more T axicabs on behalf of t he T axicab o wners.
An o wner ma y onl y designate one ag ent f or t he o wner’ s taxicabs. Fleet is a business t hat
o w ns or oper ates at leas t 25 T axicabs, has a single location t o s t ore and maintain t he T axi-
cabs and trip recor ds, and has a dispatcher on t he premise f or at leas t 18 hours per da y
who assigns driv ers t o fleet taxicabs. S tand‐b y v ehicles (SB V) are TL C-licensed v ehicles f or
use b y fleets as replacement f or Medallion taxis tem por aril y out of ser vice.
58
The lar g es t
among 46 ag ents: All T axi Manag ement Inc. (812 cabs); S&R Medallion Cor p. (397 cabs);
T r ansit Sys tems Ltd. (390 cabs); W oodside Manag ement Inc. (353 cabs); Queens Medallion
Leasing Inc. (343 cabs); Mys tic Leasing Ser vice Cor p. (267 cabs); Green Apple Manag e-
ment (231 cabs); Y ello w Cab SLS Jet Manag ement (231 cabs). The lar g es t among 15 fleets:
T eam Sys tems Cor p. (391 cab s); R onart Leasing Cor p. (325 cabs).
57
TL C R ules §51-03
58
TL C R ules §1: ag ents, fleet and mini-fleet
131
C hapter 5 Efficien cy of NY C T axi Indus tr y
Rate car d is a paper car d issued b y TL C f or each taxicab, which displa ys t he Medallion
number , driv er name, taximeter serial number , r ates of f are, and o t her inf or mation. N amed
driv er is a Medallion driv er whose name has been entered on t he r ate car d b y TL C; onl y t he
driv ers specificall y named on t he r ate car d are allo w ed t o driv e t he taxicab. A long-ter m
driv er is a named driv er of a unique T axicab who o wns or leases t he Medallion f or no less
t h an fiv e mont hs, and driv es t he T axicab at an annual r ate of at leas t 160 hours per mont h.
59
U nspecified driv er is a ter m entered on r ate car ds indicating t hat t he taxicab can be driv en
b y an y licensed taxicab driv er whose name (or categor y) has been filed b y t he o wner of t hat
taxicab wit h TL C. Driv er aut horization s tatement is a document which Medallion o wners
file t o t he TL C bef ore leasing t heir taxicabs t o licensed Medallion driv ers; subleasing is no t
allo w e d.
Leasing ter ms. Long-ter m lease, typicall y t o pairs of driv ers, las t f or mont hs and paid
w eekl y . The expenses of long-ter m lessors w as significantl y less t han expenses of t he fleet
oper at ors: long-ter m lessors a v oid t he adminis tr ativ e and o v ersight cos ts bor ne b y fleet
oper at ors t hat lease b y t he shif t.
60
Shif t lease (mus t) las t 12 hours, and taxicab mus t ha v e
“unspecified driv er” on t he r ate car d.
The oper at or -driv er relation in 2005 is categorized in T able 5.8 , see Schaller ( 2006 ). Of all
t he Medallions, 3730 (29%) ha v e o wner -driv ers, onl y 186 of which w ere mini-fleet taxicabs
driv en b y a s t ockholder of t he g roup/business. 1210 (9%) are leased b y o wners who w ere
no t regis tered wit h TL C as ag ents or fleets.
T able 5.8: T ypes of taxicab ope r ation in 2005 b y oper at or -driv er
oper at or \driv er o wner (onl y) lesser (unspecified)
o wner 3730 (59%) 1210
ag ent - 5740 (25%)
fleet - 2116 (70%)
59
TL C R ules §51-03
60
TL C, March 1 994. “Should t he T axi F are Go U p?”
132
C hapter 5 Efficien cy of NY C T axi Indus tr y
5.3.2 Pricin g
TL C controls t he pricing of NY C taxi indus tr y t hrough f are r ates and lease caps.
61
Since
1996, f are r ates w as onl y r aised once on 2012-09-04, f ollo w ed wit h ne w lease cap r ules
on 2012-09-30.
62
The 2012 f are r ate and lease cap chang e presentation
63
pro vides taxi f are
adjus ted t o NY C CPI has been decreasing since 2006. The a v er ag e price of g as per g allon
increased from $2.70 in 2006 t o $3.90 in March 2012.
TL C lease cap w as firs t enacted in 1996, limiting taxicab lease price and add-on char g es
on driv ers.
64
TL C f or med t he Lease Cap unit in 2011 t o in v es tig ate driv er com plaints
ag ains t o wners and ag ents who o v erchar g e driv ers f or t he lease of taxicabs.
65
R equired ter m s in a written lease.
66
Beginning and e nding datetime of t he lease: w eekl y
leases mus t r un f or 7 consecutiv e da ys; shif t leases mus t r un f or 12 consecutiv e hours. Lease
cos t and items co v ered, wit h ref erence t o aut horizing TL C r ules: lease of medallion (and
v ehicle, if applicable); security deposit ; percentag e credit car d pass-along; an y o t her cos ts
co v ered b y t he lease. N o tice of TL C prohibition of o v erchar g es should be clear l y legible.
Cancellation char g es mus t be reasonable char g es and canno t be char g ed when driv er is
making timel y lease pa yments. If t he cancellation f ee is char g ed, one is no long er oblig ated
t o mak e additional lease pa yments.
Official taxicab v ehicle (O TV) is t he v ehicle t hat meets t he s tandar d specifications of TL C
R ules §67-05.1B, and is t he pur pose built taxicab f or model y ears 2014–2024, manuf actured
pursuant t o t he City’ s contr act wit h Nissan N ort h America. A ccessible O TV is t he O TV
61
TL C Lease Cap R ules §58-21 (2011-04-01)
62
2012-09-30 lease cap chang e. http://www.nyc.gov/html/tlc/downloads/pdf/lease_cap_
rules_passed.pdf
63
http://www.nyc.gov/html/tlc/downloads/pdf/fare_and_lease- hearing_
presentation.pdf
64
Fleet Driv er’ s Bill Of Rights. http://www.nyc.gov/html/tlc/downloads/pdf/fleet_
drivers_rights_poster.pdf
65
A tt or ne y Gener al Eric Schneider man, 2013-12-19. https://ag.ny.gov/press- release/
ag- schneiderman- and- tlc- secure- first- its- kind- agreement- protecting- rights- taxicab- 0
66
TL C R ules §58-21(i)
133
C hapter 5 Efficien cy of NY C T axi Indus tr y
modified in a manner t hat is consis tent wit h t he City’ s contr act wit h Nissan N ort h America.
O TV activ ation date is t he date on or af ter which t he O TV is required t o be used in t he hack -
up of an y unres tricted medallion. Ho w e v er , t he O TV activ ation date has been pos tponed
at lease until af ter 2015-04-20 due t o la w suits.
67
S tandar d lease cap r ates.
68
Medallion-and-v ehicle b y shif t: da y , $105; Sun- T ue night, $115;
W ed night, $120; Thu-Sat night, $129. Medallion-and-v ehicle, w eekl y shif ts (6-7 shif ts in 7
consecutiv e da ys): $666, mus t be pror ated if t he v ehicle is una v ailable f or an y reason t he
lessee is no t responsible f or ; [2012] (bef ore including credit car d char g es) da ys-onl y , $630;
nights-onl y or combinations, $737 (ex cluding one leas t profitable shif t, Sun- T ue); [2013] f or
driv ers leasing 7 shif ts in 7 consecutiv e da ys, t he y can be char g ed f or 7 shif ts if t he y pa y t he
lease per shif t/da y , are required t o retur n t he v ehicle af ter each shif t t o a location ag reed
wit h t he lessor , and are no t required t o pa y f or shif ts giv en timel y no tice. Medallion-onl y ,
b y w eek: $800; [2012] (bef ore including credit car d char g es) $952; [2013] O TV or accessible
taxicabs in ser vice on or af ter t he O TV activ ation date, $1114. All-in, b y w eek (long-ter m
leasing or conditional purchase of t he v ehicle): [2012] (bef ore including credit car d char g es)
$1227; which can be char g ed up t o 156 w eek s (3 y ears) f or v ehicle financing, t hen t he lessor
mus t tr ansf er t he title t o one or more of t he lessees if reques ted; [2013] O TV or accessible
taxicabs in ser vice on or af ter t he O TV activ ation date, $1389; Shareholders of more t han
2% in a public cor por ation t hat sells/leases/finances v ehicles canno t lease Medallion t o
an y person or entity who has paid f or such ser vice of t he cor por ation. A djus tments f or
h ybrid electric and diesel-fueled v ehicles
69
: extr a $3 f or a shif t, 7x f or w eekl y shif ts, 14x
f or w eek leases; [2012] 6x f or w eekl y shif ts (nights and combination w as $812 in r ules but
should be a typo).
Limits on additional char g es. Medallion users ref er t o t he maximum number of driv ers
67
Indus tr y N o tice #15-15. http://www.nyc.gov/html/tlc/downloads/pdf/industry_
notice_15_15.pdf
68
TL C R ules §58-21(c)(1-4)
69
TL C R ules §67-05
134
C hapter 5 Efficien cy of NY C T axi Indus tr y
on t he lease wit h right t o use t he Medallion. Credit car d char g e (if lessor is a merchant):
5% (pass-along) of t o tal credit car d pa yments, t he res t reimbursed in cash at lease ter mi-
nation (per shif t/w eek); [2012] add in lease, $10, x6/w eek , x12/w eek (equiv alent t o 5%
out of $200/shif t credit pa yment); [2013] separ ate from lease , adjus ted each June and
December if a v er ag e credit pa yment ex ceeds $200/shif t. Security deposit is at le ase r ate,
retur ned wit hin 30 da ys of lease ter mination af ter deducting additional char g es; [2012]
$5000 f or lease wit h conditional purchase; Late char g e is $25/shif t ; [2012] Late char g e is
f or t he late retur n of a v ehicle; [2013] $25/shif t/hour f or late retur n, no t ex ceeding lease
r ate; $50/w eek f or la te pa yment. Cancellation char g e is at a reasonable amount ; lessor can-
no t cancel t he lease unless t he lessee is late in making lease pa yments; MT A T ax on taxi-
cab trips is collected b y t he lessee.
70
E-ZP ass discount t oll amount is char g ed t o t he lessor .
P ar k ing tick ets and red light violations issued t o t he lessor’ s v ehicle during t he lease. Insur -
ance co v er ag e required b y la w : liability insur ance f or t he v ehicle; double shif t insur ance,
if t he taxicab is oper ated more t han one shif t dail y .
71
TL C f ees, if applicable
72
; TL C v ehicle
inspection f ees are irrele v ant t o Medallion-onl y leases. V ehicle purchase and/or finance
cos ts. V ehicle sales tax and related cos ts. Collision repair co v ers repair cos t f or collisions
and ph ysical damag e t o t he v ehicle: deduct cos t from security deposit, if t he lease clear l y
and prominentl y s tates t hat t he driv er is responsible f or t he damag e; [2012] included in
w eekl y leases; [2013] t he 2012 re vision does no t appl y if t he driv er ag rees t o be responsible
f or damag e t o t he v ehicle caused b y t he driv er’ s neglig ence. Collision co v er ag e is [2012]
$50/w eek f or co v er ag e; [2013] $250/incident as deductible, which shall no t be char g ed
if receiving proceeds t o co v er t he cos t of repair . [2012] Driv er healt h fund is a fund f or
driv er healt hcare and disability co v er ag e, $0.06/trip s tarting from 2013-10-01 (deducted
70
NY S T ax La w , Article 29- A
71
TL C R ules §58-13
72
TL C R ules §58-07
135
C hapter 5 Efficien cy of NY C T axi Indus tr y
from credit car d pa yment).
73
. Gasoline surchar g e
74
is $21/shif t until 2012-12-31, and 6x
f or w eekl y leases; adjus ted t o t he N e w Y or k City Gasoline Price Index
75
e v er y June 30 and
N o v ember 30. [2013] Since t he O TV activ ation date, t he 2012 table applies onl y t o h ybrid
electric and diesel-fueled taxicabs, $3 more f or o t hers. [2012] V ehicle rental tax, bo t h s tate
and local; [2012] Commercial Mo t or V ehicle T ax (CMVT)
76
; [2012] NY S DMV f ees (e.g. v e-
hicle regis tr ation); [2013] Ser vices or accommodations outside t he lease are no t subject t o
lease cap r ules. An y char g e no t explicitl y mentioned are f orbidden: ser vice and mainte-
nance of a leased taxicab is t he sole responsibility of t he lessor , and t he cos t canno t be
char g ed t o t he lessee
77
; summons written t o t he lessor as respondent shall no t be paid b y
t h e lessee. T able 5.9 com pares lease cap items of 2011, 2012, 2013 r ules, in or der . Symboles
used in t he table: ✓ co v ered; + additional; ∘ op tional; × f orbidden; . unchang ed;2 no t
exis t ; Em p ty if no t applicable.
By 2012-09-24, Metropolitan T axicab Boar d of T r ade (MTBO T) and JTL Manag ement
Inc. sued TL C seeking a tem por ar y res tr aining or der (TR O), preliminar y injunction, and
per manent injunction prohibiting t he ” All-in” lease cap in TL C’ s 2012 lease cap chang e.
78
On 2012-09-26, t he N e w Y or k Supreme Court, N e w Y or k County issued a tem por ar y re-
s tr aining or der (TR O), which w as amended on 2012-10-03 b y an Amended Or der t o Sho w
Cause
79
The TR O enjoin t he TL C from appl ying t he f ollo wing “V ehicle Sale R ules” claim-
ing t he y retroactiv el y im pair contr acts entered int o bef ore t he r ules w ere passed. The lessor
is prohibited from selling or financing t he v ehicle t o t he lessee under t he medallion-onl y
lease.
80
The lessor mus t use t he “DO V All-In Lease Cap” an ytime a driv er leases a medal-
73
TL C R ules §58-21(f)(5)
74
TL C R ules §58-21(c)(6)
75
https://www.eia.gov/dnav/pet/pet_pri_gnd_dcus_y35ny_w.htm
76
TL C R ules §58-08(j)
77
TL C R ules §58-21(b)(1)
78
NY S Supreme Court Case# 103849/2012. http://iapps.courts.state.ny.us/iscroll/
SQLData.jsp?IndexNo=103849- 2012
79
Document no t f ound, but should be preser ving exis ting leases.
80
TL C R ules §58-21(c)(3)
136
C hapter 5 Efficien cy of NY C T axi Indus tr y
T able 5.9: Com parison of Lease Caps
Item taxicab, shif t taxicab, w eek taxicab, all-in Medallion
Medallion users 1.. 1.. 2 3. 2 3.
Subleasing ×.. ×.. 2 ✓. ×✓.
Security deposit +.. +.. 2 + . +..
Late char g e +.. +.. 2 × + + × +
Cancellation char g e +.. +.. 2 + . +..
MT A T ax +.. +.. 2 + . +..
Credit car d char g e +✓+ +✓+ 2 ✓+ ×✓+
Driv er healt h fund 2 + . 2 + . 2 + . 2 + .
E-ZP ass t oll +.. +.. 2 + .
T ick ets +.. +.. 2 + .
V ehicle rental tax 2 + . 2 + . 2 + .
Collision repair +.. +✓+ 2 + .
Collision co v er ag e 2 ∘ .
CMVT 2 × . 2 × . 2 ✓.
Gasoline surchar g e 2 ∘ . 2 ∘ .
Insur ance co v er ag e 2 ✓. ✓..
TL C f ees 2 ✓. 2 ✓.
NY S DMV f ees 2 ✓.
V ehicle 2 ✓.
V ehicle sales tax 2 ✓.
lion and purchases a v ehicle from t he same person or a related entity .
81
On 2012-12-05,
t h e proceeding w as discontinued and t he TR O lif ted, as MTBO T and TL C had signed a
settlement ag reement.
The F reidman Com panies ref er t o t he f our taxicab manag ement com panies Ev g en y “Gene”
F reidman is t he ma jority principal of: W oodside Manag ement Inc. ( 365); Do wnt o wn T axi
Manag ement, LL C ( 191); 28t h S treet Manag ement, Inc. ( 155); and T unnel T axi Manag e-
ment, LL C ( 156).
82
All co m panies ha v e t heir principal office address at 313 T ent h A v enue,
N e w Y or k , N e w Y or k 10001. T og et her t he y control more t han 880 medallions and is one
of t he fiv e lar g es t NY C taxi fleets. The y routinel y o v erchar g ed driv ers since at leas t 2012,
81
TL C R ules §58-21(c)(4)(i)
82
NY S Courts Electronic F iling Case# 451566/2015. https://iapps.courts.state.ny.us/
nyscef/DocumentList?docketId=fdzlXcEWWcderRN9iGc5DQ==
137
C hapter 5 Efficien cy of NY C T axi Indus tr y
via higher -t han-cap lease amounts and im per missible add-on f ees including: a $3.5/shif t
”shif t ex cess time surchar g e”, v ehicle regis tr ation, CMVT and TL C v ehicle inspection f ees.
On 2013-12-17, t he N e w Y or k S tate Office of A tt or ne y Gener al (O A G) announced t he firs t
settlement (assur ance of discontinuance, A OD) of its kind pro tecting taxicab driv ers under
lease cap r ules.
83
On 2015-04-23, O A G filed a special proceeding t o t he N e w Y or k Supreme
Court ag ains t t he F reidman Com panies, f or breaching t he A OD; additionall y , W oodside
Manag ement Inc. f ailed t o pa y credit car d f ares t o taxi driv ers in time, while no t pro vid-
ing proper receip ts t o driv ers. On 2016-04-14, t he court issued a consent or der in f a v or of
O A G’ s petition. Ev g en y F reidman w as a rres ted on 2017-06-07.
84
T axicab F are Rate
85
is sho wn in T able 5.10 , where 2012 update is in parent hesis. Metered
f are includes $2.5 initial f are, $0.4 ($0.5) per 0.2 mile (12 m ph or abo v e) or per minute (un-
der 12m ph), fr action rounded up. 0.2 mile is appro ximatel y f our do wnt o wn block s (nort h-
sout h) and one cross-t o wn block (eas t-w es t). Surchar g e hours (as of pickup time) include:
r u sh hour , 4-8pm non-holida y w eekda ys; and o v er night, 8pm-6am dail y . City Rate applies
t o L G A trips. Group r ates appl y t o w eekda ys 6-10am, non-holida y . Rates are clear l y visible
on taxi body . Alert messag e appears on meter screen when r ate chang es from #01 t o #05
at city limit. In Ma y 2004, an across-t he-boar d f are increase rose t he metered f are b y about
26 percent. In N o v 2006, s t opped/slo w r ate w as r aised. The f are has no chang e until 2012,
while driv ers ’ pa y has lagg ed behind inflation and g as price. Currentl y t here is a $4.5 r ush
hour surchar g e f or Rate #02 (no t as e xtr a ). 2012 r ate chang e also deducted from re v enue
$0.06 per trip f or healt h care ser vices and disability co v er ag e f or driv ers. Pre viousl y TL C
does no t pro vide taxi driv ers healt h insur ance or disability co v er ag e (or o t her em plo y ee
benefits s tipulated b y labor la w s), who are considered as independent contr act ors ins tead
of em plo y ees.
86
F ares and lease caps anal ysis f or m b y April 2013 f or adjus tment consider -
83
Assur ance of Discontinuance N o. 13-501. NY SCEF 451566/2015.
84
https://www.yellowcabnyctaxi.com/blog/taxi- king- arrested- for- scamming- the- state- for- millions
85
http://www.nyc.gov/html/tlc/html/passenger/taxicab_rate.shtml
86
TL C Annual R eport 2012.
138
C hapter 5 Efficien cy of NY C T axi Indus tr y
ation.
T able 5.10: F are and Driv er Surchar g e (wit h 2012-09-04 update)
Rate N ame F are
#01 S tandar d City Rate metered, wit h $1 (r ush hour) or $0.5
(o v er night ) surchar g e
#02 Betw een Manhattan and JFK $45 ($52)
#03 T o N e w ar k Air port metered, wit h initial N e w ar k Surchar g e $15
($17.5)
#04 Out of City Rate t o N assau or
W es tches ter
double metere d when be y ond t he City limit
#05 Out of City N ego tiated Flat Rate nego tiated bef ore trip
#06 Group Rate $3/person (P ort A ut hority Bus t o 59t h S t/6t h
A v e), $6/person (Y or k A v enue t o F inancial
Dis trict)
V arious ag ence char g es are also included in taxi f are, see T able t ab:ag ency -char g es. S tate
tax s tarted in 2009, and applies t o all trips ending in NY S; NJ des tinations are ex em p t.
TL C surchar g e s tarted in 2015. T olls are oper ated t hrough E-ZP ass at discounted r ates and
passed t o t he passeng er . R etur n t olls are included: from W es tches ter and N assau Counties,
o v e r t he Cross Ba y V eter ans and Marine P ar kw a y -Gil Hodg es Memorial Bridg es, and from
N e w ar k Air port.
T able 5.11: A g ency Char g es
A g ency Amount N ame Cause
MT A $0.5 MT A S tate Surchar g e s tate tax
TL C $0.3 T axicab Im pro v ement
Surchar g e
wheelchair accessible v ehicle (W A V)
con v ersion, tr aining, and fuel offset
DO T an y t olls bridg e and tunnel t olls
In 2012, t he TL C es timated t hat t he a v er ag e driv er income af ter pa ying t he lease f ee, sales
tax, g as expenses, and f ees w as appro ximatel y $125 per da y , bef ore driv ers paid Social Se-
curity and o t her tax es. The number barel y reaches t he minimum w ag e r ate f or em plo y ees.
139
C hapter 5 Efficien cy of NY C T axi Indus tr y
5.3.3 Businesses
T r ansf er of a Medallion means t he tr ansf er of all or an y portion of a Medallion o wner -
ship interes t, including t he tr ansf er of interes ts in a business entity o wning Medallions.
T r ansf er of a taxicab license ma y be accom plished b y purchase/gif t/beques t/oper ation
of la w (priv ate partie s), acquisition of t he s t ock (cor por ation), membership interes ts (LL C)
or assets, and onl y wit h t he written appro v al of t he Chair person as t o t he tr ansf eree. An y
tr ansf er mus t obtain appro v al from t he TL C.
87
In mos t cases a ne w v ehicle is required t o
be hack ed up once a medallion is tr ansf erred. The Jul y 2011 re vision allo w s ne w o wners
of independent taxicabs continue t o use t hat v ehicle until its scheduled retirement date.
Mar k et V alue in ref erence t o t he tr ansf er of a T axicab Medallion will be t he g reater of: t he
actual consider ation being paid f or t he tr ansf er ; and t he F air Mar k et V alue.
88
F air Mar k et
V alue in ref erence t o t he tr ansf er of a T axicab Medallion is t he a v er ag e v alue of ar ms-lengt h
tr ansactions f or similar Medallions during t he prior calendar mont h, as deter mined b y t he
Commission.
Medallion o wner purchase t heir o wn taximeters from a lis t of TL C licensed T aximeter
shops. T aximeters t hat w or k wit h CMT or VTS: f or VTS TPEP , T axitronic (TX -36); older
models need upg r ade; f or CMT TPEP , Centrodyne (610, 620); Pulsar (2030R). Ot her taxime-
ters which needs an upg r ade include Genie T aximeter (Genie) and MetroMeter (21R). The
f ollo wing meters are inadequate f or TPEP: Pulsar (2020R, 2010R), Synalta (720).
5.4 NY C TL C Pr ograms
Wheelchair A ccessible T axi Dispatch Prog r am w as launched on 2012-09-14. T ill t he re-
lease of TL C Annual R eport 2012, 1000 trips w ere com pleted (dispatched in Manhattan,
b y t he 233 accessible taxicabs), wit h about 20 minutes a v er ag e w ait time. The prog r am
87
TL C R ules §58-43 t o §58-48
88
TL C R ules §58-03(l, t)
140
C hapter 5 Efficien cy of NY C T axi Indus tr y
pa ys driv ers f or t he “deadhead” (tr a v el time) portion of t heir trips en route t o scheduled
pick - ups.
89
E-hail pilo t prog r am beg an on 2013-04-26 wit h t hree TL C-appro v ed applicants, which
w as interr up ted from 2013-05-01 t o 2013-06-06 due t o litig ation from an appellate judg e.
90
E-Hail wit hin a half mile in t he city’ s centr al business dis trict sout h of 59t h S treet from eas t
side t o w es t side, or wit hin a 1.5 miles else where in t he city .
91
In late 2013, dail y a v er ag e e-
hail reques ts is under 5k , wit h 30% fulfillment r ate. (0.3% com pared t o 480k dail y y ello w
cab trips).
92
E-Hail seems t o be mos t effectiv e in areas of t he city t hat are typicall y under -
ser v ed b y y ello w taxis. Mos tl y fulfilled b y SHLs (in outer boroughs). Arro
93
launched its
e-hail app on 2015-09-02, partnering wit h CMT and replacing t he latter’ s RideLinQ pa y -
ment app
94
.
E-Hail ser vices enable passeng ers t o electronicall y hail a NY C taxicab and S treet Hail
Liv er y via mobile apps. TL C appro v es se v er al priv ate com panies, including Uber , t o offer
E-Hail ser vices. Uber and L yf t driv ers are required t o ha v e a f or -hire v ehicle (FHV) license,
no t hack license.
Brief His t or y Of Uber in NY C:
95
On 2011-05-03, Uber Black ”officiall y” w ent liv e in NY C,
wit h about 100 Lincoln T o wn Cars t hat can be summoned via an iPhone app.
96
On 2012-07-
04, Uber announced UberX, a more affor dable ser vice t hat uses h ybrid v ehicles.
97
On 2012-
09-05, Uber launched UberT AXI (beta) in NY C wit h 105 Medallion taxis.
98
On 2012-10-16,
Uber ended its UberT AXI (beta) in NY C where 160 Medallion driv ers participated, claim-
89
TL C Annual R eport 2012.
90
TL C 2013 Annual R eport
91
http://www.nyc.gov/html/tlc/html/news/initiative_e_hail.shtml
92
http://www.nyc.gov/html/tlc/downloads/pdf/ehail_q5_report_final.pdf
93
https://www.goarro.com/
94
http://ridelinq.com/
95
http://techcrunch.com/gallery/a- brief- history- of- uber/
96
https://techcrunch.com/2011/05/04/uber- screenshots- video/
97
https://techcrunch.com/2012/07/01/uber- opens- up- platform- to- non- limo- vehicles- with- uber- x- service- will- be- 35- less- expensive
98
http://www.nytimes.com/2012/09/05/nyregion/as- ubers- taxi- hailing- app- comes- to- new- york- its- legality- is- questioned.
html
141
C hapter 5 Efficien cy of NY C T axi Indus tr y
ing no t enough taxis w ere a v ailable.
99
On 2013-04-30, Uber launched its TL C-appro v ed
e-hail pilo t, which an appellate judg e halted a da y later .
100
Uber had 4.5 million pickups from April t o Sep tember 2014 ( 5% y ello w cab trips).
101
Mont hl y breakup: 564516, 652435, 663844, 796121, 829275, 1028136; Dail y a v er ag e trend:
18817.2, 21046.3, 22128.1, 25681.3, 26750.8, 34271.2. A linear extr apolation back t o A ug
2013 giv es a 3k dail y pickup, 6‰ trips b y y ello w cabs, which is an o v eres timate. Uber
had 14.3 million pickups from Januar y t o June 2015, while June rides is 19.3% less t han
Uber’ s o wn s tats released on Jul 22, 2015.Uber added subs tantiall y t o t he number of f or -
hire v ehicles on t he s treet t hroughout t he da y outside t he Manhattan core and in t he o t her
f our N e w Y or k City boroughs. Uber has o v er 30 million rides since 2011, 25.9% of all Uber
rides in 2014 w ere trips t o, from, or wit hin t he outer boroughs (8.2%, 9.1%, 16.9%, 27.1%
f or 2011-2013 and 2015 till Ma y).
102
L yf t onl y s tarted oper ating in NY in late Jul y 2014, based on t he same F iv eThirtyEight
GitHub repo. By Sep tember 2014, L yf t’ s dail y trips is onl y one tent h of Uber’ s, on par wit h
some o t her FHV com panies lik e Pres tig e and Car mel.
5.5 G ame model of NY C t axi indus tr y
T o better unders tand t he e fficiency of NY C taxi indus tr y , w e sim plify t he indus tr y s tr ucture
int o a f or mal g ame model. T able 5.12 presents t he incentiv e s tr ucture of NY C taxi indus tr y .
N o t e t hat since o wner -driv ers act as bo t h ag ents and driv ers, t heir combine t he incentiv e
of taxi driv er and g ar ag e/ag ent.
The regulat or , or ultimatel y t he ma y or , ha v e man y control v ariables: t he t o tal amount
of canonical Medallion (13237 b y t he end of 2013); shif t amount of mini-fleet and indepen-
99
https://newsroom.uber.com/ubertaxi- in- nyc- shutting- down- for- now- no- changes- to- ubernyc- black- car- service/
100
https://www.theverge.com/2013/4/26/4271490/uber- becomes- first- taxi- app- to- get- approved- in- new- york- city
101
https://github.com/fivethirtyeight/uber- tlc- foil- response
102
https://newsroom.uber.com/us- new- york/4- years- moving- nyc/
142
C hapter 5 Efficien cy of NY C T axi Indus tr y
T able 5.12: Incentiv e s tr ucture of NY C taxi indus tr y
Driv er Gar ag e/A g ent Ma y or
Objectiv e 𝜋 ( s ; 𝑝) − 𝑓 − 𝑟 ∑
𝑘 𝑟 𝑘 − 𝑐 𝑃 ( reelection ∣ 𝑅 0
(𝐿, 𝑝, ̂ 𝑟 ), ⋯ )
Cons tr aints shif ts a v ailable 𝑟 𝑘 ≤ ̂ 𝑟 ; minimal
shif ts
city council (o wner); elect or ate
(passeng er)
dent Medallions. f are r ate control on taximeter ; and lease cap on taxi o wners/fleets/ag ents.
W it h t hese price controls rigorousl y enf orced, Medallion o wners (and t hus t heir ag ents)
will maximize taxicab utility (shif ts) ins tead of t o tal rent, which leads t o (tem por all y) in-
efficient use of taxicabs. The number of double-shif t taxicabs w ould ha v e increased, T o tal
indus tr y re v enue from leased taxicabs will increase. Mean while, t he mar ginal rent (equiv -
alent t o re v enue, minus cons tant labor/g as/v ehicle/insur ance cos t) on taxi suppl y will no t
be unif or m wit hin a da y , especiall y during shif t tr ansition of mos t taxicabs, 4pm-6pm; and
single shif t taxis will alw a ys w or k during shif t tr ansition hours. N o te t hat fleets ha v e been
oper ating in shif ts long bef ore TL C lease capping in 1996 (P anel, 1966 , p29-30). A possi-
ble explanation is reduced oper ational cos t on t he fleets, if shif t driv ers are concer ned; but
shif t decisions of long-ter m lessees shall no t be limited t o fleet g ar ag es.) If lease driv ers ’ real
income increases, f or exam ple increasing f are r ate while k eeping lease price unchang ed,
lease driv ers will w or k long er hours (t hat is, more intense labor suppl y).
The city go v er nment is a sla v e of its o wn creature. Medallion suppl y is less t han op ti-
mal, and e v er y Medallion sale comes wit h a f are r aise. Moreo v er , t he manag erial cos t of
g ar a g es/ag ents is a sign of inefficient ins titution.
5.6 Empiric al v alid a tion
Giv en t hat t he lease caps are onl y binding f or peak shif ts (T ue-F ri da ys, W ed-Sat nights),
ag ents/g ar ag es will ha v e incentiv e t o dela y tr ansition on t hose da ys t o mak e caps on bo t h
shif t s binding. If driv ers s till ear n more on peak shif ts, t he y will s tart ear lier in t he mor ning
143
C hapter 5 Efficien cy of NY C T axi Indus tr y
f or da y shif ts and end later int o t he night f or night shif ts. Lease driv ers alw a ys maximize
income, which equals f are deducted b y fuel cos t. Owner -driv ers will pref er t o driv e peak
shif t s and lease out shif ts wit h non-binding lease caps. A v er ag e re v enue is higher in peak
shif t s due t o limited Medallions.
Single-shif ted o wner -oper at ors will typicall y w or k in t he da y , as t he o wners ma y con-
sider t heir com port and saf ety . T o maximize rent, single shif ted taxis will w or k during
tr ansition of double-shif ted taxis, 4pm-6pm. When t he y find a partner , t he shif t will tak e
place around 5pm, matching wit h g ar ag e pr actice.
Af ter 2012-09-04 f are r aise, wit h 2012-09-30 lease cap re vision and tem por ar y res tr aining
or d er , despite reduced trip v olume, non-o wner driv ers will ha v e long er shif ts and lo w er
hour l y income increase t han could ha v e. Medallion price increases relativ el y more f or in-
dependent Medallions. N o te t hat Hurricane Sandy ma y ha v e im pact on trip v olume, 2012-
10-28 t o 11-02.
T o im pro v e taxi efficiency , Br uce Schaller sugg es ted an h ypo t hetical taxi sys tem.
103
He
no tes t hat outer -borough riders, whose needs are no t met b y medallion cabs, ha v e ready
access t o car ser vices. In Manhattan, ho w e v er , t his sys tem means t hat em p ty r adio cars
clog s treets and a v enues in t he centr al business dis trict, w aiting f or calls, e v en while it
can be difficult or im possible t o hail a y ello w cab. He sugg es ts t hat t he current “cr uising”
sys tem is no t necessaril y t he mos t efficient w a y t o match cus t omers and y ello w cabs, and
an y differentiation among different cab types w ould increase t he im portance of helping
cus t omers find t he v ehicle t he y w ant. Ideall y , taxis wit h passeng ers can use certain bus
lanes; taxi s tands ha v e been created and s taffed at ma jor tr ansportation hubs; and taxi
relief s tands, t o f acilitate driv er break s, are scattered t hroughout t he city . Similar tr affic-
separ ated lanes could also be es tablished f or taxicabs. Crime in t he city has plummeted
o v e r t he pas t decade, and as driv ers spend 8 t o 12 hours a da y sitting in t he cab, no w t he
103
http://www.schallerconsult.com/taxi/idealtaxisystem.htm
144
C hapter 5 Efficien cy of NY C T axi Indus tr y
partition mak es driv ers f eel t he y are “in a cag e” and obs tr ucts communications wit h pas-
seng ers.
104
P artitions are op tional f or o wner -driv ers who do no t lease t heir cabs and who
ins t all a security camer a. Driv er r atings could be based on acing a challenging g eog r aph y
tes t, ha ving a clean driving recor d, and/or cus t omer f eedback.
W it hout f or mal par ametrization of all possible mechanisms, here I sugg es ts an mecha-
nism f or taxi tr ansportation t hat w ould be efficient. City go v er nment shall claim t he prop-
erty rights of taxi tr ansportation wit hin its jurisdiction, and maximizes rent b y : (1) issuing
v ar ying numbers of time-limited licenses depending on demand (or city -wide tr ansporta-
tion objectiv es), so t hat license holders do no t accumulate capital or political po w er , and
double-shif ting becomes unnecessar y . (2) setting lease price and f are such t hat driv er ear n-
ing equals t heir alter nativ e income. The spatial inefficiency inherent t o s treet-hail taxi can-
no t be o v ercome, but t he dispatch model can be oper ated efficientl y . This mechanism will
s till be efficient f or municipalities sharing city limits, because mar ginal rent on t he s treets
per taxi ser vice t ime will be e qual, assuming enough driv ers are indifferent in which city t o
w or k. Such mechanism resembles T oront o ’ s 1998 “ Ambassador” course
105
, which offered
“no proper s tak e in t he indus tr y , as t he y had no v alue, did no t increase in v alue, and could
no t be sold”.
104
http://www.nytimes.com/2005/08/09/nyregion/taxi- partitions- born- of- danger- may- be- set- for- a- makeover.
html
105
http://www.toronto.ca/taxitraining/
145
Bibliography
Akamatsu, T akashi (1996). “Cy clic flo w s, Mar k o v process and s t ochas tic tr affic assignment”.
In: T r ansport ation Resear c h P art B: Met hodological 30.5, pp. 369–386.
Alonso-Mor a, Ja vier et al. (2017). “On-demand high-capacity ride-sharing via dynamic
trip-v ehicle assignment”. In: Pr oceedings of t he N ational A cadem y of Sciences 114.3, pp. 462–
467.
Anck er , CJ and A Gaf arian (1962). “Queueing wit h im patient cus t omers who lea v e at r an-
dom”. In: Journal of Indus trial Engineering 13.84-90, pp. 171–172.
Arro w , K ennet h J. and Leonid Hur wicz (1960). “S tability of t he Gr adient Process in n-
P erson Games”. In: Journal of t he Society f or Indus trial and Applied Mat hematics 8.2, pp. 280–
294.
Balaf outas, Loukas, R udolf K erschbamer , and Matt hias Sutter (Oct. 2015). “Second-Deg ree
Mor al Hazar d In A R eal- W or ld Credence Goods Mar k et”. In: The Economic Journal 127.599,
pp. 1–18.
Barrer , D. Y . (Oct. 1957a). “Queuing wit h Im patient Cus t omers and Indifferent Cler k s”. In:
Oper ations Resear c h 5.5, pp. 644–649.
– ( Oct. 1957b). “Queuing wit h Im patient Cus t omers and Or dered Ser vice”. In: Oper ations
Resear c h 5.5, pp. 650–656.
Bat or , F r ancis M. (A ug. 1958). “The Anat om y of Mar k et F ailure”. In: The Quart er l y Journal
of Economics 72.3, p. 351.
Beckmann, Martin J., C. B. McGuire, and C. B. W ins ten (1956). S tudies in t he Economics of
T r ansport ation . Originall y published in 1955 as a Rand R eport, Rand-RM-1488-PR. Y ale
U niv ersity Press.
Bell, Michael G.H. (1995). “Alter nativ es t o Dial’ s logit assignment algorit hm”. In: T r ans-
port ation Resear c h P art B: Met hodological 29.4, pp. 287–295.
Bettencourt, L uís M. A . (2013). “The Origins of Scaling in Cities”. In: Science 340.6139,
pp. 1438–1441.
Bo y ce, Da vid E., Hani S. Mahmassani, and Anna N agur ne y (2005). “A retrospectiv e on
Beckmann, McGuire and W ins ten ’ s S tudies in t he Economics of T r ansportation”. In: P a-
per s in Regional Science 84.1, pp. 85–103.
Buchholz, Nicholas (2017). “Spatial Equilibrium, Search F rictions and Efficient R egulation
in t he T axi Indus tr y”. W or king P aper .
Bur d ett, K ennet h, Shouy ong Shi, and Randall W right (2001). “Pricing and Matching wit h
F rictions”. In: Journal of P olitical Econom y 109.5, pp. 1060–1085.
Butters, Ger ar d R. (1977). “Equilibrium Dis tributions of Sales and A dv ertising Prices”. In:
The Review of Economic S tudies 44.3, pp. 465–491.
146
BIBLIOGRAPHY
Cameron, A .Colin and Pr a vin K. T riv edi (1990). “R eg ression-based tes ts f or o v er dispersion
in t he P oisson model”. In: Journal of Econometrics 46.3, pp. 347–364.
Cas tro, P ablo Samuel, Daqing Zhang, and Shi jian Li (2012). “U rban T r affic Modelling and
Prediction Using Lar g e Scale T axi GPS T r aces”. In: P erv asiv e Com puting: 10
t h
Int ernational
Conf er ence, P erv asiv e 2012, N ew cas tle, UK, June 18-22, 2012. Pr oceedings . Ed. b y Judy Ka y
et al. Ber lin, Heidelber g: Spring er Ber lin Heidelber g, pp. 57–72.
Chang, Han-w en, Y u-chin T ai, and Jane Y ung-jen Hsu (2010). “Context-a w are taxi demand
ho tspo ts prediction”. In: Int ernational Journal of Business Int ellig ence and Dat a Mining 5.1,
pp. 3–18.
Cheung, S te v en N .S. (Oct. 1998). “The tr ansaction cos ts par adigm: 1998 presidential ad-
dress w es ter n economic association”. In: Economic Inq uir y 36.4, pp. 514–521.
Coase, R. H. (1960). “The Problem of Social Cos t”. In: The Journal of La w and Economics 3,
pp. 1–44.
Cour no t, Ant oine A ugus tin (1838). Rec her c hes sur les principes mat hématiq ues de la t héorie des
ric hesses . c hez L. Hachette.
Dale y , D. J. (N o v . 1964). “Single-ser v er queueing sys tems wit h unif or ml y limited queueing
time”. In: Journal of t he A us tr alian Mat hematical Society 4.04, p. 489.
Da vis, Ott o A . and Andre w Whins t on (June 1962). “Exter nalities, W elf are, and t he Theor y
of Games”. In: Journal of P olitical Econom y 70.3, pp. 241–262.
Da vis, S tacy C, Susan W Dieg el, and R obert G Boundy (Dec. 2017). T r ansport ation Ener gy
Dat a Book . 36t h ed. O ak Ridg e N ational Labor at or y .
De ville, Pierre et al. (2016). “Scaling identity connects human mobility and social inter ac-
tions”. In: Pr oceedings of t he N ational A cadem y of Sciences 113.26, pp. 7047–7052.
Dono v an, B. and D. B. W or k (Jul y 2015). “Using coarse GPS data t o quantify city -scale
tr ansportation sys tem resilience t o extreme e v ents”. In: ArXiv e-prints .
Dono v an, Brian and Daniel B. W or k (2014). N ew Y or k City T axi T rip Dat a (2010-2013) . Dataset.
Dorfman, R obert et al. (1962). Design of W at er -Resour ce Sy s t ems: N ew T ec hniq ues f or Relating
Economic Objectiv es, Engineering Anal y sis, and Gov ernment al Planning . Har v ar d U niv ersity
Press.
Epps tein, Da vid (1998). “F inding t he k Shortes t P at hs”. In: SIAM Journal on Com puting 28.2,
pp. 652–673.
F orres ter , Ja y W right (1969). Principles of sy s t ems: t e xt and w or kbook c hap t er s 1 t hr ough 10 .
W right- Allen Press.
F rechette, Guillaume R., Alessandro Lizzeri, and T obias Salz (N o v . 2016). “F rictions in a
Com petitiv e, R egulated Mar k et: Evidence from T axis”. R&R American Economic R e-
vie w .
F udenber g, Dre w and Da vid K. Le vine (2009). “Lear ning and Equilibrium”. In: Annual
Review of Economics 1.1, pp. 385–420.
Gibbs, J W illar d (1876). “On t he Equilibrium of Heterog eneous Subs tances”. In: T r ansac-
tions of t he Connecticut A cadem y of Arts and Sciences III, pp. 108–248, 343–524.
Glaeser , Edw ar d L. (Jul y 11, 2008). Cities, A gg lomer ation, and Spatial Eq uilibrium . Oxf or d
U niv ersity Prress. 275 pp.
147
BIBLIOGRAPHY
Gonzalez, Marta C., Cesar A . Hidalgo, and Albert-Laszlo Bar abasi (June 2008). “U nder -
s tanding individual human mobility patter ns”. In: N atur e 453.7196, pp. 779–782.
Gor don, H. Sco tt (1954). “The Economic Theor y of a Common-Property R esource: The
F isher y”. In: Journal of P olitical Econom y 62.2, pp. 124–142.
Haight, F r ank A . (Dec. 1957). “Queueing wit h Balking”. In: Biometrik a 44.3/4, p. 360.
– ( Dec. 1959). “Queueing wit h reneging”. In: Metrik a 2.1, pp. 186–197.
– ( Dec. 1960). “Queueing wit h Balking. II”. In: Biometrik a 47.3/4, p. 285.
Hirshleif er , Jack , James DeHa v en, and Jerome W . Milliman (1960). W at er Suppl y : Economics,
T ec hnology , and P olicy . U niv ersity of C hicago Press.
Hodg e s, Gr aham R ussell (2007). T axi! A social his t or y of t he N ew Y or k City cabdriv er . Balti-
more: The Johns Hopkins U niv ersity Press.
K endall, Da vid G. (1951). “Some Problems in t he Theor y of Queues”. In: Journal of t he Roy al
S t atis tical Society . Series B (Met hodological) 13.2, pp. 151–185.
– ( Sep t. 1953). “S t ochas tic Processes Occurring in t he Theor y of Queues and t heir Anal ysis
b y t he Met hod of t he Imbedded Mar k o v Chain”. In: The Annals of Mat hematical S t atis tics
24.3, pp. 338–354.
Knight, F . H. (1924). “Some F allacies in t he Inter pretation of Social Cos t”. In: The Quart er l y
Journal of Economics 38.4, pp. 582–606.
K outsoupias, Elias and Chris t os P apadimitriou (1999). “W ors t-Case Equilibria”. In: S T A CS
99 . Spring er Ber lin Heidelber g, pp. 404–413.
Lagos, Ricar do (2000). “An Alter nativ e Approach t o Search F rictions”. In: Journal of P olitical
Econom y 108.5, pp. 851–873.
L ux en, Dennis and Chris tian V etter (2011). “R eal-time R outing wit h OpenS treetMap Data”.
In: Pr oceedings of t he 19
t h
A CM SIGSP A TIAL Int ernational Conf er ence on Adv ances in Geo-
gr aphic Inf ormation Sy s t ems . GIS ’11. Chica go, Illinois: A CM, pp. 513–516.
Mat he w , Bi ju (June 1, 2008). T axi! Cabs and Capit alism in N ew Y or k City . Cor nell U niv ersity
Press, p. 272. 274 pp.
Ma y or’ s Office of Oper ations (Sep t. 2017). May or’ s Manag ement Report : F iscal 2017 . T ech. rep.
City of N e w Y or k.
Meade, J. E. (Mar . 1952). “Exter nal Economies and Diseconomies in a Com petitiv e Situa-
tion”. In: The Economic Journal 62.245, p. 54.
Meier , Richar d L. (1968). “The Metropolis as a T r ansaction-Maximizing Sys tem”. In: Daedalus
97.4, pp. 1292–1313.
Mill, John S tuart (1859). On Liberty . J. W . P ar k er and Son.
Misr a, Pr atap and P er Eng e (2006). Global P ositioning Sy s t em: Signals, Measur ements, and
P erf ormance . 2
nd
. Gang a-Jamuna Press.
Monderer , Do v and Llo yd S. Shaple y (Ma y 1996). “P o tential Games”. In: Games and Eco-
nomic Beha vior 14.1, pp. 124–143.
Moreir a-Matias, L. et al. (Sep t. 2013). “Predicting T axi-P asseng er Demand Using S treaming
Data”. In: IEEE T r ansactions on Int ellig ent T r ansport ation Sy s t ems 14.3, pp. 1393–1402.
N ash, John (1951). “N on-Cooper ativ e Games”. In: Annals of Mat hematics 54.2, pp. 286–295.
148
BIBLIOGRAPHY
Nikaido, Hukukane and Kazuo Isoda (1955). “N o te on non-cooper ativ e con v ex g ames”. In:
P acific J. Mat h. 5, pp. 807–815.
P anel, Ma y or’ s T axi S tudy (Dec. 1966). Recommendations t o John V . Lindsay , May or of t he City
of N ew Y or k . T ech. rep. 54 lea v es; Benjamin Bine [and o t hers] ; John T r ubin, chair man ;
Dan T essler , direct or . City of N e w Y or k.
Phit hakkitnuk oon, Santi et al. (2010). “T axi- A w are Map: Identifying and Predicting V acant
T axis in t he City”. In: Ambient Int ellig ence: F ir s t Int ernational Joint Conf er ence, AmI 2010,
Malag a, Spain, N ov ember 10-12, 2010. Pr oceedings . Ed. b y Boris de R uyter et al. Ber lin, Hei-
delber g: Spring er Ber lin Heidelber g, pp. 86–95.
Pigou, Art hur C. (1920). The Economics of W elf ar e . 1
s t
. London: Macmillan and Co.
Pr at o, Car lo Giacomo (2009). “R oute choice modeling: pas t, present and future research
directions”. In: Journal of Choice Modelling 2.1, pp. 65–100.
R ogoff, Edw ar d G. (1980). “Theories of Economic R egulation T es ted on t he Case of t he
N e w Y or k City T axicab Indus tr y”. English. PhD t hesis. Columbia U niv ersity , p. 241.
R osen, J. B. (1965). “Exis tence and U niqueness of Equilibrium P oints f or Conca v e N-P erson
Games”. In: Econometrica 33.3, pp. 520–534.
R o t h, Al vin E. (2002). “The Economis t as Engineer : Game Theor y , Experimentation, and
Com putation as T ools f or Design Economics”. In: Econometrica 70.4, pp. 1341–1378.
R o t h, Al vin E. and Ido Ere v (1995). “Lear ning in extensiv e-f or m g ames: Experimental data
and sim ple dynamic models in t he inter mediate ter m”. In: Games and Economic Beha vior
8.1, pp. 164–212.
R oughg ar den, T im (2002). “Selfish ro uting”. PhD t hesis. It haca, N e w Y or k: Cor nell U ni-
v ersity .
Sag arr a, Oleguer et al. (A ug. 2015). “Supersam pling and N etw or k R econs tr uction of U rban
Mobility”. In: PLoS ONE 10.8.
Santi, P aolo et al. (2014). “Quantifying t he benefits of v ehicle pooling wit h shareability
netw or k s”. In: Pr oceedings of t he N ational A cadem y of Sciences 111.37, pp. 13290–13294.
Schaller , Br uce (Mar . 2006). The N ew Y or k City T axicab F act Book . T ech. rep. Schaller Consult-
ing.
– ( 2007). “Entr y controls in taxi regulation: Im plications of US and Canadian experience
f or taxi regulation and deregulation”. In: T r ansport P olicy 14.6, pp. 490–506.
– ( Dec. 2017). Em p ty Seats, F ull S tr eets: F ixing Manhatt an ’ s T r affic Pr oblem . T ech. rep. Schaller
Consulting.
Selten, R. (1970). Pr eispolitik der Mehr pr odukt enunt ernehmung in der s t atisc hen Theorie . Ök onome-
trie und U nter nehmensf orschung v . 16. Spring er - V er lag.
Shao, D. et al. (N o v . 2015). “Es timating T axi Demand-Suppl y Le v el Using T axi T r a ject or y
Data S tream”. In: 2015 IEEE Int ernational Conf er ence on Dat a Mining W or kshop (ICDMW) ,
pp. 407–413.
Sidgwick , Henr y (1883). Principles of political ec onom y . Macmillan and co.
Sil v a, Ricar do, Soong Moon Kang, and Edoar do M. Airoldi (2015). “Predicting tr affic v ol-
umes and es timating t he effects of shock s in massiv e tr ansportation sys tems”. In: Pr o-
ceedings of t he N ational A cadem y of Sciences 112.18, pp. 5643–5648.
149
BIBLIOGRAPHY
Smit h, P aul J. et al. (1981). “Appro ximating t he Moments and Dis tribution of t he Lik eli-
hood Ratio S tatis tic f or Multinomial Goodness of F it”. In: Journal of t he American S t atis ti-
cal Association 76.375, pp. 737–740.
T achet, R. et al. (Mar . 2017). “Scaling La w of U rban Ride Sharing”. In: Scientific Reports 7,
p. 42868.
T u, W ei et al. (2016). “Op timizing t he locations of electric taxi char ging s tations: A spatial–
tem por al demand co v er ag e approach”. In: T r ansport ation Resear c h P art C: Emer ging T ec h-
nologies 65, pp. 172–189.
W ang, X uesong et al. (2016). “Speed v ariation during peak and off-peak hours on urban
arterials in Shanghai”. In: T r ansport ation Resear c h P art C: Emer ging T ec hnologies 67, pp. 84–
94.
W ar drop, John Glen (1952). “Some Theoretical Aspects Of R oad T r affic R esearch”. In: Pr o-
ceedings of t he Ins titution of Civil Engineer s 1.3, pp. 325–362.
W eidlich, W olfg ang (1999). “F rom f as t t o slo w processes in t he e v olution of urban and
regional settlement s tr uctures”. In: Discr et e Dynamics in N atur e and Society 3.2-3, pp. 137–
147.
W eidlich, W olfg ang and Günter Haag (1983). Concep ts and Models of a Quantit ativ e Sociology :
The Dynamics of Int er acting P opulations . V ol. 14. Spring er Series in Syner g etics. Spring er -
V er lag.
W ilson, Alan (2010). “Entrop y in U rban and R egional Modelling: R etrospect and Prospect”.
In: Geogr aphical Anal y sis 42.4, pp. 364–394.
W ong, K.I., S.C. W ong, and Hai Y ang (2001). “Modeling urban taxi ser vices in cong es ted
road netw or k s wit h elas tic demand”. In: T r ansport ation Resear c h P art B: Met hodological
35.9, pp. 819–842.
Zhang, R uda and R og e r Ghanem (Jan. 2018). “Demand, suppl y and perf or mance of s treet-
hail taxi”. submitted t o T r ansportation R esearch P art B: Met hodological.
Zheng, Kai et al. (Apr . 2012). “R educing U ncertainty of Lo w -Sam pling-Rate T r a ject ories”.
In: ICDE 2012 . ICDE 2012.
150

Abstract (if available)

Abstract Analyzing social systems such as cities requires a set of formal methods different from those used for physical systems. Intelligent entities such as human beings act to optimize their own objectives, whose strategic decision making is constrained by rules set up in the social system. To study urban transportation systems, I propose a law-economics-engineering framework, and applies it specifically to taxicab transportation. ❧ This dissertation is effectively an institutional analysis of taxicab transportation in New York City. It comes in three parts: using models of taxi operations to estimate the spatio-temporal distribution of taxi demand and supply

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Taxi driver learns dynamic multi-market equilibrium

PDF

Silicon-based RF/mm-wave power amplifiers and transmitters for future energy efficient communication systems

PDF

Team decision theory and decentralized stochastic control

PDF

Novel queueing frameworks for performance analysis of urban traffic systems

PDF

Asymptotic analysis of the generalized traveling salesman problem and its application

PDF

Impacts of heat mitigation strategies and pollutant transport on climate and air quality from urban to global scales

PDF

Analysis, design, and optimization of large-scale networks of dynamical systems

PDF

Hierarchical planning in security games: a game theoretic approach to strategic, tactical and operational decision making

PDF

Routing problems for fuel efficient vehicles

PDF

Theory and applications of adversarial and structured knowledge learning

PDF

Efficient connectivity assessment of heterogeneous porous media using graph theory

PDF

Adaptive agents on evolving network: an evolutionary game theory approach

PDF

Integrated control of traffic flow

PDF

Developing frameworks to quantify the operational and environmental performance of energy systems within the context of climate change

PDF

Physics-based and data-driven models for bio-inspired flow sensing and motion planning

PDF

Spatiotemporal prediction with deep learning on graphs

PDF

Towards an optimal design of feedback strategies for structures controlled with smart dampers

PDF

Cathode and anode materials for sodium ion batteries

PDF

Control and optimization of complex networked systems: wireless communication and power grids

PDF

Elements of robustness and optimal control for infrastructure networks

Asset Metadata

Creator Zhang, Ruda (author)

Core Title Taxicab transportation: operations, equilibrium, and efficiency

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Civil Engineering

Publication Date 04/11/2018

Defense Date 03/01/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag economic efficiency,game theory,OAI-PMH Harvest,operations,taxicab,Urban transportation

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ghanem, Roger (committee chair), Carrillo, Juan (committee member), Savla, Ketan (committee member)

Creator Email rudazhan@gmail.com,rudazhan@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-6808

Unique identifier UC11671736

Identifier etd-ZhangRuda-6224.pdf (filename),usctheses-c89-6808 (legacy record id)

Legacy Identifier etd-ZhangRuda-6224.pdf

Dmrecord 6808

Document Type Dissertation

Rights Zhang, Ruda

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA