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USC Computer Science Technical Reports, no. 639 (1996)
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USC Computer Science Technical Reports, no. 639 (1996)

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Content A MEASUREMENTBASED ADMISSION CONTR OL ALGORITHM
F OR INTEGRA TED SER VICES P A CKET NETW ORKS
b y
Sugih Jamin
A Dissertation Presen ted to the
F A CUL TY OF THE GRADUA TE SCHOOL
UNIVERSITY OF SOUTHERN CALIF ORNIA
In P artial F ulllmen tof the
Requiremen ts for the Degree
DOCTOR OF PHILOSOPHY
Computer Science
August  Cop yrigh t  Sugih Jamin
T o m y P aren ts
for their Lo v e
Supp ort and T rust
ii
Preface
Man y designs for In tegrated Services P ac k et Net w orks  ispn oer a b ounded dela y
pac k et deliv ery service to supp ort realtime applications Net w orks ac hiev e bounded
dela y b y regulating their load and managing their resources Admission con trol al
gorithm is the to ol net w orks use to regulate their load Previous w ork on admission
con trol mainly fo cused on algorithms that compute the w orst case theoretical queue
ing dela y to guaran tee either an absolute dela y b ound for all pac k ets or a probabilistic
b ound on the statistical distribution tail of aggregate trac Since w orstcase b ounds
are computed from parameterized source mo dels w e call suc h algorithms parameter
based algorithms Our o wn w ork prop oses a me asur ementb ase d admission con trol
algorithm for pr e dictive service Instead of guaran teeing an absolute or a n umerically
enforced probabilistic b ound predictiv e service promises a r eliable bound With the
more relaxed b ound an admission con trol algorithm can op erate without requiring
a precise c haracterization of trac instead it can use measured trac c haracteris
tics The reliance of our admission con trol algorithm on measuremen t dictates that
it w orks w ell only when there is a high degree statistical m ultiplexing Sev eral re
searc hers ha v e disco v ered that net w ork trac is longrange dep enden t whic h rises
and ebbs with p ossibly long ebb times One dangerous implication of longrange
dep enden t trac on an y measuremen tbased admission con trol algorithm is that the
algorithm ma y allo w to o man y new o ws in to the net w ork during the ebb times
resulting in prolonged dela y bound violations during the ensuing tides In our sim
ulations b esides traditional source mo dels w e also use source mo dels that exhibit
longrange dep endence both in themselv es and in their aggregation As with most
iii
measuremen tbased con trol systems there are sev eral knobs that go v ern the degree
of conserv ativ eness of the measured v alues and resulting decisions W e will explore
these and also lo ok at some dynamic in teractions bet w een o ws with dieren t re
source requiremen ts W e will presen t results from a comparativ e study of sev eral
measuremen tbased admission con trol algorithms and nally conclude this disserta
tion b y p oin ting out sev eral p ossible extensions to our w ork
Appreciations
If one though t of the do ctoral program as an appren ticeship in researc h one could
hardly ask for b etter teac hers than those who taugh t and guided me I thank m y
advisor P eter Danzig for the nancial and moral supp ort o v er the past six y ears
for patien tly lling in the gaps in m y kno wledge of statistics and probabilit y and
queueing theories And I thank him for the in tellectual freedom that allo w ed me to
explore on myo wn Scott Shenk er added rigor to myw ork Tohim I o wem y anc hor
p ersp ectiv e and approac h to researc h Lixia Zhang sho w ed me ho w to scrutinize
data She taugh t me ho w to seek in w ard for answ ers and not lo ok out w ard nor
bac kw ard I also thank her for arranging the Na vy con tract that partly supp orted
m y researc h I thank Deb orah Estrin for in tro ducing me to the w orld of computer
net w orking and the real w orld of researc h John Silv ester kindly serv ed as the outside
mem ber of m y committee and help ed clarify m y presen tation Sally Flo yd and W alter
Willinger patien tly explained the in tricacies of longrange dep enden t trac to me I
w ould also lik e to thank Carolyn Hill for teac hing me ho w to write coheren tly  An y
mistak es omissions and blemishes of this w ork are of course attributable only to
me and not to an y of the illustrious masters ab o v e
I thank Allyn Romano w and Allison Mankin for supp orting m y researc h I ha v e
b eneted from discussions tec hnical and otherwise with Lee Breslau Ron F rederic k
Charley Liu and Dann y Mitzel Finally  I thank m y family and all m y other friends
for making life less dreary in these past sev en y ears I esp ecially thank John Bell
who lured me in to Computer Science and who has b een m y constan t spiritual guide
iv
Kim Korner w as a go o d teac her and a caring p erson whose un timely departure is
sorely regretted
Sp onsor Ac kno wledgemen ts
This researc h w as supp orted in part b y the Uniforum Researc h Aw ard and b y the
Oce of Na v al Researc h Lab oratory under con tract n um b er NP This
researc h also b eneted from af osr a w ard n um b er F the nsf small
scale infrastructure gran t a w ard n um ber CD A and equipmen t loan from
Sun Microsystems Inc These funds and infrastructure a w ards ga v e me great inde
p endence to pursue myideas and I am thankful for the supp ort
v
Con ten ts
Preface iii
In tro duction   T raditional Realtime Services   Deterministic Bound                              Probabilistic Bound Equiv alen t Bandwidth                 Relaxed Realtime Services   Against DelayBound                            
Unadv ertised Bound                            
Predictiv e Service                              
Measuremen tbased Admission Con trol   F ramew ork                                  
W orstcase Dela y Predictiv e Service                  
W orstcase Dela y Guaran teed Service                  
Equiv alentT ok en Buc k et Filter                      
The Admission Con trol Algorithm                    
A Simple Timewindo w Measuremen t Mec hanism   Measuremen t Pro cess                            
P erformance T uning Knobs                        
Sim ulations   Sim ulated T op ologies                            
Source Mo dels                                
P arameter Choices                            
vi
On the Viabilit y of the Algorithm   Homogeneous Sources The Singlehop Case              
Homogeneous Sources The Multihop Case              
Heterogeneous Sources The Singlehop Case              
Heterogeneous Sources The Multihop Case              
Practical Deplo ymen t Issues   Cho osing aWindo w Size                          
Cho osing a Utilization T arget                      
Structural Limitations                          
If P eak Rate is Incoming Link Bandwidth                
On Unequal Flo w Rejection Rates   Eect of Hop Coun t on Rejection Rates                  
Eect of Resource Requiremen ts on Rejection Rates          
A Quota Mec hanism                            
Comparison of Admission Con trol Algorithms   Fiv e Admission Con trol Algorithms                    
Exp onen tialW eigh ted Mo ving Av erage                  
Sim ulation Results                            
Summary and Extensions   A Better Estimator                            
Other Admission Criteria                          
Additional Issues                              
Bibliograph y  vii
List of T ables
F ort yv e Host P airs on TBone                      
Six Instan tiations of the Three Source Mo dels              
Singlehop Homogeneous Sources Sim ulation Results          
Multihop Homogeneous Sources Link Utilization            
Singlehop Single Source Mo del Multiple Predictiv e Services Link
Utilization                                  
Singlehop Multiple Source Mo dels Single Service Link Utilization  
Singlehop Multiple Source Mo dels Multiple Predictiv e Services Link
Utilization                                  
Single and Multihop All Source Mo dels All Services Link Utilization
Eect of T and L                              
Ecacy of Quota Mec hanisms                      
Benets of Measuremen tbased Quota Mec hanism            
Six Instan tiations of the Tw o Source Mo dels              
Singlehop Homogeneous Sources Sim ulation Results          
Multiplehop All Sources Sim ulation Results              
P ercen tage Comp osition of T yp e of Admitted Flo ws          
viii
List of Figures
Example of In tegrated Services P ac k et Net w ork               Statistical m ultiplexing of three o ws and their equiv alen t bandwidth
Eect of new predictiv e o w on same priorit y trac          
Eect of new predictiv e o w on lo w er priorit y trac          
Eect of a guaran teed o w on predictiv e trac            
Measuring dela y                              
Measuring rate                              
The OneLink Tw oLink and F ourLink top ologies        
The TBone top ology                            
Exp erienced dela y of exp and poo sources              
Onoff trac mo del with tok enbuc k et lter              
Eect of T on Exp erienced Dela y                    
Eect of T on Link Utilization                      
Distribution of exp erienced queueing dela y of exp sources      
Distribution of exp erienced queueing dela y of poo sources      
Distribution of exp erienced queueing dela y of poo sources      
Distribution of exp erienced queueing delayof poo sources under the
Measured Sum and b ounded dela y algorithms for dieren t utilization
target ut and dela y bound db                    
ix
Chapter  In tro duction
The tec hnical and regulatory dev elopmen ts of the past decade ha v e created the p os
sibilit y of merging digital telephon ym ultimedia transp ort and data comm unication
services in to a single In tegrated Services P ac k et Net w ork  ispn F rom an economic
p ersp ectiv e an ispn oering m ultiple service selections increases net w orks total util
ityb y matc hing services closer to application needs She  Chief among the services
required b y m ultimedia applications is b ounded dela y pac k et deliv ery  There ha v e
been man y prop osals for supp orting b ounded dela y deliv ery in pac k et net w orks see
OON FV  GAN  for a few represen tativ e examples The abilit y of bounded
dela y services to ac hiev e high utilization and also meet their service commitmen ts
dep ends crucially on their admission con trol algorithm Con v ersely  the abilityof an
admission con trol algorithm to increase net w ork utilization is ultimately constrained
b y the service commitmen ts the net w ork mak es A service mo del is a service com
mitmen ts con tract bet w een the net w ork and its users T raditional realtime service
pro vides a hard or absolute bound on the dela y of ev ery pac k et in FV  CSZ
this service mo del is called the guar ante e dor deterministic guar ante e d service When
a o w requests realtime service it m ust c haracterize its trac so that the net w ork
can mak e its admission con trol decision T ypically  sources are describ ed b y either
p eak and a v erage rates FV  or a lter lik e a tok en buc k et OON  these descrip
tions pro vide upp er b ounds on the trac that can be generated b y the source The

admission con trol algorithm for guaran teed service uses a priori c haracterizations of
sources to calculate the w orstcase beha vior of all the existing o ws in addition to
the incoming one Calculating the w orstcase dela ys ma y be v ery complex but the
underlying admission con trol principle is conceptually simple do es gran ting a new
request for service cause the w orstcase beha vior of the net w ork to violate an y dela y
bound See FV  for an example of this approac h Net w ork utilization under
this mo del is lo w when sources are burst y  Ho w ev er net w ork utilization can be in
creased if one can precisely c haracterize the oered trac suc h aswhenpla ying bac k
recorded data GKT WKZL  when o ws carry liv e burst y data ho w ev er their
trac c haracterizations m ust necessarily b e quite lo ose in that the a v erage b eha vior
of the o ws is signican tly less than the upp er b ound of the trac descriptions and
guaran teed service inevitably results in lo w utilization ZF  A service mo del that promises a more relaxed dela y b ound than guaran teed service
allo ws its admission con trol algorithm to admit more o ws and attain a higher lev el of
net w ork utilization There are man y approac hes to admission con trol that attempt to
ac hiev e higher utilization b y w eak ening the degree of reliabilityof the dela y bound F or instance the probabilistic dela y bound service describ ed in ZK  do es not
pro vide for the w orstcase scenario instead it guaran tees a b ound on the probabilit y
of lostlate pac k ets based on statistical c haracterization of trac VPV In most
cases the a priori c haracterization of o ws is based on a statistical mo del Hui  SS or on a uid o w appro ximation GAN  Kel  In this kind of approac h
eacho w is allotted an equiv alen t bandwidth that is larger than its a v erage rate but
less than its p eak rate If one can precisely c haracterize trac a priori this approac h
will increase net w ork utilization Ho w ev er w e think it will be quite dicult if not
imp ossible to pro vide accurate and tigh t statistical mo dels for eac h individual o w
F or instance the a v erage bit rate pro duced b y agiv en co dec in a teleconference will
dep end on the participan ts body mo v emen ts This cant p ossibly be predicted in
adv ance with an y degree of accuracy  Therefore the a priori trac c haracterizations
handed to admission con trol will inevitably b e fairly lo ose upp er b ounds

F or this reason w e think that me asur ementb ase d admission con trol will playak ey
role in ac hieving high net w ork utilization The measuremen tbased admission con trol
approac h adv o cated in CSZ JSZC uses the a priori source c haracterizations
only for incoming o ws and those v ery recen tly admitted it uses measuremen ts to
c haracterize those o ws that ha v e b een in place for a reasonable duration Therefore
net w ork utilization do es not suer signican tly if the trac descriptions are not tigh t
F or instance if a source describ es itself as conforming to a tok en buc k et with a rate
of  Mbps but t ypically sends at an a v erage rate of  Mbps the measuremen tbased
admission con trol approac h do es not indenitely con tin ue to set aside  Mbps for
this o w unlik e the more traditional forms of admission con trol Because it relies
on measuremen ts and source b eha vior is not static in general the measuremen t
based approac h to admission con trol can nev er pro vide the completely reliable dela y
bounds needed for guaran teed or ev en probabilistic service Ho w ev er man y real
time applications suc h as vat ivs nv and vic ha v e recen tly been dev elop ed for
pac k etswitc hed net w orks These applications can adapt to actual pac k et dela ys and
are rather toleran t of dela y b ound violations they do not need an absolutely reliable
bound F or these toler ant applications references CSZ SCZ prop ose pr e dictive
service whic h oers a fairly  but not absolutely  reliable bound on pac k et deliv ery
times The abilit y to o ccasionally incur dela y violations giv es admission con trol a
great deal more exibilit y  and is the c hief adv an tage of predictiv e service The
measuremen tbased approac hes to admission con trol can only b e used in the con text
of predictiv e service and other more relaxed service commitmen ts F urthermore when
there are only a few o ws presen t the unpredictabilityof individual o ws b eha vior
dictates that these measuremen tbased approac hes m ust be v ery conserv ativ eb y
using some w orstcase calculation for example Th us a measuremen tbased admission
con trol algorithm can deliv er signican t gain in utilization only when there is a high
degree of m ultiplexing
The use of measuremen t in admission con trol algorithm has been men tioned in
the literature prior and subsequen t to this w ork The authors of HLP GKK  for example use measuremen ts to determine admission but the admission decisions

are precomputed based on the assumption that all sources are exactly describ ed b y
one of a nite set of source mo dels This approac h is clearly not applicable to a
large heterogeneous and ev erc hanging application base and is v ery dieren t from
our approac h to admission con trol that is based on ongoing measuremen ts Using on
going measuremen ts of load in making admission decisions is suggested but not fully
dev elop ed nor explored in OON  Sev eral recen t pap ers suc h as SS AS use
measuremen t to learn the parameters of certain assumed trac distributions The
authors of DJM Floa  use measuremen t of existing trac in their calculation
of equiv alen t bandwidth In references Hir  CLG  a neural net w ork is used
for dynamic bandwidth allo cation In LCH the authors use precomputed lo w
frequency of o ws to allo cate bandwidth dynamically b y renegotiation Hardw are
implemen tation of measuremen t mec hanisms are studied in C
 W CK G  Inci
den tally  the w ork presen ted in this dissertation has been extended in DKPS to
supp ort adv ance reserv ation The authors of DKPS ha v e also replicated some of
our results on their indep enden tly dev elop ed net w ork sim ulator
Sev eral service mo dels oering ev en more lax con tractual agreementbet w een the
net w ork and its users than predictiv e service ha v e recen tly b een prop osed in the In ter
net Engineering T ask F orce  ietf The Contr ol le dlo ad service describ ed in reference
W ro  and Committe dr ate service describ ed in reference BGK  are examples of
suc h service mo dels The service they pro vide do not in general in v olv ed an adv er
tised quan titativ e service target suc h as loss rate or delaybound rather they simply
ensure that o ws are alloted some reserv ed resources and exp erience lo w queueing
dela ys The minimal commitmen t made b y these services mak es them esp ecially w ell
suited to the decen tralized and heterogeneous In ternet Our measuremen tbased ad
mission con trol algorithm can th us also be used in conjunction with these more lax
services
In summary  when dela y bound is strict one can ac hiev e high lev el of net w ork
utilization only when one has a v ery precise c haracterization of oered trac By
relaxing the strictness of the dela y bound probabilistic service mo del can increase
net w ork utilization without requiring the tigh test trac c haracterization Predictiv e

service do es not makean y assumptions on source mo dels and pro vides only reliable
not guaran teed dela y b ound Sev eral new service mo dels ha v e recen tly b een pro
p osed that oer ev en more lax con tractual agreemen t bet w een the net w ork and its
users Wesho w in this dissertation that when measuremen tbased admission con trol
algorithm is used in conjunction with services oering lax dela y b ound and predic
tiv e service in particular it can at times deliv er order of magnitude higher lev el of
net w ork utilization than those ac hiev able under parameterbased algorithm oering
guaran teed service and still main tain reliable dela y bound Earlier v ersions of this
w ork ha v e been published as references JSZC JDSZ  JDSZ  
Chapter  T raditional Realtime Services
Under the sync hronous transfer mo de  stm sources send data at a constan t bit
rate  cbr Sources with data rate higher than the constan t bit rate m ust lo w er
their qualit y either b y dropping data or queueing it for later transmission Sources
with data rate less than the constan t bit rate m ust pad their data Constan t bit
rate leads to v arying service qualit y or lo w net w ork utilization With the adv en t
of async hronous transfer mo de  a tm and on pac k etswitc hed net w orks suc h as the
In ternet sources can transmit at v ariable bit rate  vbr deliv ering constan t service
qualit y VPV  In tegrated services pac k et net w orks built on top of a tm or In ternet
tec hnology allowpac k ets from dieren t t yp es of vbr sources to b e statistically m ul
tiplexed Fig  sho ws an example of an ispn where pac k ets from traditional data
sources are m ultiplexed with pac k ets from audio and video sources The gure also
sho ws a p ossible arc hitecture of an ispn switc h consisting of a realtime sc heduler
suc h as the unied sc heduler prop osed in reference CSZ an admission con trol
algorithm and a reserv ation proto col suc hasthe rsvp resource reserv ation proto col
prop osed in Z
 By allo wing statistical m ultiplexing an ispn can increase net
w ork utilization ho w ev er with statistical m ultiplexing bursts of data could arriv e
sim ultaneously at a switc h leading to long queue and pac k et losses Whereas the
qualit y requiremen ts of traditional data trac are high throughput and short round
trip dela y  the service requiremen ts of realtime trac are short queueing dela y and

WFQ
PRIO
Guaranteed
Flows
Class 1
Class 2
Datagram
FIFO
FIFO+
FIFO
CSZ Scheduler
Admission
Controller
E
x
i
s
t
i
n
g
f
l
o
w
s
N
e
w
f
l
o
w
s
Accept
Reject
ISPN
Switch
RSVP
Figure  Example of In tegrated Services P ac k et Net w ork

small loss rate The goal of all admission con trol algorithms is to meet users qual
it y of service requiremen ts In most cases a secondary goal of an admission con trol
algorithm is to meet users requiremen ts at as high a lev el of net w ork utilization as
feasible The abilit y of an admission con trol algorithm to increase net w ork utilization
is ultimately constrained b y the service commitmen ts the net w ork mak es W e no w
lo ok at the commitmen ts dieren t service mo dels en tail and the ensuing constrain ts
put on the admission con trol algorithm
Deterministic Bound
T raditional realtime service pro vides a hard or absolute b ound on the delayof ev ery
pac k et in the literature this service mo del is called the guar ante e d service A de
terministic guaran teed service pro vides for the w orstcase requiremen ts of o ws The
w orstcase requiremen ts of o ws are usually computed from parameterized mo dels of
trac sources The source mo dels used for this computation ma y be v ery complex
but the underlying admission con trol principle is conceptually simple do es gran ting
a new request for service cause the w orstcase b eha vior of the net w ork to violate an y
dela y b ound
The admission con trol algorithms prop osed in reference KS KU OST
require sources to pro vide p eak rate c haracterization of their trac The algorithms
then c hec k that the sum of all p eak rates is less than link capacit y  If sources are
willing to tolerate queueing dela ythey can use a tok en buc k et lter instead of p eak
rate to describ e their trac The net w ork ensures that the sum of all admitted
o ws tok en rate is less than link bandwidth and the sum of all tok en buc k et depths
is less than a v ailable buer space This approac h is prop osed in L V In ZF  the authors presen ted an admission con trol algorithm for deterministic service based
on calculation of maxim um n um ber of bits b
that can arriv e from a source during
an y in terv al    b
 min  d  mo d   pe  da e
   da e    W e assume negligible pac k et size

where  is the a v eraging in terv al for a the sources a v erage rate and p is the sources
peak rate Queueing dela y p er switc h is then calculated as
D
 max
   f
P
n
i b
i
    g
   b eing the link bandwidth The admission con trol c hec ks that D
do es not violate
an y dela y b ounds This algorithm p erforms b etter than those requiring peak rate
c haracterization and can ac hiev e acceptable   ! link utilization when sources
are not v ery burst y p eaktoa v erage ratio   and the dela y bound is not to o
tigh t    ms per switc h when o ws are burst y  ho w ev er deterministic service
ultimately results in lo w utilization In references Gol  RD  the authors pro
pose reshaping users trac according to net w ork resources a v ailable at call setup
time While reshaping users trac according to a v ailable resources ma y increase
net w ork utilization the reshap ed trac ma y not meet users endtoend qualit y re
quiremen ts Instead of imp osing a trac shap er at call setup time authors of ref
erences GKT  WKZL  prop ose c haracterizing dieren t segmen ts of a realtime
stream and renegotiating the o ws resource reserv ation prior to the transmission of
eac h segmen t Renegotiation failure results in trac from the next segmen t to be
reshap ed according to reserv ations already in place for the o w This sc heme maybe
applicable to videoondemand application where the en tire data stream is a v ailable
for a priori c haracterization prior to transmission
Probabilistic Bound Equiv alen t Bandwidth
Statistic al multiplexing is the in terlea ving of pac k ets from dieren t sources where the
instan taneous degree of m ultiplexing is determined b y the statistical c haracteristics
of the sources Con trast this to slotted Time Division Multiplexing TDM for
example where pac k ets from a source is serv ed for a certain duration at xed in terv als
and the degree of m ultiplexing is xed b y the n um ber of sources that can be ted
in to an in terv al The probabilit y densit y function  p df of statistically m ultiplexed
indep enden t sources is the con v olution of the individual p dfs and the probabilit y

Oil
Vinegar
Water
statistical
multiplexing
μ
equivalent
bandwidth
peak-rate
allocation
Figure  Statistical m ultiplexing of three o ws and their equiv alen t bandwidth
that the aggregate trac will reac h the sum of the p eak rates is innitesimally small
e m uc h smaller than the loss c haracteristics of ph ysical links A tm net w ork
for example has a loss probabilit y of ein whic h case guaran teeing a e loss
rate at the upp er la y er is sucien t VPV  Hence net w orks that supp ort statistical
m ultiplexing can ac hiev e higher lev el of utilization without sacricing m uc h on qualit y
of service
Pr ob abilistic guaran teed service exploits this statistical observ ation and do es not
pro vide for the w orstcase sum of p eak rates scenario Instead using the statistical
c haracterization of the curren t and incoming trac it guaran tees a bound on the
probabilit y of lost pac k ets
Probaggregate trac  a v ailable bandwidth   where  is the desired loss rate In en vironmen ts where the a v ailable bandwidth is
a p ortion of link capacit y alloted to realtime trac and realtime trac is allo w ed
to use the remaining bandwidth during o v ero w  simply b ounds the o v ero w rate
W e do not mak e the distinction b et w een loss rate and o v ero w rate in the remainder
of this dissertation The aggregate trac of the statistically m ultiplexed sources
is called the e quivalent b andwidth or ee ctive b andwidth or e quivalent c ap acity of
the sources WKFR  Rob  In Fig  w e sho w the statistical m ultiplexing of
the three o ws water vine garand oil and their bandwidth requiremen ts according

to p eak rate allo cation and equiv alen t bandwidth Using the equiv alen t bandwidth
metho d to compute the bandwidth requiremen t of the three o ws w e decide that
they can b e serv ed b y a link with capacit y   Whereas if w e consider only p eak rate
allo cation w ew ould not ha v e admitted all three o ws in to the net w ork F or switc hes
with buer the probabilistic b ound can be form ulated as
Probaggregate trac a v ailable bandwidth   buer   where  is atime in terv al
W e no w lo ok at the dieren t approac hes used to compute equiv alen t bandwidth
Let X
it
be the instan taneous arriv al rate of o w i at time t Assume that X
it
s are
indep enden t iden tically distributed Let S
t
P
n
i
X
it
be the instan taneous arriv al
rate of n o ws W e w an t S
t
suc h that
Prob S
t
  where  is the link bandwidth S
t
can b e computed directly from aggregate trac or
b y summing up X
it
i   n  If the switc h has buer w e can dene X
i
to b e the
instan taneous arriv al rate of o w i during time p erio d   X
i
s are again assumed
to be indep enden t iden tically distributed Let S
 P
n
i
X
i
be the instan taneous
arriv al rate of n o ws And w e w an t S
suc h that
Prob S
    B    where B is the buer size
Bernoulli T rials In references RS  SS the authors mo del X
i
as Bernoulli
random v ariables The aggregate arriv al rate is then the con v olution of the Bernoulli
v ariables The b ound on buer o v ero w probabilityo v er  can b e calculated as

P
           
n
  P
 
   
n
   
where  is the n um ber of bits   j
  is the probabilit y that  bits arriv ed from source
j   denotes con v olution and
 j
 
         if        if     otherwise
Binomial Distribution The n um ber of arriv als in a sequence of Bernoulli trials
has a binomial distribution Assuming sources are homogeneous t w ostate Mark o v
pro cesses the con v olution in Eqn  reduces to a binomial distribution KS
RSKJ  MSST  The bound on buer o v ero w probabilit y b ecomes

P
n
i C
 i iC    nm
where   i is the binomially distributed probabilit y that i sources are activ e
 i
n
i
 i
   n i
 and  is the probabilit y of success in a Bernoulli trial This computation results in
o v erestimation of actual bandwidth for sources with short burst p erio d b ecause the
buer allo ws short bursts to be smo othed out and the appro ximation do es not tak e
this smo othing eect in to accoun t GAN In ZK  instead of a single binomial
random v ariable the authors used a family of timein terv aldep enden t binomial ran
dom v ariables ie asso ciated with eac h time in terv al is a binomial random v ariable
that is sto c hastically larger than the actual bit rate generated This metho d of mo d
eling bit rate w as rst prop osed b y the author of reference Kur It allo ws a tigh ter
bound on S
 The main dra wbac k of mo deling S
with binomial distribution is the
cost of con v oluting the arriv al probabilities of heterogeneous sources In ZK  for
example the authors suggest using the F ast F ourier T ransform FFT to calculate
the con v olution FFT has a complexit y of " n
b
B log
b
B  where n is the n um ber of
sources and
b
B the size of the largest burst from an y source F urthermore when the

n um ber of sources m ultiplexed is small this appro ximation of equiv alen t bandwidth
underestimates the actual requiremen t RSKJ
Fluido w Appro ximation A uido wmodel c haracterizes trac as a Mark o v
mo dulated con tin uous stream of bits with p eak and mean rates Let b c be the equiv
alen t bandwidth of a source as seen b y a switc h computed using the uido w
appro ximation In GAN b c is computed using
b c  n     p  B
q
n     p  B    Bn     p
n       where  is the sources utilization a v eragep eak p the sources p eak rate   ln    and B the switc hs buer size This appro ximation assumes o ws are not
v ery burst y and ha v e short a v erage burst p erio d
When o ws do not conform to
this assumption the bandwidth requiremen t is o v erestimated GAN Equiv alen t
bandwidth for more general source mo dels ha v e also be computed see for example
references AMS Mit  EM Kel  KW C  MP  Computing the equiv a
len t bandwidth of a source using this metho d dep ends only on the o ws uido w
c haracteristics and not on the n um ber nor c haracteristics of other existing o ws The
computation of equiv alen t bandwidth for general sources ho w ev er is computationally
exp ensiv e  O  n
 is quoted in Mit  where n is the n um ber of sources
Gaussian Distribution In references VPV LPP GAN Sai  AS
SRLL  S
t
is appro ximated with a Gaussian distribution Let
b
C
G
be the equiv
alen t capacit y of the aggregate trac Giv en a desired loss rate reference GAN
computes C
G
using
C
G
     where    q
ln     ln      P
n
i a
i
and    P
n
i
 i
where  and   are the a v erage and v ariance of the aggregate trac resp ectiv ely and a
i
and   i
are
The length of a burst is measured relativ e to the buer size of a switc h

those of eac h source Hence the C
G
bounds the righ t tail of the Gaussian distri
bution This appro ximation trac ks the actual bandwidth requiremen t w ell when
there is a large n um ber of sources eg more than  homogeneous sources with
long burst p erio d When only a small n um ber of sources are m ultiplexed this ap
pro ximation o v erestimates the required bandwidth It also o v erestimates required
bandwidth when sources ha v e short bursts b ecause short bursts are smo othed out b y
the switc h buer and the appro ximation do es not tak e this in to accoun t The authors
of reference GG  use the minim um of the uido w and Gaussian appro ximations
b
C  min f     P
n
i
b c
i
g in making admission con trol decisions
Large Deviation Appro ximation Originally prop osed b y the author of reference
Hui  an appro ximation based on the theory of large deviation w as later generalized
in reference Kel  to handle resource with buer The theory of large deviation
b ounds the probabilit y of rare ev en ts o ccuring In this case the rare ev en t is S
t
 The appro ximationn in references Hui Kel  are based on the Cherno s b ound
while the one in Floa  is based on the Ho edings bound The Ho edings b ound
do es not require that X
it
b e indep endentof X
it    Equiv alen t bandwidth computed
using the Ho edings b ound is giv en b y
C
H
 fp
i
g
 i n
 
s
ln   P
n
i
p
i
    where  is the a v erage arriv al rate of the aggregate trac and p
i
source is p eak rate
F urther approac hes to admission con trol based on the theory of large deviation are
presen ted in references dVKW CT EMW  P oisson Distribution The ab o veappro ximations of equiv alen t bandwidth all as
sume high enough degree of statistical m ultiplexing When the degree of statis
tical m ultiplexing is lo w or when buer space is small appro ximations based on
Gaussian distribution and theory of large deviation o v erestimate required bandwidth
GAN  AS Floa  while appro ximations using b oth uido wc haracterization
and binomial distribution underestimate it Fil  NRSV  RSKJ In suc h cases

the authors of references RSKJ  Fil  suggest calculating equiv alen t bandwidth
b y solving for an MD   B queue assuming P oisson arriv als
Measuremen tbased Eac h approac h to compute equiv alen t bandwidth ab o vecan
be appro ximated b y using measuremen t to determine the v alues of some of the pa
rameters used In reference SS the authors prop oses measuring the con v olution
of arriv al probabilities used in Eqn  instead of computing them

P
k
k  t  b
n  k  P
k  k b    n  k   where b  is the measured arriv al probabilities of existing trac and   n
the arriv al
probabilit y of the prosp ectiv e source The authors of reference dVKW prop ose
measuring the eectiv e bandwidth of eac h source while the authors of references
AS DJM prop ose measuring the mean and v ariance of trac assuming it has
a Gaussian distribution Giv en the unreliable nature of measuremen t the authors of
reference DJM  further pro vide an estimate of the measuremen t errors In reference
Floa  the author prop oses using measured arriv al rates in the computation of
equiv alen t bandwidth based on the Ho edings b ound
b
C
H
b  fp
i
g
 i n
 b  
s
ln   P
n
i  p
i
    In reference LCH the authors prop ose measuring the sp ectral densit y of traf
c Bandwidth is pro visioned according to the lo w frequency of trac and buer
space according to the high frequency  The authors further suggest using a resource
renegotiation metho d similar to the one men tioned in Section  to increase net w ork
utilization This approac h is app ealing ho w ev er it is not clear what should the cuto
frequency b e and ho w trac sp ectral densit y can be computed online
Tw o other metho ds to estimate equiv alen t bandwidth are sp ecically suited to
measuremen tbased approac h The rst is based on the Ba y esian Estimation metho d
F rom a giv en initial load and a set of recursiv e equations one can estimate fu
ture load from successiv e measuremen ts This approac h is presen ted in references

W CK G GKK  The authors of reference W CK G  further describ e a hardw are
implemen tation of the measuremen t mec hanism The second metho d is a tabledriv en
metho d An admissible r e gion is a region of space within whic h service commitmen ts
are satised The space is dened b y the n um ber of admitted o ws from a nite set
of o w t yp es The rst approac h to compute an admissible region uses sim ulation
DTVV HLP DLM  F or a giv en n um ber of o ws from eac h o w t yp e sim
ulate ho w man y more o ws of eac h t yp e can be admitted without violating service
commitmen ts Running suchsim ulations rep eatedly with a dieren t set of initial o w
mix one ev en tually maps out the admissible region for the giv en o w t yp es The
admissible region is enco ded as a table and do wnloaded to the switc hes When a
prosp ectiv e o w mak es a reserv ation the admission con trol algorithm lo oks up the
table to determine whether admittance of this o w will cause the net w ork to op erate
outside the admissible region if not the o w is admitted The ma jor dra wbac ks of
this metho d for doing admission con trol are  it supp orts only a nite n um ber
of o w t yp es and  the sim ulation pro cess can be computationally in tensiv e The
authors of reference GKK  use a Ba y esian metho d to precompute an admissible
region for a set of o w t yp es The admissible threshold is c hosen to maximize the
rew ard of increased utilization against the p enalt y of lost pac k et The computation
assumes kno wledge of link bandwidth size of switc h buer space o ws tok en buc k et
lter parameters o ws burstiness and the desired loss rate it also assumes P oisson
call arriv al pro cess and indep enden t exp onen tially distributed call holding times
Ho w ev er the authors of GKK  claim that this algorithm is robust against uctu
ations in the v alue of the assumed parameters The measuremen tbased v ersion of
this algorithm ensures that the measured instan taneous load plus the peak rate of a
new o w is b elo w the admissible region The authors of references Hir  CLG
use a neuralnet w ork to learn the admissible region for a giv en set of o w t yp es In
Chapter  w e presen t a comparativ e study of a couple of the measuremen tbased
admission con trol algorithms presen ted in this section next to our o wn

Chapter  Relaxed Realtime Services
T raditional realtime service mo dels ha v e been designed on t w o assumptions rst
trac sources can be w ell c haracterized b y Mark o v c hains and second receiv ers re
quire rigid dela y b ound Recen t studies sho w that net w ork trac exhibits longrange
dep endence a phenomenon not consisten t with the rst assumption Longrange
dep endence has b een observ ed in isdn trac MH
 telephone trac DMR W
lo calarea ethernet trac L TWW widearea In ternet trac PF KM w orld
widew eb trac CB video trac BSTW  GW  and audio trac Floa  Longrange dep enden t trac has been sho wn to eect queue beha vior and loss rate
L W ENW  GB  and its cause has b een traced bac k to source pro cesses with
hea vytailed on andor off times distributions WTSW  PK C  Floa  As to
the second assumption recen t realtime applications sp ecically designed for the In
ternet suc has the vat ivs nv and vic teleconferencing programs can buer receiv ed
pac k ets and adjust their pla ybac k p oin t to adapt to exp erienced dela y  Giv en suc h
adaptive playb ack applications the net w ork is not required to pro vide absolute dela y
bound This relaxation of dela y bound enables the net w ork to further increase uti
lization Recognizing the ab o v e t w o trends and the heterogeneous and decen tralized
nature of the In ternet sev eral relaxed realtime service mo dels ha v e b een prop osed
in the literature W e review them in the remainder of this c hapter

Against Dela y Bound
There is only one service mo del a v ailable on the currentIn ternet the b esteort ser
vice mo del Under this mo del neither pac k et deliv ery time nor loss rate is b ounded
Some researc hers b eliev e that there will be suc h abundance of net w ork bandwidth
in the future that this service mo del will be sucien t to supp ort realtime trac
Without adding extra mec hanism that will only slo w do wn pac k et transmission the
net w ork can attain high lev el of utilization b y admitting all oered o ws users dis
satised with net w ork p erformance can lea v e the net w ork resulting in b etter p erfor
mance for those who remain W C  Where net w ork bandwidth is not in abundance
applications should be written to adapt to a v ailable bandwidth Applications that
can gracefully adapt to heterogeneous en vironmen t are more robust and will surviv e
those that cannot Hui  Aside from the abilit y of video sources to adapt their com
pression ratio to a v ailable bandwidth Cha GG  YH GV  W C KMR
V C video sources can also be hierarc hically enco ded in to separate lev els In ref
erences MJV HS eac h lev el of the hierarc hically enco ded data is transmitted
as a separate o w under the con trol of receiv ers Dep ending on a v ailable bandwidth
and receiv er in terest more or few er lev els are actually transmitted The abilit y of
applications to adapt to a v ailable bandwidth th us further ob viate the need for the
net w ork to guaran tee a dela y bound Next w e question the meaning of a dela y b ound Giv en the heterogeneous decen
tralized and nondeterministic nature of the In ternet is it ev en realistic to exp ect
the net w ork to guaran tee a dela y bound If a o w is routed through a p ortion of
the In ternet that do es not supp ort dela y b ound the guaran tees pro vided b y the rest
of the path b ecomes con tractually unenforceable Suc h routing could happ en either
at o w setup time or during the o ws lifetime F urthermore ho w should the dela y
bound at eac h switc h be c hosen Assuming appropriate p erhop bounds one still
has to determine the endtoend dela y bound is this to be a simple sum of the per hop b ounds Finally  if net w ork trac is indeed longrange dep enden t trac tides
happ en when sources burst sim ultaneously at whic h time the most eectiv e con trol
is to ensure sucien t bandwidth lac k of whic h will result in buer o v ero w for an y

reasonable buer sizes The purp ose of buer space in switc hes is merely to hold
pac k ets that arriv e sim ultaneously b ecause they w ere jostled a bit in upstream
switc hes not to reshap e trac tide Floa  LCH Except on net w orks where
o ws are isolated from eac h other b y means of a w eigh ted fair queue for example
and buer space is allo cated for w orstcase requiremen ts dela y bound is inheren tly
unenforceable
Related to the question of howto pro vision for longrange dep enden t trac is ho w
to c ho ose the tok en buc k et lter parameters to c haracterize a source If longrange
dep endence in aggregate trac is caused b y onoff sources with innite v ariance
on times for all buc k et depths one c ho oses there is a longer on time than what the
c hosen buc k et depth can accommo date F urthermore unless one is willing to tolerate
long queues at the tok en buc k et lters o ws m ust b e assigned tok en rates v ery close
to their peak rates If o ws are reserv ed bandwidth close to their peak rates there
will not b e long queueing dela y an yw a y   Unadv ertised Bound
While assuming innite bandwith giv es us a simple net w ork arc hitecture that is v ery
app ealing it is still to b e determined whether there really will b e suc h abundance of
bandwidth in the future A more conserv ativev ersion of the ab o v e mo del allowusers
to reserv e a minim um bandwidth for eac h o w trac exceeding this minim um rate
comp etes for the remaining capacit y  The admission con trol algorithm c hec ks that the
sum of bandwidth requested do es not exceed link capacit y  Eac h o w ma y increase
its transmission rate un til it receiv es congestion feedbac k from the net w ork Up on
congestion the o w throttles bac k its oered load accordingly do wn to the minim um
bandwidth reserv ed KMR  W C Alternativ ely  one could mak e reserv ations to
ensure that the base lev el of an hierarc hically enco ded stream will be successfully
transmitted The service mo dels discussed in this section recognizes the need of
ev en adaptiv e applications to sometimes ha v e some resources reserv ed Conceding
the dicult y of guaran teeing dela y b ound as raised in the previous section ho w ev er
they do not pro vide a con tractually strict dela y b ound

The c ontr ol le dlo ad service mo del dened in reference W ro  tigh tly appro xi
mates the b eha vior visible to applications receiving b esteort service under unlo ade d
c onditions o v er the same path F urthermore applications requesting con trolled
load service ma y assume that its pac k et loss rate is on the order of the transmission
mediums error rate and that its t ypical exp erienced dela y should be on the order
of the paths transmission and propagation dela ys More sp ecically a v erage pac k et
queueing dela y should be no greater than the o ws burst time and there should
be minimal loss rate a v eraged o v er timescales larger than burst timewhere the
burst time is dened as the time required to serv e a o ws maxim um burst at the
o ws reserv ed rate F or a o w describ ed b y a tok en buc k et lter the burst time
is br  where b is the tok en buc k et depth and r its replenishmen t rate Switc hes
ensures adequate resources b y doing admission con trol While the sp ecication of
con trolledload service do es not dictate sp ecic quan titativev alues for service param
eters suc h as dela y bound or loss rate op erationally the admission con trol decisions
m ust still be computed and ev aluated based on meeting one or b oth of these con
strain ts In Chapter  w e in v estigate v e admission con trol algorithms that could
supp ort con trolledload service
The c ommitte d r ate service mo del describ ed in reference BGK  pro vides re
source reserv ation as in guaran teed service but without an y dela y or loss guaran
tee nor the abilit y to precompute endtoend dela y  Committedrate diers from
con trolledload service in that it allo ws for trac p olicing and reshaping thereb y
more closely em ulates a dedicated circuit
Predictiv e Service
Adaptiv e pla ybac k applications do not require an absolute dela y bound ho w ev er
they ma y still prefer an upp er bound on the tail of their dela y distributions Ev en
if the dela y distribution has a v ery small median it ma y be useful to some applica
tions to ha v e a b ounded w orstcase A small dynamic range of a parameter should
not be confused with the uselessness of that parameter F urthermore applications
using the net w orks ma y ha v e dieren t lev els of dela y b ound tolerance b y pro viding

dieren tlev els of realtime service with order of magnitude dierence in dela y b ound
a net w ork can increase its p ortion of realtime trac While the heterogeneous and
decen tralized nature of the In ternet do es p ose an implemen tation problem for services
pro viding dela y b ound predictiv e service can nev ertheless b e implemen ted on priv ate
in ternet w orks or commercial p ortions of the In ternet
Unlik e the con trolledload and committedrate service mo dels predictiv e service
oers a dela y b ound Nev ertheless predictiv e service diers in t w o imp ortan t w a ys
from traditional guaran teed service  the service commitmen t is somewhat less
reliable  while predictiv e service requires that sources be c haracterized b y tok en
buc k et lters at admission time the b eha vior of existing o ws is determined b y mea
suremen t rather than b y a priori c haracterizations It is imp ortantto k eep these t w o
dierences distinct b ecause while the rst is commonplace the second ie the use
of me asur ementb ase d admission con trol is more no v el On the reliabilityof service
commitmen t w e note that the denition of predictiv e service itself do es not sp ecify
an acceptable lev el of dela y violations This is for t w o reasons First it is not par
ticularly meaningful to sp ecify a failure rate to a o w with a short duration NK
Second reliably ensuring that the failure rate nev er exceeds a particular lev el leads
to the same w orstcase calculations that predictiv e service w as designed to a v oid In
stead the csz approac h prop oses that the lev el of reliabilitybe a con tractual matter
bet w een a net w ork pro vider and its customersnot something sp ecied on a p ero w
basis W e presume that these con tracts w ould only sp ecify the lev el of violations o v er
some large time scale eg da ys or w eeks rather than o v er a few h undred pac k et
times
Hence the bound oered b y predictiv e service is not a probabilistic bound Probabilistic b ounds as discussed in Section  are based on the statistical c harac
terizations of the trac Under probabilistic service a o w can request an y amoun t
of bandwidth and thereb y exibly tune its resultan tdela y b ound or statistical loss
rate In con trast the dela y b ounds for predictiv e service are less exible eac h switc h
has a few predictiv e service classes whic h ha v e preestablished target dela y b ounds
A net w ork pro vider migh t promise to giv e its customers their money bac k if dela y violations
exceed some lev el o v er the duration of their o w no matter ho w short the o w ho w ev er wecon tend
that the pro vider cannot realistically assure that excessiv e violations will nev er o ccur

These b ounds will t ypically be c hosen to be roughly an order of magnitude apart
Prosp ectiv e o ws can c ho ose whic h class of predictiv e service they desire based on
the dela y b ound they can tolerate The v alidit y of these bounds are assessed when
making admission con trol decisions based on actual measured c haracteristics of traf
c rather than the theoretical w orstcase beha vior Since our measuremen tbased
admission con trol algorithm do es not rely on preexisting measuremen ts or computa
tions suc h as the ones in Section  predictiv e service is not limited to serv e only
a small and w ellc haracterized set of trac sources

Chapter  Measuremen tbased Admission
Con trol
Our admission con trol algorithm consists of t w o logically distinct asp ects The rst
asp ect is the set of criteria con trolling whether to admit a new o w these are based
on an appro ximate mo del of trac o ws and use measured quan tities as inputs The
second asp ect is the measuremen t pro cess itself whic hw e will describ e in Chapter  In this c hapter w e presen t the analytical underpinnings of our admission con trol
criteria
F ramew ork
Weha v e studied the b eha vior of our admission con trol algorithm mostly under the csz
sc heduling discipline CSZ  ho w ev er w e b eliev e that the observ ations w e made on
our measuremen tbased admission con trol algorithm and our metho dology for study
ing suc h an algorithm apply equally to other sc heduling disciplinesfor example in
Chapter  w e apply our metho dology and observ ations in studying sev eral admis
sion con trol algorithms for the con trolledload service mo del While w e b eliev e that
most future realtime applications written for async hronous pac k et switc hed net w orks
will be adaptiv e pla ybac k applications w e do not discoun t the need for guaran teed

service In the csz sc heme guaran teed service is pro vided b y the w eigh ted fair queue
ing  wf q algorithm describ ed in DKS also kno wn as the generalized pro cessor
sharing  gps algorithm in PG Wf q assigns a share of link capacit y to eac h
activ e o w the admission con trol criterion is merely that the sum of the previously
assigned bandwidths plus the bandwidth requested b y the prosp ectiv e o w do es not
exceed link capacit y  The sc heduling discipline for predictiv e service is a priorit y
queue as describ ed in CSZ the sc heduler attempts to minimize the maximal
minimax dela ys actually exp erienced in eac h class but do es not guaran tee an ab
solute maxim um dela y b ound Because of the minimax sc heduler w e exp ect that for
the same amoun t of bandwidth reserv ed predictiv e service users will see lo w er dela y
than guaran teed service users Under the csz mo del a switc h can supp ort m ultiple
lev els of predictiv e service eac h with its o wn dela y b ound Ween vision that the dela y
b ounds of dieren tlev el of predictiv e service will b e on the order of magnitude apart
In our sc heme the admission con trol algorithm at eachswitc h enforces the queueing
dela y b ound at that switc h assuming innite buer space Welea v e the satisfaction
of endtoend dela y requiremen ts to the end systems An end system could for ex
ample use adaptiv e source routing suc h as the one prop osed in reference Bre to
select a route that satises its endtoend requiremen ts W e also assume the existence
of a reserv ation proto col suc has the one in Z
 whic h the end systems could use
to comm unicate their resource requiremen ts to the net w ork W e require that there
b e comp elling incen tiv es suc has qualit y of service based pricing eg CESZ for
users to alw a ys request the least costly qualit y of service satisfying their needs
Sources requesting service m ust c haracterize the w orstcase b eha vior of their o w
In CSZ this c haracterization is done with a tok en buc k et lter A tok en buc k et
lter for a o w has t w o parameters its tok en generation rate r  and the depth of its
buc k et b ie no more than b tok ens can be accum ulated Eac h tok en represen ts a
single bit sending a pac k et consumes as manytok ens as there are bits in the pac k et
Without loss of generalit y  in this study weassumepac k ets are of xed size and that
eac h tok en is w orth a pac k et sending a pac k et consumes one tok en Ao w is said to
conform to its tok en buc k et lter if no pac k et arriv es when the tok en buc k et is empt y  
When the o w is idle or transmitting at a lo w er rate tok ens are accum ulated up to
b tok ens Th us o ws that ha v e b een idle for a sucien tly long period of time can
dump a whole buc k et full of data bac k to bac k F or constan t bit rate sources one
can set the tok en rate r  to the p eak trac generation rate and let the buc k et depth
b be  In this case the tok enbuc k et lter precisely c haracterizes the trac coming
out of the sender Man y nonconstan t bit rate sources do not naturally conform to a
tok en buc k et lter with tok en rate less than their p eak rates The user then should
pic k a tok en buc k et lter whic h lo oks lik e a reasonable upp er b ound on its b eha vior
It is conceiv able that future realtime applications will ha v e a mo dule that can o v er
time learn a suitable r and b to b ound their trac
When admitting a new o w not only m ust the admission con trol algorithm
decide whether the o w can get the service requested but it m ust also decide if ad
mitting the o w will prev en t the net w ork from k eeping its prior commitmen ts Let
us assume for the momen t that admission con trol cannot allo w any dela y viola
tions Then the admission con trol algorithm m ust analyze the w orstcase impact
of the newly arriving o w on existing o ws queueing dela y  Ho w ev er with burst y
sources where the tok en buc k et parameters are v ery conserv ativ e estimates of the
a v erage trac dela ys rarely approac h these w orstcase b ounds T o ac hiev e a fairly
reliable b ound that is less conserv ativ e w e appro ximate the maximal dela y of pre
dictiv e o ws b y replacing the w orstcase parameters in the analytical mo dels with
measured quan tities W e call this appro ximation the e quivalent token bucket lter  This appro ximation yields a series of expressions for the exp ected maximal dela y
that w ould result from the admission of a new o w As men tioned ab o v e in the csz
arc hitecture switc hes serv e guaran teed trac with the w eigh ted fair queueing  wf q sc heduling discipline and serv e predictiv e trac with priorit y queueing Hence the
computation of w orstcase queueing dela y is dieren t for guaran teed and predictiv e
services In this c hapter w e will rst lo ok at the w orstcase dela y computation of
predictiv e service then that of guaran teed service F ollo wing the w orstcase dela y
computations w e presen t the equiv alen t tok en buc k et lter W e close this c hapter

b y presen ting the details of the admission con trol algorithm based on the equiv alen t
tok en buc k et lter appro ximations
W orstcase Dela y Predictiv e Service
T o compute the eect of a new o w on existing predictiv e trac w e rst need a mo del
for the w orstcase dela y of priorit y queues Cruz in Cru  deriv ed a tigh t b ound
for the w orstcase dela y  D
j
of priorit y queue lev el j  Our deriv ation follo ws P arekhs
P ar whic h is a simpler but lo oser b ound for D
j
that assumes small pac k et sizes
ie the transmission time of eac h pac k et is sucien tly small as compared to other
dela ys and hence can be ignored This assumption of small pac k et sizes further
allo ws us to ignore dela ys caused b y the lac k of preemption F urther w e assume
that the aggregate rate aggregated o v er all trac classes is within the link capacit y
P
r
j
  Theorem  Par ekh Par The worstc ase class j delay with fif o discipline within
the class and assuming innite p e ak r ates for the sour c es is
D
j
P
j
i b
i
 P
j   i
r
i
for e ach class j F urther this delay is achieve d for a strict priority servic e discipline
under which class j has the le ast priority
Pro of Let j be the session with the lo w est priorit y at the rst switc h from the
source of j  Session j dumps a buc k et full of data at time t
 Werstpro v e that the
dela y seen b y the last bit of session j s buc k et is Eqn  W e then pro v e that this
dela y is the w orstcase dela y   Case  All higher priorit y sessions also dump their buc k et full of data at time
t
 Session j s queue is empt y  After dumping their buc k et full of data the higher
priorit y sessions con tin ue sending at their resp ectiv e tok en rate r
i
  i  j    In terested readers ma y also refer to P ar  Theorem  for an alternate pro of

The rst bit of data from session j s buc k et will b e serv ed only after all the pac k ets
of higher priorit y sessions ha v e been serv ed The n um ber of accum ulated higher
priorit y pac k ets is
P
j   i b
i
since all the higher priorit y sessions con tin ue sending at
their resp ectiv e rate after dumping their buc k et full of pac k ets the bandwidth left to
serv e
P
j   i b
i
is   P
j   i
r
i
Th us the rst bit of session j s buc k et will b e serv ed at
time
t
s
t

P
j   i
b
i
 P
j   i r
i
T o determine the queueing dela y exp erienced b y the last bit of session j s pac k et
w e rst determine ho w long it tak es to drain b
j
at the source In the w orst case
scenario session j has innite amoun t of data to transmit The buc k et drain rate is
then C
j
the transmission rate of session j s source Since the buc k et is replenished
at rate r
j
ittak es  j
time to drain the buc k et Note that w e ha v e accoun ted for the
buc k et replenishmentrate here
During session j s buc k et draining time it sends C
j
j
amoun t of data on to the
net w ork It tak es
C
j
j
 P
j   i r
i
time to serv e this data But since the last bit of session j s pac k et do es not arriv ed
un til time  j
and  r
j
the dela y seen b y the last bit of session j s pac k et is only
aected b y the size of the sessions buc k et size Hence Eqn  Wenowpro v e that Eqn  is the maximal dela yseenb y all session j s pac k ets
Case  If session j s queue is not empt y at time t
 Some higher priorit y session
m ust ha v e dump ed their data b efore t
 Since r
j
  P
j   i r
i
session j s queue
could not ha v e been longer than the amoun t of higher prioritypac k ets serv ed b efore
t
 Th us the rst bit of session j s buc k et will see service earlier than t
s
of Eqn  Case  Some higher priorit y sessions dump their data b efore t
 and session j s
queue is empt y at time t
 The rst bit of session j s buc k et will again see service
earlier than t
s
of Eqn  
Case  Some upp er priorit y sessions dump their data after t
 This case reduces
trivially to the case when all of them dump their data b efore or at t
 ie case  or  ab o v e
The theorem sa ys that the dela y b ound for class j is the onetime dela y burst that
accrues if the aggregate buc k et of all classes  through j o ws are sim ultaneously
dump ed in to the switc h and all classes  through j   sources con tin ue to send at
their reserv ed rates
Weno w use Eqn  as the base equation to mo del the eect of admitting a new
o w  on existing predictiv e trac First w e appro ximate the trac from all o ws
b elonging to a predictiv e class j as a single o w conforming to a   j
b
j
tok en buc k et
lter A conserv ativ e v alue for  j
w ould be the aggregate reserv ed rate of all o ws
b elonging to class j  Next w e recognize that there are three instances when the
computed w orstcase dela y of a predictiv e class can c hange  when a o w of the
same class is admitted  when a o w of a higher priorit y class is admitted and  when a guaran teed o w is admitted The switc h priorit y sc heduling isolates higher
priorit y  k  classes from a new o w of class k  so their w orstcase dela y need not
be reev aluated when admitting a o w of class k  In the remainder of this c hapter
w e compute eac h of the three eects on predictiv e trac individually  A t the end
of these computations w e will observ e that admitting a higher priorit y predictiv e
o w do es more harm to lo w er priorit y predictiv e trac than admitting either a
guaran teed o w or a predictiv e o w of the same priorit y  In the equations belo w w e denote newly computed dela y b ound b y D
  W e
denote the sum of guaran teed o ws reserv ation b y  G
The link bandwidth a v ailable
for serving predictiv e trac is the nominal link bandwidth min us those reserv ed b y
guaran teed o ws    G
 Eect of new predictiv e o w  on same priorit y trac W e can mo del
the eect of admitting a new o w  of predictiv e class k b y c hanging the classs

WFQ
Prio
Queue
Guaranteed
Predictive
Best effort
μ
r
1
G
r
1
G
r
2
G
r
2
G
r
n
G
r
n
G
. . .
. . .
μ − ν
G
r
2
P2
b
2
P2
n
Figure  Eect of new predictiveo w on same priorit y trac
tok en buc k et parameters to   k
r
k
b
k
b
k
where  r
k
b
k
are the tok en buc k et
parameters of the new o w
D
 k
P
k   i b
i
  G
P
k   i
i
b
k
b
k
  G
P
k   i  i
D
k
b
k
  G
P
k   i  i
 W e see that the dela y of class k gro ws b y a term that is prop ortional to o w  s
buc k et size
Fig  depicts a csz sc heduler with n n um b er of guaran teed o ws and one class  predictiveo w When the class  o w arriv es there is no other predictiv eo winthe
system Hence the w orstcase dela y seen b y the new o w is the time it tak es to drain
the its buc k et full of data  b
P   at rate    n
G
where  n
G
is the sum of the n guaran teed
o ws reserv ed rates The new w orstcase dela y for class is D
 P   b
P     n
G

WFQ
Prio
Queue
Guaranteed
Predictive
Best effort
μ
r
1
G
r
1
G
r
2
G
r
2
G
r
n
G
r
n
G
r
1
P1
b
1
P1
r
2
P2
b
2
P2
. . .
. . .
μ − ν
G
n
Figure  Eect of new predictiv e o w on lo w er priorit y trac
Eect of predictiv e o w  on lo w er priorit y trac W e compute the new
dela y b ound for class j  where j is greater than the requested class k  directly from
Eqn  adding in the buc k et depth b
k
and reserv ed rate r
k
of o w   D
 j
P
k   i b
i
b
k
b
k
P
j
i k  b
i
  G
P
k   i
i
 k
r
k
P
j   i k
i
D
j
  G
P
j   i
i
  G
P
j   i  i
r
k
b
k
  G
P
j   i
i
r
k
k j  K  where K is the n um ber of predictiv e classes The rst term reects a sque ezing
of the pip e in that the additional bandwidth required b y the new o w reduces the
bandwidth a v ailable for lo w er priorityo ws The second term is similar to the dela y
calculated ab o v e and reects the eect of the new o ws burstiness
Fig  adds a new class  o w to the system depicted in Fig  The new o w
is the highest priorit y predictiv e o w and there is no other o w of the same priorit y
in service The w orstcase dela y seen b y this new o w is when it dumps its buc k et

full of data  b
P   Maximal dela y of class  is D
 P   b
P     n
G
Class  trac m ust
no w w ait for the class  queue to drain b efore it sees service Hence the w orstcase
dela y of class  trac b ecomes
D
 P   D
P     n
G
  n
G
r
P  
b
P     n
G
r
P     Eect of a guaran teed o w  on predictiv e trac Again w e compute
the new dela y b ound D
 for al l predictiv e classes directly from Eqn  adding in
the reserv ed rate r
G
ofo w   D
 j
P
j
i
b
i
  G
P
j   i  i
r
G
D
j
  G
P
j   i
i
  G
P
j   i  i
r
G
  j  K  Notice ho w the new guaran teed o w simply squeezes the pip e reducing the a v ailable
bandwidth for predictiv e o ws new guaran teed o ws do not con tribute an y dela y
due to their buc k ets b ecause wf q smo oths out their bursts Also observ e that the
rst term of Eqn  is equiv alen t to Eqn  the impact of a new guaran teed o w
is lik e adding a zerosize buc k et higher priorit y  predictiv e o w
Fig  sho ws a new guaran teed o w added to the system in Fig  The new
guaran teed o w do es not eect existing guaran teed o ws nor is it itself eected b y
an y other o ws Ho w ev er it do es aect the bandwidth a v ailable to predictiv e trac
The new maximal dela y of class and class  predictiv e services are resp ectiv ely
D
 P   D
P     n
G
  n
G
r
n G
and
D
 P   D
P     n
G
r
P     n
G
r
n G
r
P    Con trasting Eqns   and  w e see that the exp erienced dela y of lo w er
priorit y predictiv e trac increases more when a higher priorit y predictiv e o w is
admitted than when a guaran teed o w or a samepriorit y predictiveo w is admitted

WFQ
Prio
Queue
Guaranteed
Predictive
Best effort
μ
r
1
G
r
1
G
r
2
G
r
2
G
r
n
G
r
n
G
r
1
P1
b
1
P1
r
2
P2
b
2
P2
. . .
. . .
r
n+1
G
r
n+1
G
μ − ν
G
n+1
Figure  Eect of a guaran teed o w on predictiv e trac
The wf q sc heduler isolates predictiv e o ws from attempts b y guaran teed o ws to
dump their buc k ets in to the net w ork as bursts In con trast lo w er priorit y predictiv e
trac sees b oth the rates and the buc k ets of higher priorit y predictiveo ws A higher
priorit y predictiv e o w not only squeezes the pip e a v ailable to lo w er priorit y trac
but also preempts it
W orstcase Dela y Guaran teed Service
In reference P ar the author pro v es that in a net w ork with arbitrary top ology  the wf q sc heduling discipline pro vides guaran teed dela y bounds that dep end only
on o ws reserv ed rates and buc k et depths Under wf q eac h guaran teed o w is
isolated from the others This isolation means that as long as the total reserv ed rate
of guaran teed o ws is belo w the link bandwidth new guaran teed o ws cannot cause
existing ones to miss their dela y b ounds Hence when accepting a new guaran teed
o w our admission con trol algorithm only needs to assure that  the new o w will
not cause predictiveo ws to miss their dela y b ound see Eqn  ab o v e and that  it will not o v ersubscrib e the link  G
r
G
 where  is the link bandwidth and

is the utilization target see Chapter  for a discussion on utilization target In
addition to protecting guaran teed o ws from eac h other wf q also isolates protects
guaran teed o ws from all predictiv e trac
Equiv alen t T ok en Buc k et Filter
The equations ab o v e describ e the aggregate trac of eac h predictiv e class with a
single tok en buc k et lter Ho w do w e determine a classs tok en buc k et parameters
A completely conserv ativ e approac h w ould be to mak e them the sum of the param
eters of all the constituen t o ws when data sources are burst y and o ws declare
conserv ativ e parameters that co v er their w orstcase bursts using the sum of declared
parameters will result in lo w link utilization Our algorithm is appro ximate and
optimistic w e tak e adv an tage of statistical m ultiplexing b y using measured v alues
instead of pro viding for the w orst p ossible case to gain higher utilization risking
that some pac k ets ma y o ccasionally miss their dela y b ounds In essence w e describ e
existing aggregate trac of eac h predictiv e class with an e quivalent token bucket lter
with parameters determined from trac measuremen t
The equations ab o v e can be equally describ ed in terms of curren t dela ys and
usage rates as in buc k et depths and usage rates Since it is easier to measure dela ys
than to measure buc k et depths w e do the former Th us the measured v alues for
a predictiv e class j are the aggregate bandwidth utilization of the class b  j
and
the exp erienced pac k et queueing dela y for that class
c
D
j
F or guaran teed service
w e coun t the sum of all reserv ed rates  G
and w e measure the actual bandwidth
utilization b  G
of all guaran teed o ws Our appro ximation is based on substituting
in the ab o v e equations the measured rates b  j
and b  G
for the reserv ed rates and
substituting the measured dela ys
c
D
j
j    K for the maximal dela ys W e no w
use the previous computations and these measured v alues to form ulate an admission
con trol algorithm

The Admission Con trol Algorithm
New Predictiv e Flo w If an incoming o w  requests service at predictiv e class
k  the admission con trol algorithm
Denies the request if the sum of the o ws requested rate r
k
and curren t usage
w ould exceed target link utilization
 r
k
b  G
N
X
i b  i
  Denies the request if admitting the new o w could violate the dela y b ound D
k
of the same priorit y lev el
D
k
b
D
k
b
k
 b  G
P
k   i
b  i
 or could cause violation of lo w er priorit y classes dela y bound D
j
D
j
b
D
j
 b  G
P
j   i b  i
 b  G
P
j   i b  i
r
k
b
k
 b  G
P
j   i b  i
r
k
k j  K  New Guaran teed Flo w If an incoming o w  requests guaran teed service the
admission con trol algorithm
Denies the request if either the bandwidth c hec k in Eqn  fails or if the
reserv ed bandwidth of all guaran teed o ws exceeds target link utilization
 r
G
 G
 
Denies the request if the dela y b ounds of predictiv e classes can b e violated when
the bandwidth a v ailable for predictiv e service is decreased b y the new request
D
j
b
D
j
 b  G
P
j   i b  i
 b  G
P
j   i b  i
r
G
  j  K  If the request satises all of these inequalities the new o w is admitted

Chapter  A Simple Timewindo w
Measuremen t Mec hanism
The form ulae describ ed in the previous c hapter rely on the measured v alues
c
D
j
b  G
and b  j
as inputs W e describ e in this c hapter the timewindo w measuremen t
mec hanism w e use to measure these quan tities While w e b eliev e our admission
con trol equations ha v e some fundamen tal principles underlying them w e mak e no
suc h claim for the measuremen t pro cess Our mec hanism is extremely simple and
could be replaced b y a n um ber of other approac hes W e consider the simplicit y of
our approac h an adv an tage in our study b ecause it helps us isolate prop erties inheren t
to our admission con trol criteria from those induced b y the measuremen t mec hanism
Our measuremen t pro cess uses the constan ts  S and T  discussion of their roles as
p erformance tuning knobs follo ws our description of the measuremen t pro cess
Measuremen t Pro cess
W e tak e t w o measuremen ts exp erienced dela y and utilization T o estimate dela y  w e measure the queueing dela y
b
d of ev ery pac k et T o estimate utilization w e sample
the usage rate of guaran teed service b  S
G
and of eac h predictiv e class j  b  S
j
o v er a
sampling p erio d of length S pac k et transmission units F ollo wing w e describ e ho w

packet delay
time
T T
delay
estimate
new flow
end of T
d
^
λ
d
^
above
estimate
restart T
Figure  Measuring dela y  these measuremen ts are used to compute the estimated maximal dela y
c
D
j
and the
estimated utilization b  G
and b  j
Measuring dela y  The measuremen t v ariable
c
D
j
trac ks the estimated maxim um
queueing dela y for class j  W e use a measuremen t windo w of T pac k et transmission
units as our basic measuremen t blo c k As sho wn in Fig  the v alue of
c
D
j
is
up dated on three o ccasions Atthe end of the measuremen t blo c k w e up date
c
D
j
to
reect the maximal pac k et dela y seen in the previous blo c k Whenev er an individual
dela y measuremen t exceeds this estimated maxim um queueing dela y  w e kno w our
estimate is wrong and immediately up date
c
D
j
to b e  times this sampled dela y  The
parameter  allo ws us to b e more conserv ativeb y increasing
c
D
j
to a v alue higher than
the actual sampled dela y  Finally  w e up date
c
D
j
whenev er a new o w is admitted
to the v alue of pro jected dela y from our admission con trol equations Algebraically  the up dating of
c
D
j
is as follo ws
b
D
j
                   MAX  b
d   of past T measuremen t windo w
b
d if
b
d
b
D
j
Righ t side of
Eqn   or  when adding a new o w dep ending
on the service and class requested b y
the o w
Measuring rate The measurementv ariables b  G
and b  j
trac k the highest sampled
aggregate rate of guaran teed o ws and eac h predictiv e class resp ectiv ely heretofore

rate
time
rate
estimate
new flow
end of T
S S S S S S S S S S S
T
S S S S S S S S S S S
T
S S S S S S S S S S S
ν
^ s
above
estimate
restart T
Figure  Measuring rate
w e will use  b   as a shorthand for  b  G
andor b  j
and  b  S
for  b  S
G
andor b  S
j
As sho wn in Fig  the v alue of b  is up dated on three o ccasions A t the end of
the measurementbloc k w eupdate b  to reect the maximal sampled utilization seen
in the previous blo c k Whenev er an individual utilization measuremen t exceeds b   w e immediately up date b  with the new sampled v alue Finally  w e up date b  up on
admission of new o ws Algebraicallythe up dating of b  is as follo ws
b                 MAX  b  S
 of past T measuremen t windo w
b  S
if b  S
b   where b  S
is the a v erage rate
o v er S a v eraging p erio d b   r
 when adding a new o w    The measured rate of guaran teed trac is capp ed at the sum of guaran teed reserv ed
rate  b   G
MI N  b  G

G

When a o w lea v es the net w ork w e do not explicitly adjust the measured
v alues instead w e allo w the measuremen t mec hanism to adapt to the observ ed trac
automatically  W e do ho w ev er subtract the reserv ed rate of a departing guaran teed
o w from the sum of all guaran teed reserv ed rate  G

P erformance T uning Knobs
W e no w lo ok at the constan ts used in the algorithm
 In a simple M M  queue the v ariance in dela y div erges as the system ap
proac hes full utilization A measuremen tbased approac h is do omed to fail when
dela y v ariations are exceedingly large whic h will o ccur at v ery high utilization It is
th us necessary to iden tify a utilization tar get and require that the admission con trol
algorithm striv e to k eep link utilization b elo w this lev el
The appropriate utilization target of anygiv en link dep ends on the c haracteristics
of the trac o wing through it If eac h sources rate is small compared to link capacit y
small grain size and bursts are short the links utilization target can b e set higher
Burst y sources with big long bursts or long idle p erio ds will require a lo w er link
utilization target In this study  w e set utilization target at ! capacit y    In our sim ulations a single instance of pac k et delayabo v e the curren t estimate
t ypically indicate that subsequen t dela ys are lik ely to be ev en larger so when a
pac k ets queueing dela y  b
d  is higher than its classs estimated maximal dela y
c
D
j
w e
bac k o our dela y estimate to a m uc h larger v alue  b
d  In this study  w e use   S  The a v eraging p erio d S in Eqn  con trols the sensitivit y of our rate mea
suremen t The smaller the a v eraging p erio d the more sensitiv e w e are to bursts
the larger the a v eraging p erio d the smo other trac app ears An S that captures
individual bursts ma y mak e the admission con trol more conserv ativ e than desired
In this study w e use S of at least  pac k et transmission times
T  Once
c
D or b  is increased their v alues stayhigh un til the end of their resp ectiv e
measuremen t windo w T  The size of T con trols the adaptabilit y of our measuremen t
mec hanism to drops in trac load Smaller T means more adaptabilit y  but larger
T results in greater stabilit y  The windo w size for load measuremen t should allo w
for enough utilization samples ie T should be sev eral times S  The measuremen t
windo ws of the load and the dela y can b e main tained indep enden tly  When weadmit
a new o w and add its w orst case eect to the measured v alues w e also restart the

measuremen t windo ws to giv e the measuremen t mec hanism one whole windo w to
gather information on the new o w

Chapter  Sim ulations
Admission con trol algorithms for guaran teed service can b e v eried b y formal pro of
Measuremen t based admission con trol algorithms can only b e v eried through exp er
imen ts on either real net w orks or a sim ulator Weha v e tested our algorithm through
sim ulations on a wide v ariet y of net w ork top ologies and driv en with v arious source
mo dels w e describ e a few of these sim ulations in the follo wing c hapters In eac h
case w e w ere able to ac hiev e a reasonable degree of utilization when compared to
guaran teed service and a lo w dela y bound violation rate w e try to be v ery conser
v ativ e here and alw a ys aim for no dela y bound violation o v er the course of all our
sim ulations Before w e presen t the results from our sim ulations w e rst presen tthe
top ologies and source mo dels used in these sim ulations
Sim ulated T op ologies
Werun oursim ulations on four top ologies the OneLink  Tw oLink  F ourLink  and TBone top ologies depicted in Figs a b c and  resp ectiv ely  In the
rst three top ologies eac h host is connected to a switchb y an innite bandwidth link
The connection b et w een switc hes in these three top ologies are all  Mbps links with
innite buers In the OneLink top ology  trac o ws from HostA to HostB In
the Tw oLink case trac o ws bet w een three host pairs in source#destination
order HostA#HostB HostB#HostC HostA#HostC Flo ws are assigned to one of

HostA
Switch2 Switch1
HostB
L1 L2
L3
(a) One-Link
(b) Two-Link (c) Four-Link
HostA
Switch2 Switch1
HostB
L1 L2
L4
L5
Switch3
L3
HostA
Switch1 Switch2
HostB
L1 L2
L7
L6
Switch3
L3
Switch4
HostD
L9
L4
L8
HostE
Switch5
L5
HostC
HostC
Figure  The OneLink Tw oLink and F ourLink top ologies
these three host pairs with uniform probabilit y  In the F ourLink top ologies trac
o ws bet w een six host pairs HostA#HostC HostB#HostD HostC#HostE HostA#
HostD HostB#HostE HostD#HostE again o ws are distributed among the six host
pairs with uniform probabilit y  In Fig  these host pairs and the paths their
pac k ets tra v erse are indicated b y the directed curv e lines
The TBone top ology consists of   and  Mbps links as depicted in
Fig a T rac o ws bet w een  hostpairs follo wing four ma jor curren ts as
sho wn in Fig b the n um b ers     next to eac h directed edge in the gure
denote the curren t presen t on that edge The  hostpairs are listed in T able  Flo ws b et w een these hostpairs ride on only one curren t for example o ws from host
H to H ride on curren t  In Fig a a c hec k ered bo x on a switc h indicates
that weha v e instrumen ted the switc h to study trac o wing out of that switchon to
the link adjacen t to the c hec k ered bo x
Source Mo dels
W e curren tly use three kinds of source mo del in our sim ulations All of them are
onoff pro cesses They dier in the distribution of their on and off times and
call holding time  cht whic h w e will also call o w duration or o w lifetime
One of these is the t w ostate Mark o v pro cess used widely in the literature Recen t

S13 S12 S8
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L38
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L40
L12
L13
L14
L15
L16
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L21
L22
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L25
= Instrumentation
=  10 Mbps
=  45 Mbps
= 100 Mbps
(a) TBone topology
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(b) Four traffic "currents" on TBone
Figure  The TBone top ology

T able  F ort yv e Host P airs on TBone
Source Destinations Source Destinations
H H H H H H and H H H and H H H and H H H and H H H and H
H H and H H H
H H H H H and H H H and H H H
H H H H
H H H H
H H H H H H
H H and H H H and H H H and H H H and H
H H H H and H
H H H H
studies L TWW DMR W  PF KM  GW BSTW ha v e sho wn that
net w ork trac often exhibits longrange dep endence  lrd with the implications
that congested p erio ds can b e quite long and a sligh t increase in the n um b er of activ e
connections can result in large increase in pac k et loss rate PF  The authors
of reference PF Floa  further call atten tion to the p ossibly damaging eect
longrange dep enden t trac migh t ha v e on measuremen tbased admission con trol
algorithms T o in v estigate this and other lrd related questions w e augmen t our
sim ulator with t w o lrd source mo dels
EXP Mo del Our rst mo del is an onoff mo del with exp onen tially distributed
on and off times During eac h on p erio d an exp onen tially distributed random
n um ber of pac k ets with a v erage N  are generated at xed rate p pac k etsec Let
I milliseconds be the a v erage of the exp onen tially distributed off times then the
a v erage pac k et generation rate a is giv en b y  a  I N  p  The exp mo del
describ ed in the next section is a mo del for pac k etized v oice enco ded using adpcm
at  Kbps

1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160
pdf
packet transmission times
’EXP’
’POO’
Figure  Exp erienced dela y of exp and poo sources
LRD P areto onoff  Our next mo del is an onoff pro cess with P areto dis
tributed on and off times for ease of reference w e call this the Par eto onoff
mo del During eac h on period aP areto distributed n um ber of pac k ets with mean
N and P areto shap e parameter   are generated at p eak rate p pac k etsec The off
times are also P areto distributed with mean I milliseconds and shap e parameter   P areto shap e parameter less than  giv es data with innite mean shap e parameter
less than  results in data with innite v ariance The P areto lo cation parameter is
mean   shape   shape  Eac h Par eto onoff source b y itself do es not generate
lrd series Ho w ev er the aggregation of them do es WTSW  The Hurst parameter
that reects the degree of longrange dep endency of a timeseries is determined b y
the hea vier tailed of the on or off time distribution If  is the shap e parameter of
the hea vier tailed P areto distribution the Hurst parameter of the aggregate trac is
H       CB
Fig  sho ws the exp erienced dela y of  exp sources and  poo sources at
the b ottlenec k link of the Onelink top ology  Both source mo dels ha v e a p eak rate
of  Kbps a v erage idle time of  msec and a v erage burst length of  pac k ets
W e can see that ev en though b oth source mo dels ha v e p eak to a v erage rate of  the
dela y distribution of poo sources has a m uc h hea vier tail

LRD F ractional arima W e use eac h n um ber generated b y the fr actional au
tor e gr essive inte gr ate d moving aver age f arima pro cess HR as the n um ber of
xedsize pac k ets to be sen t bac k to bac k in eac h on p erio d In terarriv als of on pe rio ds are of xed length F or practical programming reasons w e generate a series of
f arima data p oin ts at the b eginning of eachsim ulation Eac h farima source
then pic ks a uniformly distributed n um ber bet w een  and  to be used as its
index in to that series On reac hing the end of the series the source wraps around to
the b eginning This metho d is similar to the one used b y the authors of GW to
sim ulate data from sev eral sources using one v ariable bit rate  vbrvideo trace
Let fX
t
g denote data poin ts from a timeseries An arma p q  pro cess has the
form
X
t
  X
t    X
t
  p
X
t p
 t
   t      t      q
t q
 where the  t
are uncorrelated Gaussian noise the  j
j    p  are the autore
gressiv e w eigh ts and the  j
j    q  are the mo ving a v erage w eigh ts The arma
pro cess is stationary if    
    BJ  p  Next dene a lag op erator B
as X
t   BX
t
and the dierence op erator r as  X
t
X
t   rX
t
hence rX
t
  B  X
t
Let $ B     B     p
B
p
and " B     B     q
B
q
Then an arima p d q  pro cess is dened as
$ B  r
d
X
t
" B   t
 A fractional arima pro cess has a d of fractional v alue A farima p d q  pro cess
with  d     generates longrange dep enden t series with Hurst parameter H  d    Hos L TWW Hence the farima mo del tak es three parameters the
autoregressiv e pro cess order with the corresp onding set of w eigh ts the degree of
in tegration and the mo ving a v erage pro cess order with the corresp onding set of
w eigh ts it also requires an inno v ation with a Gaussian marginal distribution The
marginal distribution of a farima generated series is also Gaussian whereas vbr
video traces exhibit lo w a v erage with high p eaks Th us w e can not use the farima

output to mo del trac from a single vbr video source Nev ertheless sim ulation
results in GW  indicate that aggregation of farima generated series ma y w ell
mo del aggregate vbr video tracsuc h as that coming from a subnet w ork In our
sim ulations w e rst generate a normally distributed inno v ation with mean N and
standard deviation s pac k ets If the minim um of the farima output is less than
zero w e shift the whole series b y adding the absolute v alue of its minim um to ev ery
n um b er in the series This w a y of obtaining nonnegativ e series is also used in AM
Note that this shifting pro cess constrains the maxim um v alue of the generated series
to be alw a ys t wice its a v erage The Whittle maxim um lik elihood estimator Ber
conrms that our shifting cropping and o v erla ying of the farima generated series
do not destro y its longrange dep enden t c haracteristic
T o ease discussion on the eect of dieren t source mo dels on trac c haracteristics
it is useful to dene the follo wing additional notations and concepts let  be a
o ws density the ratio of its a v erage to p eak rates ap  R its gr ain size the ratio
of its p eak rate to link bandwidth p  and   its burstiness Aggregation of
o ws with    results in smo oth trac and reliable measuremen t Burst y o ws
with short bursts     N  D
j
will ha v e their bursts smo othed out b y the
switc hs buer resulting again in reliable measuremen t v alues Burst y o ws with
large bursts eg P areto distributed on time but small grain size     N  D
j
and R       still allo w for large degree of statistical m ultiplexing Ho w ev er
burst y o ws with long burst and large grain size     N  D
j
and R      migh t b est be alloted their o wn guaran teed bandwidth
In addition to eac h sources c haracteristics of densit y and grain size net w ork
trac dynamics is also shap ed b y the arriv al pattern and duration of o ws Our
sim ulator allo ws us to driv e eac h sim ulation with a n um ber of o w generators for
eac h generator w e can sp ecify its start and stop times the a v erage o w in terarriv al
time the maxim um n um ber of concurren tly activ e o ws and the mix of transp ort
proto col source mo del tok en buc k et lter and service request ascrib ed to eac ho w
W e giv e exp onen tially distributed lifetimes to the exp mo del follo wing Mol  The duration of for lrd sources ho w ev er are tak en from a lognormal distribution

Tokens
generated
at rate r
b
tokens
Token Bucket
Filter
User Process
N packet
on time
1/p
M packet
off time
Host max
transmission
rate C
C
Host
Network
Packets
transmitted
at rate G,
r <= G <= C
Q packet
data queue
averaging interval
ρ = N/(N+M) a = ρ p μ R = p/
On/Off
Traffic
generator
Figure  Onoff trac mo del with tok enbuc k et lter
follo wing Bol  DMR W  The in terarriv al times of all o ws are exp onen tially
distributed PF
P arameter Choices
Fig  sho ws a pac k etarriv al depiction of an onoff source in the con text of a
host with tok enbuc k et lter T o mak e a giv en trac generation source conform to a
particular tok en buc k et lter a host can queue pac k ets arriving at an empt y buc k et
un til more tok ens are a v ailable If the data queue length  Q is  pac k ets that arriv e
at an empt y tok en buc k et are immediately dropp ed W e c hose six instan tiations of
the ab o v e three source mo dels as summarized in T able  In the table p   means that after eac h off time pac k ets for the next on p erio d are transmitted bac k
to bac k On real net w orks pac k ets are sen t bac k to bac k when the applications
generate trac faster than the net w ork can transmit it In the same table w e also
list the settings of the tok en buc k et parameters assigned to eac h source Column  of
the table lab eled cut r ate indicates the a v erage n um ber of pac k ets that w ould ha v e

T able  Six Instan tiations of the Three Source Mo dels
Mo dels P arameters T ok en Buc k et P arameters Bound ms
Mo del Name p pkt I N pa r tkn b cut max
sec msec pkts sec tkns rate qlen
D
D
j
exp           exp       e    exp       e     poo           poo       e    s
farima
f g  
     e    b een dropp ed b y eacho ws tok en buc k et lter over the total n umberofpac k ets sen t
b y the o w had the data queue length b een  ie pac k ets are immediately dropp ed
up on arriving at an empt y tok en buc k et Column  lab eled max qlen sho ws the
maxim um data queue length a o w can exp ect to see if the data queue has innite
length W e assign eac h o w a data queue with innite length in all our sim ulations
ie pac k ets that arriveatan empt y tok en buc k et are alw a ys queued and the queue
nev er o v ero ws Recall that in this study w e use xed pac k et size and eac h of our
tok en is w orth  Kbits of data whic h is also our pac k et size
The shap e parameter of the P areto distributed on time   of the P areto onoff
sources are selected follo wing the observ ations in WTSW According to the same
reference the shap e parameter of the P areto distributed off time    sta ys mostly
belo w  in this study w e use      for all poo sources F or the poo mo del
w e use a tok en buc k et rate equals to the sources peak rate suc h that the tok en
buc k et lter do es not reshap e the trac F or the poo mo del some of the generated
pac k ets w ere queued this means during some of the sources alleged  off times it
ma y actually still be draining its data queue on to the net w ork Th us for the poo
mo del the trac seen on the wire ma y not b e P areto onoff  
When a o w with tok en buc k et parameters  rb  requests guaran teed service the
maximal queueing dela y ignoring terms prop ortional to a single pac k et time is giv en
b y br P ar  Column  of the table lab eled D
 lists the guaran teed dela y b ound
for eac h source giv en its assigned tok en buc k et lter Column  lab eled D
j
lists
the predictiv e dela y b ound assigned to eac h source W e sim ulate only t w o classes
of predictiv e service A predictiv e bound of  msecs means rst class predictiv e
service  msecs second class Weha vec hosen the tok en buc k et parameters so that
in most cases the dela y b ounds giv en to a o wb y predictiv e and guaran teed services
are the same This facilitates comparison bet w een the utilization lev els ac hiev ed
with predictiv e and guaran teed services In the few cases where the dela ys are not
the same suc h as in the poo and farima cases the utilization comparison is less
meaningful In the poo case for example the predictiv e dela y bound is smaller
than the guaran teed bound so the utilization gain w e nd here understates the true
gain
F or the farima source w e use an autoregressiv e pro cess of order  with w eigh t
and degree of in tegration  resulting in a generated series with Hurst param
eter  The rst order autoregressiv e pro cess with w eigh t  means our f arima
trac also has strong shortrange dep endence The in terarriv al time bet w een on
p erio ds is th of a second The Gaussian inno v ation fed to the farima pro cess has
amean of pac k ets with standard deviation  Except for sim ulations on the TBone top ologyo w in terarriv al times are exp o
nen tially distributed with an a v erage of  milliseconds Because of system memory
limitation w e set the a v erage o w in terarriv als of sim ulations on the TBone top ol
ogy to  seconds The a v erage holding time of all exp sources is  seconds The
poo and farima sources ha v e lognormal distributed holding times with median  seconds and shap e parameter  W e run sim ulations with Mark o v onoff  exp sources for  seconds sim ulated time The data presen ted are obtained from the
later half of eac h sim ulation By visual insp ection w e determined that  sim u
lated seconds is sucien t time for the sim ulations to w arm up Sim ulations in v olving
P areto onoff sources require a longer w arm up p erio d and a longer sim ulation time

for the lrd eect to be seen th us w e run them for  hours sim ulation time with
rep orted data tak en from the later  seconds

Chapter  On the Viabilit y of the Algorithm
In this c hapter w esho w that measuremen tbased admission con trol algorithm when
used with predictiv e service indeed yields higher lev el of link utilization than that
ac hiev eable under parameterbased algorithms with guaran teed service W e pro vide
supp orting evidence from results of sim ulations with b oth homogeneous and hetero
geneous trac sources on b oth singlehop and m ultihop net w orks Dep ending on
trac burstiness the utilization gain ranges from t wice to order of magnitude
Homogeneous Sources The Singlehop Case
By homogeneous sources w e mean sources that not only emplo y just one kind of
trac mo del but also ask for only one kind of service F or this and all subsequen t
singlehop sim ulations w e use the top ology depicted in Fig a F or eac h source
w e run t w o kinds of sim ulation The rst has all sources requesting guaran teed
service The second has all sources requesting predictiv e service The results of the
sim ulations are sho wn in T able  The column lab eled !Util con tains the link
utilization of the b ottlenec k link L The %Actv column con tains a snapshot
of the a v erage n um ber of activ e o ws concurren tly running on that b ottlenec k link
The  dd
j
e column con tains the maxim um exp erienced dela y of predictiv e class j
pac k ets The  LT  column lists the ratio of a v erage o w duration to measuremen t
windo w used with eac h source mo del W e rep eat the predictiv e service sim ulations

T able  Singlehop Homogeneous Sources Sim ulation Results
Mo del Guaran teed Predictiv e
Name !Util %Actv !Util %Actv dd
j
e LT
exp      
exp      
exp      
poo      
poo      
farima      
nine times eac h time with a dieren t random seed to obtain condence in terv als
W e nd the condence in terv al for the all the n um b ers to b e v ery tigh t less than one
least signican t digit in most cases
As men tioned in Chapter  w e consider the p erformance of our admission con
trol algorithm good if there is no dela y bound violation during a sim ulation run
Ev en with this v ery restrictiv e requiremen t one can see from T able  that pre
dictiv e service consisten tly allo ws the net w ork to ac hiev e higher lev el of utilization
than guaran teed service do es The utilization gain is not large when sources are
smo oth F or instance the source mo del exp has a p eak rate that is only t wice its
a v erage rate Consequen tly  the data only sho ws an increase in utilization from !
to ! One can argue that the theoretical upp er bound in the utilization increase
is the p eak to a v erage ratio In con trast burst y sources allo w predictiv e service to
ac hiev e sev eral orders of magnitude higher utilization compared to that ac hiev able
under guaran teed service Source mo del exp  for example is a v ery burst y source
it has an innite peak rate ie sends out pac k ets bac k to bac k and has a tok en
buc k et of size  The exp o ws request reserv ations of  Kbps corresp onding to
the tok en buc k et rate at the sources Under guaran teed service only  o ws can b e
admitted to the  Mbps b ottlenec k link with ! utilization target The actual

link utilization is only !
Under predictiv e service  o ws are serv ed on the
a v erage resulting in actual link utilization of !
In this homogeneous scenario with only one class of predictiv e service and con
stan tly o v ersubscrib ed link our measuremen tbased admission con trol algorithm eas
ily adapts to lrd trac bet w een the coming and going of o ws The utilization
increased from ! to ! and from ! to ! for the poo and poo sources re
sp ectiv ely  The utilization gain for the farima sources w as more mo dest from !
to ! This is most probably b ecause the sources maxim um on time is at most
t wice its a v erage an artifact of the shifting w e do as discussed in Chapter  to
obtain nonnegativ e v alues from the farima generated series In all cases w e are
able to ac hiev e high lev els of utilization without incurring dela y violations T o further
test the eect of long off times on our measuremen tbased algorithm w esim ulated
poo sources with innite duration With utilization target of ! link capacit yw e
do see a rather high p ercen tage of pac k ets missing their dela y bound Lo w ering the
utilization target to ! ho w ev er pro vide us enough ro om to accommo date trac
bursts Th us for these scenarios w e see no reason to conclude that lrd trac p oses
sp ecial c hallenges to our measuremen tbased approac h
Homogeneous Sources The Multihop Case
Next w e run sim ulations on m ultihop top ologies depicted in Figs b and c The
top half of T able  sho ws results from sim ulations on the Tw oLink top ology  The
utilization n um b ers are those of the t w o links connecting the switc hes in the top ology  The source mo dels emplo y ed here are the exp exp  and poo mo dels one per
sim ulation The bottom half of T able  sho ws the results from sim ulating source
mo dels exp poo  and farima on the F ourLink top ology  F or eac h source
mo del w e again run one sim ulation where all sources request guaran teed service and
another one where all sources request one class of predictiv e service
P arameterbased admission con trol algorithms ma y not need to set a utilization target and th us
can ac hiev e a somewhat higher utilization for the scenario sim ulated here t w o more guaran teed
o ws could ha v e b een admitted

T able  Multihop Homogeneous Sources Link Utilization
Link Mo del Guaran teed Predictiv e
T op ology
Name Name !Util !Util dd
j
e
exp    L exp  
poo    Tw oLink
exp    L exp  
poo  
exp    L poo    farima  
exp  
L poo    farima  
F ourLink
exp  
L poo    farima  
exp  
L poo    farima  

The most imp ortan t result to note is that once again predictiv e service yields
reasonable lev els of utilization without incurring an y dela y violations The utiliza
tion lev els and the utilization gains compared to guaran teed service are roughly
comparable to those ac hiev ed in the single hop case
Heterogeneous Sources The Singlehop Case
W e no w lo ok at sim ulations with heterogeneous sources F or eac h of the sim ulation
w e use t w o of our six source mo del instan tiations Eac h source is giv en the same
tok en buc k et as listed in T able  and when requesting predictiv e service requests
the same dela y b ound as listed in the said table W e run three kinds of sim ulation with
heterogeneous sources  single source mo del requesting m ultiple lev els of predictiv e
service  m ultiple source mo dels requesting a single class of predictiv e service and
m ultiple source mo dels requesting m ultiple lev els of predictiv e service In all cases
w e compare the ac hiev ed utilization with those ac hiev ed under guaran teed service
F or the rst and third cases w e also exp erimen t with sources that request b oth
guaran teed and predictiv e services When m ultiple source andor service mo dels are
in v olv ed eac h mo del is giv en an equal probabilit y of b eing assigned to the next new
o w In all these sim ulations the exp erience dela ys are all within their resp ectiv e
b ounds
T able  sho ws the utilization ac hiev ed when o ws with the same source mo del
request t w o classes of predictiv e service PP guaran teed and one predictiv e class
GP and guaran teed and t w o predictiv e classes GPP In the GP case o ws request
the predictiv e class assigned to the source mo del under study see T able  In
the other cases b oth predictiv e classes are requested Compare the n um b ers in eac h
column of T able  with those in the !Util column of T able  under guaran teed
service The presence of predictiv e trac in v ariably increases net w ork utilization
Next w e lo ok at the sim ulation results of m ultiple source mo dels requesting a
single service mo del T able  sho ws the utilization ac hiev ed for selected pairings of
the mo dels The column headings name the source mo del pairs The rst ro wsho ws

T able  Singlehop Single Source Mo del Multiple Predictiv e Services Link Uti
lization
Mo del PP GP GPP
exp   #
exp   #
exp   #
poo    poo   #
farima    T able  Singlehop Multiple Source Mo dels Single Service Link Utilization
exp exp exp exp exp poo
Service
poo exp poo farima farima farima
Guaran teed       Predictiv e       the utilization ac hiev ed with guaran teed service the second predictiv e service W e
let the n um b ers sp eak for themselv es
Finally in T able  w e sho w utilization n um bers for o ws with m ultiple source
mo dels requesting m ultiple service mo dels The rst ro wsho ws the utilization ac hiev ed
when all o ws ask ed only for guaran teed service The second ro w sho ws the utiliza
tion when half of the o ws requests guaran teed service and the other half requests
the predictiv e service suitable for its c haracteristics see T able  And the last ro w
sho ws the utilization ac hiev ed when eac h source requests a predictiv e service suitable
to its c haracteristics
Heterogeneous Sources The Multihop Case
W e next run sim ulations with all six source mo dels on all our top ologies In T able  wesho w the utilization lev el of the b ottlenec k links of the dieren t top ologies Again
con trast the utilization ac hiev ed under guaran teed service alone with those under b oth

T able  Singlehop Multiple Source Mo dels Multiple Predictiv e Services Link
Utilization
exp exp exp exp exp poo
Service
exp farima poo poo poo farima
Guaran teed      
GuarPred      
Predictiv e      
guaran teed and predictiv e services The observ ed lo w predictiv e service utilization
on link L is not due to an y constrain t enforced b y its own admission decisions but
rather is due to lac k of trac o ws caused b y rejection of m ultihop o ws b y later
hops as w e will explain in Chapter  Utilization gains on the TBone top ology are
not so pronounced as on the other top ologies This is partly because w e are limited
b y our sim ulation resources and cannot driv e the sim ulations with higher oered
load Recall that o w in terarriv als on sim ulations using the TBone top ology ha v e
an a v erage of  seconds whic h is order of magnitude larger than the  milliseconds
used on the other top ologies
Our results so far indicate that a measuremen tbased admission con trol algo
rithm can pro vide reasonably reliable dela y bounds at signican t utilization gains
These conclusions app ear to hold not just for single hop top ologies and smo oth trac
sources but also for m ultihop congurations and longrange dep enden t trac W e
cannot within reasonable time v erify our approac h in an exhaustiv e and compre
hensiv e w a y  but our sim ulation results are encouraging

T able  Single and Multihop All Source Mo dels All Services Link Utilization
T op ology Link Guaran teed Guaran teed and Predictiv e
Name Name !Util !Util dd
e dd
e
OneLink L    
L    
Tw oLink
L    
L    
L    
F ourLink
L    
L    
L    
L    
L    
TBone
L    
L    
L    

Chapter  Practical Deplo ymen t Issues
In this c hapter w e consider sev eral practical issues related to deplo ymen t of our
algorithm In particular w e lo ok at the eect of dieren t measuremen t windo w  T  settings on the b eha vior of the admission con trol algorithm Wesho w that a smaller
T  relativ etoo w lifetime  L yields higher utilization but less reliable dela y b ound
while a larger one pro vides more stable dela y estimate at lo w er utilization W e also
presen t a few sample path snapshots illustrating the eect of T   Cho osing a Windo w Size
V arying the measuremen t windo w size T  has t w o related eects on the admission
con trol algorithm First since T is the length of the measuremen t blo c k used to
determine howlong wek eep the previous maximal pac k et dela y and sampled utiliza
tion increasing T mak es these estimates more conserv ativ e whic h in turn mak es the
admission con trol algorithm itself more conserv ativ e Th us larger T means few er
dela y violations and lo w er link utilization Second T also con trols ho w long w e con
tin ue to use our calculated estimate of the dela y and utilization induced b y a newly
admitted o w Recall that whenev er a new o w is admitted w e articially increase
the measured v alues to reect the w orstcase exp ectations and then restart the mea
suremen t windo w Th us w e are using the calculated eects of new o ws rather than
the measured eects un til w e survivean en tire T p erio d without anynew o w arriv al

Let r be the a v erage o w reserv ation rate and  the link bandwidth for con v enience
assume w e only p erform bandwidth c hec k Eqn  and    w e will admit at
most A   r n um ber of o ws for ev ery T  Th us at the end of its a v erage lifetime
L an a v erage o w w ould ha v e seen appro ximately
F  A  LT  n um ber of o ws If the a v erage rate of an a v erage o w is
b
r  ideally w e w an t F  b
r  a links stable utilization lev el to be near   Ho w ev er o ws also depart from the
net w ork The exp ected n um ber of o w departures during the period T dep ends on
the n um ber of admitted o ws and their duration If this n um ber of departures is
signican t a o w will see a m uc h smaller n um ber of o ws during its lifetime ie the
stable F  b
r b ecomes much smaller than   F or the same a v erage reserv ation rate r  and a giv en T  the size of the stable F is determined b y the a v erage o w duration
L A shorter a v erage o w duration means more departure per T  In the long run
w e aim for F  b
r    or equiv alen tly  LT  r
b
r  If all o ws use exactly what they
reserv ed w e ha v e LT  meaning that w e should not try to giv e a w a y the o ws
reserv ations
In other w ords T has t w o related eects on the admission con trol algorithm
to o small a T results in more dela y violations and lo w er link utilization  to o
long a T depresses utilization b y k eeping the articially heigh ten measured v alues
for longer than necessary  While the rst eect is link ed to o w duration only if the
o w exhibits longrange dep endence the second eect is closely link ed to the a v erage
o w duration in general Note that when T is innite w e only use our computed
v alues whic h are conserv ativ e bounds and ignore the measuremen ts en tirely  That
is w e will nev er suer an y dela y violations at a giv en hopifw e use an innite v alue
for T  Th us the parameter T alw a ys pro vides us with a region of reliabilit y  W e
no w presen t some illustrativesim ulation results on the imp ortance of the LT ratio
These results are mean t to b e canonical illustrations th us w e do not pro vide the full
details of the sim ulations from whic h they are obtained

T able  Eect of T and L
a V arying T  L   secs
T !Util dd
j
e
e   e   e   e   e   b V arying L secs
T
L e e
!Util dd
j
e !Util dd
j
e
                        In T able a w e sho w the a v erage link utilization and maxim um exp erienced
dela y from sim ulations of o ws with a v erage duration of  seconds W e v aried the
measuremen t windo w T  from  e pac k et times to  e pac k et times Notice ho w
smaller T yields higher utilization at higher exp erienced dela y and larger T k eeps
more reliable dela y b ounds at the exp ense of utilization lev el Next w e xed T and
v aried the a v erage o w duration T able b sho ws the a v erage link utilization and
maxim um exp erienced dela y for dieren tv alues of a v erage o w duration with T xed
at  e and  e W e v aried the a v erage o w duration from  seconds practically
innite giv en our sim ulation duration of the same length to  seconds Notice ho w
longer lasting o ws allo w higher ac hiev ed link utilization while larger measuremen t
periods yield lo w er link utilization Link utilization is at its highest when the LT
ratio is the largest and at its lo w est when this ratio is the smallest On the other
hand the smaller LT ratio means lo w er exp erienced dela y and larger LT means
the opp ositeth us lo w ering the LT ratio is one w a y to decrease dela y violation rate
In Figs  and  w e pro vide sample path snapshots sho wing the eect of T on
dela y and link utilization W e note ho w ev er a T that yields articially lo w utilization
when used in conjunction with one source mo del ma y yield appropriate utilization
when used with burstier sources or sources with longer burst time

2035 2050
010 30
Simulated Time (secs.)
Delay (msecs.)
Actual/Measured
a Smaller T
2035 2050
010 30
Simulated Time (secs.)
Delay (msecs.)
Actual/Measured
b Larger T
Figure  Eect of T on Exp erienced Dela y
1880 1940 2000
012
Simulated Time (secs.)
Utilization
Measd Actual/
# Flows
74 90
a Larger T
1880 1940 2000
012
Simulated Time (secs.)
Utilization Utilization
Measd Measd Actual/
# Flows
173
b Smaller T
Figure  Eect of T on Link Utilization

Cho osing a Utilization T arget
Imagine no w that o ws ha v e innite duration b y Eqn  the n um b er of admissible
o ws w ould also be innite In practice this means o ws will b e admitted un til the
link reac hes ! utilization As w e noted in Chapter  v ariance in dela y div erges
in a simple M M  queue as the system approac hes full utilization Ob viously  w e
need to prev en t the net w ork from reac hing suc h high load b y instituting a maxim um
utilization target Sources with small grain size and short bursts will allo w an higher
utilization target High densit y sources with long bursts will require a lo w er utilization
target In Chapter  w e will study sev eral attempts to set the utilization target
b oth formal and adho c  Structural Limitations
As w e men tioned in Chapter  when there are only a few o ws presen t or when a
few largegrain o ws dominate the link bandwidth the unpredictabilit y of individual
o ws b eha vior dictates that a measuremen tbased admission con trol algorithm m ust
be v ery conserv ativ e One ma y need to rely less on measuremen ts and more on the
w orstcase parameters furnished b y the source and p erform the follo wing bandwidth
c hec k instead of Eqn    e  G

K
X
i e  i
 where
e  G
b  G
 MAX  
G
b  G
 e  j
b  j
 MAX
j
b  j
 j   K  G
is the sum of all reserv ed guaran teed rates  j
is the sum of all reserv ed rates
in class j  K is n um ber of predictiv e classes and  is a fraction bet w een  and  
F or    w e ha v e the completely conserv ativ e case Similarly  one could do the
follo wing dela y c hec k
D
j
P
j
i  P
f ig
b
i
  G
 P
j   i
i
 for ev ery predictiv e class j for whic h one needs to do a delayc hec k as determined in
Chapter  Ev en with a high enough degree of statistical m ultiplexing a o w migh t b ecome
idle for prolonged periods of time suc h that the measuremen t mec hanism b ecomes
oblivious to it When the idle o w resumes transmission dela y b ound violations could
ensue W e recognize t w o kinds of idle of times  those of timescale larger than
the a v erage o w duration  those that are some small m ultiples of T  Examples
of the rst are o ws with adv ance or dynamic reserv ations This w ould require non
measuremen t based mec hanism to accommo date them and is not part of our curren t
researc h The second kind ma y be common in t w ow a y con v ersations or database
lo okup applications One could either mak e a separate reserv ation for eac h burst
of activit y  risking admission con trol failure or mak e some p ortion of eac h o ws
reserv ation not sub ject to the measuremen t pro cess The latter approac h is adopted
in reference C
  W e should also note that our measuremen tbased approac h is vulnerable to sp on
taneous correlation of sources suc h as when all the tv c hannels air co v erage of a
ma jor ev en t Eac h source mo del used in this study has uncorrelated on and off
times The on and off times bet w een sources are also not correlated If all o ws
suddenly burst at the same time dela y violations will result W e are not a w are of
anyw ayto prev en t this kind of dela y violation since the net w ork cannot predict suc h
correlations b eforehand Instead w e rely on the uncorrelated nature of statistically
m ultiplexed o ws to render this p ossibilitya v ery unlik ely ev en t
If P eak Rate is Incoming Link Bandwidth
Eqn  is an upp er b ound on the w orstcase dela y of a class assuming innite
source rate In realit y  the p eak rate of trac arriving at a switc h is b ounded bythe

bandwidth of the incoming link In this section w e consider the eect of incoming link
bandwidth on our algorithm By expanding the last term of Eqn  and applying
the distributivelaww e get
D
j
P
j   i
b
i
 P
j   i r
i

C
j
b
j
C
j
r
j
 P
j   i
r
i
   P
j   i r
i
b
j
C
j
r
j
 P
j   i
r
i
P
j   i
b
i
 P
j   i r
i

h
C
j
   P
j   i
r
i
i
b
j
C
j
r
j
 P
j   i r
i
 Substituting  in
the incoming link bandwidth for C
j
the sources peak rate and
com bining the t w o terms the equation b ecomes
D
j
P
j   i
b
i

in
   P
j   i
r
i
 in
r
j
b
j
 P
j   i
r
i
 As men tioned in the pro of of Theorem  w e require
P
j
i r
i
at all switc hes hence
r
j
 in
If   P
j   i r
i
 in
r
j
b
j
will not be queued Hence the w orstcase
dela y for  in
is
D
j
P
j   i b
i

h
in
   P
j   i
r
i
i
 in
r
j
b
j
 P
j   i
r
i
 where
x      x x     x    Applying Eqn  to our admission con trol algorithm a prosp ectiv e predictiv e o w
of class k is denied admittance if the dela y bound of the same priorit y trac D
k
is violated
D
k
c
D
k

h
in
   b  G
P
k   i b  i
i
 in
r
j
b
k
 b  G
P
k   i
b  i
 
or if lo w er priorit y classes dela y b ounds D
j
s are violated
D
j
c
D
j
 b  G
P
j   i
b  i
 b  G
P
j   i
b  i
r
k

h
in
   b  G
P
k   i b  i
i
 in
r
j
b
k
 b  G
P
j   i
b  i
r
k
k j  K  Ho w ev er if  in
 Eqn  applies Hence w e do not use Eqns  and  in our
admission con trol algorithm

Chapter  On Unequal Flo w Rejection Rates
Most of the admission con trol algorithms in the literature are based on the violation
pr evention paradigm eac h switc h decides to admit a o w if and only if the switc h
can still meet all of its service commitmen ts In other w ords the only criteria con
sidered b y admission con trol algorithms based on the violation prev en tion paradigm
is whether an y service commitmen ts will b e violated as a result of a new admission
In this section w e discuss some policy or allo cation issues that arise when not all
o ws are completely equiv alen t When o ws with dieren t c haracteristicseither
dieren t service requests dieren t holding times or dieren t path lengthscomp ete
for admission admission con trol algorithms based purely on violation prev en tion can
sometimes pro duce equilibria with some categories of o ws exp eriencing higher rejec
tion rate than other categories do In particular w e iden tify t w o causes of unequal
rejection rate  o ws tra v ersing a larger n um ber of hops ha v e a higher c hance of
b eing rejected b y the net w ork and  o ws requesting more resources are more lik ely
to b e rejected b y the net w ork
Eect of Hop Coun t on Rejection Rates
As exp ected when the net w ork is as loaded as in our sim ulations m ultihop o ws
face an increased c hance of being denied service b y the net w ork F or example in
our sim ulation with homogeneous sources on the Tw oLink net w ork as rep orted in

T able  more than ! of the  new exp sources admitted under guaran teed
service are singlehop o ws This is true for b oth of the b ottlenec k links A somewhat
smaller p ercen tage of the more than  o ws admitted under predictiv e service are
singlehop o ws This eect is ev en more pronounced for sources that request larger
amountof resources eg the poo or the farima sources And it is exacerbated b y
sources with longer lifetimes with few er departures from the net w ork new o ws see
an ev en higher rejection rate
Aside from disparit y in the kinds of o w presen t on the link this phenomenon
also aects link utilization upstream switc hes switc hes closer to source hosts could
yield lo w er utilization than do wnstream switc hes W e observet w o causes to this  switc hes that carry only m ultihop o ws could be starv ed b y admission rejections
at do wnstream switc hes The utilization n um b ers of link L in b oth T ables  and
are consisten tly lo w er than the utilization of the other links in the F ourLink
top ology  Notice that w e set these sim ulations up with no single hop o w on link
L The lo w utilization is th us not due to the constrain t put on b y link Ls own
admission decisions but rather is due to m ultihop o ws being rejected b y do wn
stream switc hes  Nonconsummated reserv ations depress utilization at upstream
switc hes to illustrate a o w admitted b y an upstream switc h is later rejected b y a
do wnstream switc h mean while the upstream switc h has increased its measuremen t
estimates in an ticipation of the new o ws trac trac that nev er come It tak es
time to the expiration of the curren t measurementwindo w for the increased v alues
to come bac k do wn During this time the switc h cannot giv e the reserv ed resources
a w a y to other o ws W e can see this eect b y comparing the utilization at the t w o
b ottlenec k links of the Tw oLink top ology as rep orted in T able  Note ho w ev er
ev en with the presence of this phenomenon the utilization ac hiev ed under predictiv e
service with our measuremen tbased admission con trol algorithm still outp erforms
those ac hiev ed under guaran teed service

Eect of Resource Requiremen ts on Rejection Rates
Sources that request smaller amoun t of resources can prev en t those requesting larger
amoun t of resources from en tering the net w ork F or example in the sim ulation using
the expexp source pair rep orted in T able  ! of the  new guaran teed
o ws admitted after the sim ulation w arm up p erio d w ere exp o ws whic h are less
resource demanding In con trast ! of o ws admitted under predictiv e service
with our measuremen tbased admission con trol algorithm w ere the more resource
demanding exp o ws Another manifestation of this case is when there are sources
with large buc k et sizes trying to get in to a high priorit y class Because the dela y
of a lo w er priorit y class is aected b y b oth the rate and buc k et size of the higher
priorit y o w as explained in Chapter  the admission con trol algorithm is more
lik ely to reject o ws with a large buc k et size and high priorit y than those with a
smaller buc k et size or lo w priorit y  W e see this phenomenon in the sim ulation of
source mo del exp rep orted in T able  When all sources request either of the
t w o classes of predictiv e service with equal probabilit y  of the  o ws admitted
after the sim ulation w arm up p erio d ! w ere of class  When sources request
guaran teed or second class predictiv e service only ! of the  new o ws ends
up b eing guaran teed o ws In b oth of these scenarios the link utilization ac hiev ed
is ! whic h is lo w er than the ! ac hiev ed when all o ws request only class  predictiv e service see T able  but still order of magnitude higher than the !
ac hiev ed when all o ws request only guaran teed service again see T able  W e consider the unequal rejection rate phenomenon a policy issue or rather
sev eral p olicy issues b ecause there is no dela y violations and the net w ork is still
meeting all its service commitmen ts whic h is the original purp ose of admission con
trol the resulting allo cation of bandwidth is ho w ev er v ery unev en and migh t not
meet some p olicy requiremen ts of the net w ork W e w an t to stress that this unequal
rejection rate phenomenon arises in al l admission con trol algorithms based on the
violation pr evention paradigm In fact our data sho ws that these unev en allo cations
o ccur in sharp er con trast when all o ws request guaran teed service when admission

con trol is a simple bandwidth c hec k In Chapter  w e presen t further evidence that
this phenomenon occurs under other admission con trol algorithms Clearly  when
p ossible service commitmen t violations is the only admission con trol criteria one
cannot ensure that p olicy goals will b e met
A Quota Mec hanism
One p ossible approac h to con trol the allo cation of resources to o ws of diering re
quiremen ts is b y instituting a quota p olicy  In this section wepro vide a simple mec ha
nism b y whic h quota p olicies ma y b e implemen ted W e hasten to note ho w ev er that
w e do not in tend to study the fair allo cation of resources b y v arious quota p olicies
W e refer the in terested readers to references KS KU in whic h the authors
study allo cation strategies for t w o t yp es of o ws that reduce blo c king probabilit y  or to reference DM  in whic h the authors prop ose a gametheoretic approac h to
ensure fairness to v arious supp orted o w t yp es
Flo w opp ortunit y cost metric T o design a quota mec hanism w e m ust rst
dene a ow opp ortunity c ost metric that w ould allo w us to compare the resource
requiremen ts of one o w to that of ano other W e require the follo wing c haracteristics
of the metric itm ust b e a function of the o ws tok en buc k et parameters  rb  and the requested dela y bound D   the metric of a o w m ust be indep enden t of
existing trac and  the metric m ust supp ort arbitrarily complex quota p olicies
On a switc h with fif o sc heduling discipline w ekno w from Eqn  that the largest
demand a o w places on the switc h is to serv e its buc k et full of data T o meet the
requested dela y b ound the switc hm ust servethe o w at rate  bD  Th us the w orst
case rate required b y a o w is MAX bD  r  A simple opp ortunit y cost metric is
the ratio b et w een this rate and link bandwidth
 MAX  bD  r     F or example the  of exp source mo del dened in Section  on a  Mbps link is
e and the  of poo source mo del is e

Expressing quota p olicy  Once w e ha v e a metric to compare the resource re
quirementofv arious o ws w e can use them in an expression of quota p olicy  Instead
of allo cating bandwidth to sp ecic  v alues w e sp ecify quota p olicy for dieren t   classes An  class is a range of  v alues  classes should be set at least an order
of magnitude apart Th us a simple sample quota p olicy could b e
x!      y !        z !       The ab o v e p olicy allots x! of capacit y to o ws with  v alues less than  y !
capacit y to  v alues bet w een  and  and z ! to  v alues larger than  On
a system with exp and poo sources w e could allo cate ! of link bandwidth to
exp sources and ! to poo sources b y the follo wing quota p olicy
!     !          The remaining ! of link bandwidth will be allo cated to v arious o ws at the dis
cretion of the admission con trol algorithm
A w orstcase quota mec hanism A straigh t forw ard implemen tation of a quota
p olicy w ould be to partition link capacit y according to the p ercen tages expressed in
the quota policy and to assign eac h p ortion to the corresp onding  class Av ailable
bandwidth of eac h  class is adjusted up on the arriv al and departure of o ws of
that class When an  class exhausts its a v ailable bandwidth no more o w of that
class will be admitted un til more bandwidth b ecomes a v ailable The accoun ting of
a v ailable bandwidth ma y be done fractionally according to the declared w orstcase
requiremen ts of eac h o w
A measuremen tbased quota mec hanism A quota mec hanism that enforces
quota conformance b y the declared w orstcase requiremen ts of o ws could result in
lo w utilization A me asur ementb ase d extension of the ab o v e algorithm allo ws an
class that has exhausted its w orstcase quota allotmen t to b orro w from the pool
of me asur e d a v ailable bandwidth Borro wing is p ermitted as long as there is enough

lefto v er bandwidth to supp ort b oth the b orro w ed amoun t and the nonconsummated
quotas of the other  classes The accoun ting of an  class that b orro ws bandwidth
sho ws a decit When ao w of an  class with decit lea v es the net w ork the quota
coun t of that class is incremen ted as usual As long as an  class is in decit o w
admittance to that class m ust ensure enough pro visioning for the nonconsummated
quotas of the other classes
Sim ulation results W e run some sim ulations to ev aluate the ecacy of the ab o v e
t w o quota mec hanisms In our ev aluation w e test our abilit y to con trol the result
ing mixture of a links trac suc h that o ws requesting large amoun t of resources
are not unin ten tionally discriminated W e further require that our quota mec hanism
do es not unduly lo w er link utilization All the results rep orted here are from sim u
lations on the OneLink top ology of Fig a In the tables belo w the nq ro ws
con tain results from sim ulations with no quota mec hanism the w q ro ws con tain re
sults from the w orstcase quota mec hanism and the mq ro ws con tain results from
the measuremen tbased quota mec hanism In all scenarios that implemen t a quota
mec hanism there are t w o  classes The tuple follo wing w q or mq con tains the p er
cen tages of bandwidth that constitute the quota p olicy for the t w o classes F or eac h
sim ulation w e rep ort the n um ber of concurren tly activ e o ws in eac h  class after
the w arm up p erio d The second column of all the tables showthe n um ber of concur ren tly running o ws in the rst  class the third column the second On all tables
the !Util column sho ws the a v erage link utilization after the w arm up period F or the rst set of sim ulations w e use source mo dels exp and farima T able  sho ws the sim ulation results On the  Mbps b ottlenec k link of the Onelink
top ology  the  of farima sources is  This  class is alloted ! of the utilization
target or ! of link bandwidth whic h allo ws accommo dation of  farima o ws
The table sho ws that this quota is honored in b oth w q and mq cases and that there
are more farima o ws when quota is instituted The w q case sho ws lo w utilization as
predicted and the measuremen t extension do es increase utilization bac k to the lev el
ac hiev ed without quota F or this particular source mo dels the utilization gain of the
measuremen tbased quota mec hanism b enets only the exp sources nev ertheless

T able  Ecacy of Quota Mec hanisms
Sc heme exp farima !Util
nq    w q     mq     T able  Benets of Measuremen tbased Quota Mec hanism
Sc heme exp exp !Util
nq     w q      w q      mq      mq     mq      the quota p olicy is met In sim ulations with the exp and exp source mo dels b oth
kinds of sources b enet from the measuremen tbased quota mec hanism as sho wn in
T able  F rom the sim ulation results w e conclude that giv en a metric with whic h to com
pare the resource requiremen t of v arious o ws w e can implemen t a quota mec ha
nism to regulate the trac mix of a link A quota policy can then be instituted on
top of this mec hanism to prev en t the exclusion of resource demanding o ws The
measuremen tbased quota mec hanism restore the ac hiev able link utilization lo w ered
b y the w orstcase quota mec hanism

Chapter
Comparison of Admission Con trol
Algorithms
In this c hapter w e rep ort on a comparativ e study of v e admission con trol algorithms
to supp ort the con trolledload service mo del describ ed in Chapter  Since the role of
admission con trol is to ensure that service commitmen ts are not violated the main
criterion used in ev aluating an y admission con trol algorithm m ust be ho w w ell it
fullls this role The simplest w a y to ensure complete conformance to commitmen ts
made is to giv e eac h o w enough resources to meet its w orstcase requiremen ts F or
burst y sources ho w ev er this sc heme ultimately results in lo w net w ork utilization
Hence the second ev aluation criterion is ho w high a lev el of net w ork utilization an
admission con trol algorithm can ac hiev e while still meeting its service commitmen ts
The third ev aluation criterion is the implemen tation and op erational costs of an
algorithm An algorithm that can ac hiev e high lev el of utilization without violating
an y service commitmen ts w ould not be useful if it cannot be implemen ted in a cost
eectiv e manner or if it cannot driv e a fast link W e only consider the rst t w o
criteria in this study  Since admission con trol is a sessionlev el not pac k etlev el
con trol mec hanism w e do not exp ect its implemen tation or op erational cost to be
a prohibitiv e factor On the other hand doing measuremen t could be op erationally
exp ensiv e

Our ev aluation of the algorithms in v olv e sim ulating them under v arious scenar
ios W e ha v e tried to mak e the sim ulation en vironmen ts under whic h w e in v estigate
the b eha vior of the v arious algorithms as comparable as p ossible but this do es not
mean the op erating conditions w ould not b e unfairly disadv an tageous to an y partic
ular algorithm In our ev aluation of these algorithms w e try to answ er the question
whic h algorithm pro vides the highest lev el of net w ork utilization at the lo w est pac k et
loss rate or exp erienced dela y The main conclusion of our study is T o satisfy
con trolledload service commitmen ts the admission con trol algorithm m ust iden tify
a link utilization target conditioned up on the c haracteristics of observ ed trac F or
mal attempts to compute this utilization target suc h as the ones found in references
GKK  Floa  that rely solely on p eak rate and tok en buc k et lter c haracteri
zation of sources and do not tak e in to accoun t sources burst length and idle times
distributions can be either to o optimistic or to o conserv ativ e In an en vironmen t
where b esteort trac con tin ues to constitute a large fraction of bandwidth adho c
metho ds of engineering the utilization target shall p erform v ery w ell
Fiv e Admission Con trol Algorithms
Simple Sum The rst admission con trol algorithm simply ensures that the sum
of requested resources do es not exceed link capacit y  Let  be the sum of reserv ed
rates  the link bandwidth  the name of a o w requesting admission and r
the
rate requested b y o w   This algorithm accepts the new o w if the follo wing c hec k
succeeds
r
  W e call this the Simple Sum algorithm This is the simplest admission con trol al
gorithm and hence is b eing most widely implemen ted b y switc h and router v endors
Often to ensure lowqueueing dela y called for b y con trolledload service an appro x
imation of the w eigh ted fair queueing  wf q sc heduling discipline is implemen ted
with this admission con trol algorithm Wf q assigns eac h o w its o wn queue serv ed
at its o wn reserv ed rate thereb y isolating o ws from eac h others bursts W e use
wf q with the Simple Sum admission con trol algorithm in this studyinciden tally  
this setup also satises the c ommitte d r ate service mo del describ ed in BGK  F or
the other measuremen tbased algorithms w e use rstinrstout  fif o sc heduling
discipline
Measured Sum Whereas the Simple Sum algorithm ensures that the sum of
existing reserv ations plus a newly incoming reserv ation do es not exceed capacit ythe
Measured Sum algorithm uses measuremen t to estimate the load of existing trac
This algorithm admits the new o w if the follo wing test succeeds
b  r
  where  is a userdened utilization target as explained in Chapter  and b  the
measured load of existing trac W e let      except otherwise noted The
measuremen t mec hanism is the timewindo w measuremen t mec hanism describ ed in
Chapter  Up on admission of a new o w the load estimate is increased with
b    b  r
  Admissible Region The second measuremen tbased algorithm as prop osed b y
the authors of reference GKK  computes an admissible region that maximizes the
rew ard of utilization against the p enaltyof pac k et loss Giv en link bandwidth switc h
buer space a o ws tok en buc k et lter parameters the o ws burstiness and desired
probabilit y of actual load exceeding b ound one can compute an admissible region for
a sp ecic set of o wt yp es b ey ond whic h no more o w of those particular t yp es should
be accepted The computation of the admissible region assumes P oisson call arriv al
pro cess and indep enden t exp onen tially distributed call holding times Ho w ev er the
authors of GKK  claim that this algorithm is robust against uctuations in the
v alue of the assumed parameters W e refer the in terested readers to GKK  for
the computation of the admissible region The measuremen tbased v ersion of this
algorithm ensures that the measured instan taneous load plus the p eak rate of a new
o wis belo w the admissible region Ev en though reference GKK  do es not sp ecify

adjusting measured load up on admittance of a new o w w e adjust the measured load
according to the admission c hec k b y adding the new o ws p eak rate  p
toitupon
admitting a new o w   b    b  p
  F or o ws describ ed b y a tok en buc k et lter  rb  but not p eak rate w e deriv e their
peak rates  b p from the tok en buc k et parameters using the equation
b p  r bU  where U is a userdened a v eraging p erio d Floa  Ifao w is rejected the admission
con trol algorithm do es not admit another o wun til an existing one lea v es the net w ork
In the remainder of this c hapter w e use the terms utilization target and utilization
threshold in terc hangeably with admissible region
Equiv alen t Bandwidth The third measuremen tbased algorithm computes the
equiv alen t bandwidth for a set of o ws using the Ho eding bounds as explained
in Section  T o recapitulate the equiv alen t bandwidth of a set of o ws is the
bandwidth C    suc h that the stationary bandwidth requiremen t of the set of o ws
exceeds this v alue with probabilit y at most   W e call  the loss rate in the re
mainder of the c hapter ho w ev er as poin ted out in Section  in an en vironmen t
where large p ortion of trac is b esteort trac realtime trac rate exceeding its
equiv alen t bandwidth is not lost but simply encroac hes up on b esteort trac In
suc h an en vironmen t  is more appropriately called the o v ero w rate W e mak e
no suc h distinction in the remainder of this c hapter F ollo wing GKK  w e use
 e except otherwise noted The admission con trol c hec k when a new o w  requests admission is
b
C
H
p
   where
b
C
H
is dened in Eqn  In reference Floa  the author men tions that
instead of measuring a v erage arriv al rate measuring a v erage bandwidth actually used
w ould b e sucien t W e use measured arriv al rate in our study of this algorithm and

measured actual bandwidth usage for the other algorithms Up on admission of a new
o w the load estimate is increased using Eqn  Again if a o ws peak rate is
unkno wn it is deriv ed from its tok en buc k et lter parameters  rb  using Eqn  Similar to the algorithm in GKK  if a o w is denied admission no other o w of
similar t yp e will b e admitted un til an existing one departs
Bounded Dela y  The last measuremen tbased algorithm w e consider is our o wn
algorithm Whereas the previous four algorithms b ound bandwidth usage in their
admission decisions our algorithm bounds b oth bandwidth usage and exp erienced
dela y  Since con trolledload service consists only of one service lev el w e use only a
subset of our algorithm when a new o w  requests admission to the net w ork w e
use the Measured Sum algorithm ab o veto c hec k that the bandwidth requiremen ts
of admitted o ws will be met then w e c hec k that the dela y b ound  D  of existing
trac will not b e violated b y the admittance of the new o w Presumably the dela y
boundofa o w is dened as D  br  where r and b are its tok en buc k et parameters
The o w  is denied admission if it fails the follo wing c hec k
c
D
b
 D  where
c
D is the measured dela y  Up on admittance ofanew o w w e adjust both the
load measure using Eqn  and the dela y measure b y adding b
 to the dela y
estimate
W e w ould lik e to remind the readers that while the admission con trol algorithms
describ ed here are based on meeting qualit y of service constrain ts of either loss rate
or dela y b ound the sp ecic v alues used b y the admission con trol algorithms are not
adv ertised to the users of con trolledload service
Exp onen tialW eigh ted Mo ving Av erage
W e use the same timewindo w measuremen t mec hanism describ ed in Chapter  to
measure net w ork load with all but the equiv alen t bandwidth based admission con trol

algorithms With the equiv alen t bandwidth based admission con trol algorithm w e
use an exp onen tialw eigh ted mo ving a v erage metho d to estimate the a v erage arriv al
rate as suggested in reference Floa  The a v erage arriv al rate  b  S
is measured
once ev ery S sampling p erio d The a v erage arriv al rate is then computed using an
innite impulse resp onse function with w eigh t w  whic h w e set to e in this study
b     w   b  w  b  S
 If the trac arriv al rate c hanges abruptly from  to  and then remains at  a w
of e allo ws the estimate to reac h ! of the new rate after  sampling p erio ds
A larger w mak es the a v eraging pro cess more adaptiv e to load c hanges a smaller
w giv es a smo other a v erage b y k eeping a longer history  Recall that the equiv alen t
bandwidth based admission con trol algorithm requires p eak rate p olicing and deriv es
a o ws peak rate from its tok en buc k et parameters using Eqn  when the peak
rate is not explicitly sp ecied The author of Floa  suggests that U should b e set
smaller than S  the sampling p erio d of the measuremen tmec hanism Flob  In this
study  w e let U  S to reect the peak rate seen b y the measuremen t mec hanism
A smaller S not only mak es the measuremen t mec hanism more sensitiv e to bursts
it also mak es the p eak rate deriv ation more conserv ativ e A larger S ma y result
in lo w er a v erages ho w ev er it also means that the measuremen t mec hanism k eeps a
longer history b ecause the a v eraging pro cess Eqn  is in v ok ed less often
Sim ulation Results
W e run our sim ulations on the OneLink and F ourLink top ologies describ ed in
Chapter  with the Exp onen tial onoff  exp and P areto onoff  poo source
mo dels T able  summarizes the six instan tiation of the t w o mo dels Sources exp
exp exp poo and poo are the same ones weha v e b een using throughout the
dissertation Columns in T able  that ha v e the same names as the ones in T able  ha v e the same meaning W e refer the readers to Section  for their descriptions

T able  Six Instan tiations of the Tw o Source Mo dels
Mo del P arameters TB Filter Switc h P arameters
Mo del
Name
p pkt I N pa r tkn b max D
D  S b p pkt
sec msec pkts sec tkns qlen msec msec ! ptt sec
exp           e #
exp           e  exp          # e   poo           e #
poo           e #
poo           e  The maximal dela y for eac h source listed in column  is also the burst time queue
ing dela y acceptable under the denition of con trolledload service giv en its assigned
tok en buc k et lter Again w e ha v e c hosen the tok en buc k et parameters suc h that
in most cases the dela y b ounds giv en to a o w will b e the same as its burst time
queueing dela y  This facilitates analyzing the p erformance of the algorithms under
con trolledload service F or eachsim ulation with measuremen tbased admission con
trol algorithm w e size the buer at the switc hes with enough space to accommo date
the dela y b ound  D  F or example sim ulations with exp source giv en a link sp eed
of  Mbps use a buer size of  pac k ets In sim ulations with m ultiple source
mo dels ha ving dieren t dela y bound requiremen ts w e use the maxim um of the re
quired buer sizes for example in a sim ulation with b oth exp and exp mo dels
w e use a buer size of  pac k ets Sim ulations with the parameterbased admis
sion con trol algorithm assume innite buer size Column  lab eled   con tains
the utilization threshold used when sim ulating eac h of the source mo del with the
admissible region based admission con trol algorithm This should not be confused
with the utilization target used with the other measuremen tbased admission con trol
sc hemes where the v alue is set to ! link bandwidth When w e sim ulate more than

T able  Singlehop Homogeneous Sources Sim ulation Results
Mo del Simple Sum Measured Sum Adm Rgn Eqv Bw
Name !Util %Actv !Util %Actv !Util %Actv !Util %Actv
exp         exp         exp     # #   poo         poo         poo         one source mo dels with the admissible region based admission con trol algorithm w e
use the most conserv ativ e of the utilization threshold F or example in a sim ulation
with b oth exp and exp sources w e use a utilization threshold of ! The next
column lab eled S  giv es the sampling p erio d used with the measuremen t mec hanisms
in pac k et transmission time  ptt F or the timewindo w mec hanism the windo w size
is   S  Both the equiv alen t bandwidth and admissible region based algorithms tak e
as a parameter in their admission computation F ollo wing GKK  w e use   e except where otherwise noted Both the equiv alen t bandwidth and admissible
region based algorithms also need to deriv e a o ws p eak rate using Eqn  when
the o ws tok en buc k et depth is greater than  The last column lab eled b p con tains
the deriv ed p eak rates Note that for source poo  the deriv ed peak rate is larger
than the actual p eak rate W e also lo ok at using the tok en rate  r  as the p eak rate in
our sim ulations of the equiv alen t bandwidth and admissible region based algorithms
belo w Flo w in terarriv al times durations and w arm up p erio ds are as explained in
Section  The singlehop homogeneous sources case Weno w presen t sim ulation results
from sim ulations on the Onelink top ology  A summary of the results is presen ted
in T able  Eachro w of the table con tains results from up to six sim ulations using
the source mo del named at the leftmost column and the admission con trol algorithm

indicated at the head of the columns The !Util columns list the a v erage utilization
ac hiev ed at the b ottlenec k link of the Onelink top ology  The %Activ e columns
list the a v erage n um ber of concurren tly running o ws in steady state
Therstt w o columns of T able  sho w results from sim ulation using the Simple
Sum parameterbased admission con trol algorithm There are no lost pac k ets The
second set of t w o columns sho w results from the Measured Sum algorithm F or the
scenarios sim ulated here where there is only a singlelev el of service and the dela y
bounds are v ery lo ose w e do not see an y discernible dierence bet w een results from
Measured Sum and those from b ounded dela y based algorithms hence w e do not
sho w results from the b ounded dela y algorithm Except for the poo cases where
b oth the Measured Sum and b ounded dela y algorithms giv e a loss rate on the order
of e sim ulations with other source mo dels using these t w o algorithms do not result
in an y loss F or b oth algorithms w e can ac hiev e no loss with poo sources if w e
reduce the utilization target to ! of link bandwidth in whic h case the a v erage
link utilization ac hiev ed is ! and the a v erage n um ber of concurren tly serv ed o ws
is  Alternativ ely  w e could also ac hiev e no loss with poo sources under the
b ounded dela y algorithm b y main taining utilization target at ! link bandwidth
but reducing dela y bound to  ms k eeping buer space at  pac k ets in this case
the ac hiev able a v erage link utilization is ! the a v erage n um ber of concurren tly
activ e o ws is  The next t w o columns under the heading Adm Rgn giv e the results of sim u
lations with the admissible region algorithm here the p eak rate of sources with tok en
buc k et greater than  is deriv ed from their tok en buc k et parameters using Eqn  W e do not study the p erformance of this algorithm for exp source b ecause the uti
lization threshold for this mo del comes out to be  using the computation pro vided
in GKK  The loss rate for sources poo and poo are e and e resp ec
tiv ely  m uc h higher than  of e used to compute the utilization targets While
the p erformance of this algorithm is impressiv e for the exp source it results in to o
manylossesfor the poo and poo sources Since the exp and poo sources ha v e
mostly the same c haracteristics except for the distribution of their on and off times

w e conclude that b y not taking these in to accoun t the admissible region algorithm
b ecomes o v erly optimistic when giv en sources with hea vytailed on and off times
distributions As the grain size of o ws ie the ratio p  b ecomes larger this algo
rithm b ecomes more conserv ativ e F or the exp and poo sources the ac hiev able
utilization is only ! to ! of the Measured Sum utilization the same measure
men t mec hanism is used with b oth algorithms W e next consider the eect of peak
rate deriv ation on the p erformance of the algorithm W e run some sim ulations using
the admissible region algorithm where the p eak rate is assumed to b e the tok en buc k et
rate ignoring the buc k et depth The utilization thresholds used with the exp and
poo sources in these sim ulations are main tained at ! of link bandwidth as in
the previous case The p erformance of the algorithm using this more lax p eak rate
do es not impro vem uc h for exp mo del the a v erage n um b er of concurren tly serv ed
o ws b ecomes  at a v erage link utilization of ! for poo mo del the n um bers
are  and ! resp ectiv ely  The limitation to the a v erage n um ber of admissible
o ws is inheren t in the computation of the utilization threshold
Analysis of the equiv alen t bandwidth algorithm The t w o columns of T a
ble  under the heading Eqv Bw sho w results from sim ulations using the equiv
alen t bandwidth based admission con trol algorithm here the p eak rate of sources with
tok en buc k et depth greater than  is similarly deriv ed using Eqn  Comparing the
Eqv Bw columns against results from the other measuremen tbased algorithms
one sees that ev en though it is measuremen tbased the p erformance of this algo
rithm is not m uc h b etter than the parameterbased Simple Sum one T o better
understand the equiv alen t bandwidth algorithm w e tak e a closer lo ok at Eqn  b
C
H
b  fp
i
g
 i n
 b  
s
ln   P
n
i  p
i
    One realizes that a smaller b   ie an estimator that more closely trac ks actual uti
lization will giv e a smaller estimated equiv alen t bandwidth resulting in higher o w
admittance rate Increasing the sampling frequency of the exp onen tial a v eraging pro
cess ie using smaller Smak es the estimator more adaptiv e and giv es us an estimate

that is closer to actual utilization Indeed in a sim ulation of exp sources using S
of e w e see  concurren tly activ e o ws ac hieving link utilization of ! Can
w e do better with an ev en more accurate measuremen t mec hanism Notice that in
scenarios with homogeneous sources likeweha v e here kno wing the p eak  p and a v
erage  a rates of the sources w e can deterministically compute the a v erage n um ber
of o ws admissible under the equiv alen t bandwidth metho d b y solving for n in the
quadratic equation
C
H
na
s
ln   np
   The n um ber of admissible o w is the n that also satises C
H
na   Ac hiev able
utilization is then na  F or the exp source and C
H
   Mbps the admissible
n um ber of o w is n   with ac hiev able utilization na    This means
that indep enden t of the accuracy of the measuremen t mec hanism the equiv alen t
bandwidth metho d cannot admit more than  o ws Ev en an oline p ost facto
rerun of the sim ulations using actual utilization as the measured a v erage arriv al
rate will not result in higher n um ber of admitted o ws
One could admit more o ws in to the net w ork if actual aggregate utilization of
n o ws is lo w er than na where a is the sources declared a v erage rate Recall that
the poo mo del has the same p eak and a v erage rates as exp mo del but that it
has hea vy tailed on and off times distributions whic h leads to burstier aggregate
trac T able  sho ws that the burstier aggregate trac results in more poo
o ws b eing admitted under all measuremen tbased algorithms when compared to the
n um ber of admitted exp o ws But notice also that for the equiv alen t bandwidth
case ev en with the higher n um ber of admitted o ws ac hiev able utilization remains
belo w ! This can be explained b y analyzing Eqn  Let & be the second
term of Eqn  ie &  r
ln   P
n
i
p
i
   Since the admission algorithm requires
that
b
C
H
ac hiev able utilization b  is constrained b y
b     &  
Hence admitting  poo sources constrains link utilization to ! whic hisindeed
the utilization ac hiev ed for the sim ulation Similarly for poo sources admitting  o ws constrains ac hiev able utilization to b elo w !
Aside from lo w ering b  either b y using a b etter estimator or ha ving sources send
aggregate trac belo w the computed a v erage w e could also increase admittance
rate b y lo w ering & The t w o v ariables in & are  and the sources peak rate  p By lo w ering  from e to e w e can admit  exp o ws ac hieving !
utilization up from  and ! resp ectiv ely  These increases are in close agreemen t
with computation using Eqn  F or   e Eqn  giv es  exp o ws at
! link utilization whic h also applies to poo sources F or poo sources similar
 Eqn  giv es ! link utilization for  o ws A closer in v estigation of
Eqns  and  rev eals that ac hiev able link utilization is b ounded b y b   na
when n is small and b     &when n is large F or the exp source   e the
in tersection of the t w o lines b   na and b     & is at n   and b     !
meaning that w e can nev er hop e to admit more than  exp o ws or ac hiev e
utilization higher than ! link bandwidth if w e insist on   e In eect
& acts as a safet y zone to accommo date trac that bursts bey ond the measured
a v erage
In the case of sim ulations with exp exp and poo sources the o ws peak
rates are deriv ed from their tok en buc k et parameters using the Eqn  W e sho w ed
the deriv ed p eak rates for the three sources in T able  and p oin ted out that in the
poo case the deriv ed peak rate is actually higher than the actual peak rate In
reference Floa  the author suggests that the tok en buc k et parameters b e set with
a small buc k et depth and p eak rate as tok en rate The tok en buc k et is th us only
in tended to accommo date small v ariations in pac k et dela y that accum ulate in the
net w ork T o see ho w a less conserv ativ e peak rate eects the p erformance of the
algorithm on the exp exp  and poo sources w e sim ulate them with the tok en
buc k et rate of eac h as its p eak rate ignoring the tok en buc k et depths With tok en rate
as p eak rate sim ulation with exp sources ac hiev e a v erage link utilization of !
serving  concurren t o ws for exp sources the ac hiev ed a v erage link utilization

is ! with  concurren t o ws and for poo sources the n um b ers are ! and
o ws resp ectiv ely  While the p erformance of the algorithm impro v es b y order of
magnitude compared to the original case they are scan tly b etter compared to results
from the other measuremen tbased algorithms Next w e exp erimen t with   e
using the tok en rate as p eak rate for sources exp and poo  F or exp  Eqn
giv es  o ws at ! utilization poo results in  o ws at ! utilization Note
that these n um b ers are still lo w er than those ac hiev ed with the Measured Sum
algorithm and w e cannot relax an y parameters further to increase them W e conclude
that the equiv alen t bandwidth based metho d is inheren tly conserv ativ e Inciden tally  this exercise also p oin ts out the dicult y of deriving p eak rate from the tok en buc k et
parameters T o be safe the a v eraging period U in Eqn  should be smaller than
or equal to S  the measuremen t sampling p erio d on the other hand to o small a U
could results in practically innite peak rate when the buc k et depth is large Due
to its conserv ativ eness w e nev er exp erience pac k et loss with an y of the sim ulations
in v olving the equiv alen t bandwidth algorithm
Our next attempt to impro v e the p erformance of the equiv alen t bandwidth algo
rithm in tro duces agam bling factor to Eqn  b        &   F or   w e k eep the original & safet y zone If after an observ ation at timescales
of da ys or w eeks w e decide that our trac is not that burst y and w e can safely
increase link utilization w e can increase   F or example in a sim ulation with exp
sources   e setting      w e are able to admit  o ws ac hieving !
link utilization with no lost pac k ets W e hasten to add ho w ev er in tro ducing  to
the equiv alen t bandwidth equation destro ys its rigorousness and mak es it as adho c
as setting the utilization target of the Measured Sum algorithm
Analyzing the exp erienced queueing dela y  Aside from ac hiev able utilization
and loss rate one migh t also be in terested in pac k ets exp erienced dela y under the

1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160
pdf
packet transmission times
’Measured_Sum’
’Equivalent_Bandwidth’
’Admissible_Region’
Figure  Distribution of exp erienced queueing dela y of exp sources
v arious algorithms In this section w e lo ok at the distribution of exp erienced queue
ing dela y under the Measured Sum admissible region and equiv alen t bandwidth
algorithms Figs   and  sho w these distributions at the switc h con
nected to the b ottlenec k link in top ology Onelink  for sources exp poo  and
poo resp ectiv ely  Recall that under the denition of con trolledload service mo del
the acceptable a v erage burst length queueing dela y for all three source mo dels is
msecs Comparing the exp erienced delayof exp and poo under the admissible
region admission con trol algorithm one can see from Figs  and  that for the
same p eak rate and degree of burstiness poo sources m ust certainly be allo w ed a
smaller utilization target than that used with exp sources Ho w ev er as w e p oin ted
out earlier the admissible region computation in GKK  do es not tak ein to accoun t
the distributions of on and off times resulting in massiv e losses for poo and poo
sources under that algorithm The burstier poo source giv es us a shorter dela y tail
note ho w ev er that the distribution of poo exp erienced dela ys still exhibits a longer
tail than that of exp sources attesting to the lrd eect on exp erienced queueing
dela y  Giv en the acceptable queueing dela y of  ms and the capabilit y of the Mea
sured Sum algorithm to exploit this b ound to ac hiev e a high lev el of link utilization
without exp eriencing an y loss w e think that the equiv alen t bandwidth based algo
rithm is to o conserv ativ e W e men tioned earlier that ev en though w e exp erience loss

1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160
pdf
packet transmission times
’Measured_Sum’
’Equivalent_Bandwidth’
’Admissible_Region’
Figure  Distribution of exp erienced queueing delayof poo sources
1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160
pdf
packet transmission times
’Measured_Sum’
’Equivalent_Bandwidth’
’Admissible_Region’
Figure  Distribution of exp erienced queueing delayof poo sources

1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160
pdf
packet transmission times
’Measured_Sum_ut=90’
’Measured_Sum_ut=80’
’Bounded_Delay_ut=90_db=8ms’
Figure  Distribution of exp erienced queueing dela y of poo sources under the
Measured Sum and b ounded dela y algorithms for dieren t utilization target ut
and dela y bound db
T able  Multiplehop All Sources Sim ulation Results
Link Measured Sum Adm Rgn  Adm Rgn  Equiv alen t Bw
!Util %Actv !Util %Actv !Util %Actv !Util %Actv
L        
L        
L        
L        
rate of e for poo sources with the Measured Sum algorithm when the utiliza
tion target is set at ! link bandwidth w e suer no loss b oth when the utilization
target is set to ! and when w e use the b ounded dela y algorithm with dela y b ound
set to ms Fig  sho ws the exp erienced dela y of the three cases
The m ultiplehop heterogeneous sources case T able  con tains the a v
erage link utilization and a v erage n um ber of connections of the four links in the
F ourlink top ology from sim ulations where w e run all six sources with the c hoice
of sources uniformly distributed All the sim ulations use a sampling period of e

T able  P ercen tage Comp osition of T yp e of Admitted Flo ws
Algorithm exp exp exp poo poo poo
Measured Sum !    
Admissible Rgn      
Admissible Rgn      
Equiv alen t Bw      
pac k et transmission times and buer space for  pac k ets F or sources with tok en
buc k et depth greater than  w euse the tok en buc k et rate as the p eak rate ignoring
the buc k et depth The table sho ws that the equiv alen t bandwidth based algorithm
is again rather conserv ativ e in this scenario The Adm Rgn  scenario uses a
utilization target of ! whereas the Adm Rgn  scenario uses ! None of
the sim ulation suers an y pac k et loss Link L consisten tly ac hiev es lo w er utiliza
tion than the other links W e called this the underr epr esentation phenomenon in
Chapter  and attributed its cause to unconsummated reserv ations when m ultihop
o ws admitted b y the switc h attac hed to L are rejected b y one of the do wnstream
switc hes T o b etter understand wh y  when compared to the Adm Rgn  n um b ers
the larger n um ber of o w coun ts under the Measured Sum algorithm results in
lo w er utilization w ein v estigate the mix of admitted o ws Again w e do not include
results from b ounded dela y algorithm b ecause they are practically iden tical to the
Measured Sum results T able  sho ws the comp osition of the t yp e of admitted
o ws in p ercen tages W e can immediately see that under Admissible Rgn  more
o ws with deep er buc k et depth are admitted resulting in higher utilization ev en
at a lo w er o w coun t compared to the n um b ers of Measured Sum T able
also conrms our earlier observ ation that more resource demanding o ws can suer
from another form of underr epr esentation where they are discriminated against b y
the net w ork This problem is ev en more pronounced in the Equiv alen t Bw case
where the peak rates of all curren tly admitted o ws are used in ev ery admission de
cision While the p erformance of the admissible region algorithm is excellen t when
the utilization threshold is ! the c hoice of this utilization threshold is not from

computation in GKK  rather it is a b est case though adho c  c hoice for this
scenariohence do es not allo w the load estimation error to b e quan tied and assessed
an y more more rigorously than under the Measured Sum metho d The Measured Sum metho d seems to w ork as w ell as the bounded dela y algo
rithm under the scenarios sim ulated here The admissible region based algorithm
suggested b y the authors of reference GKK  is either to o conserv ativ e when o ws
grain size is large or to o optimistic when the o ws ha v e hea vytailed on and off
times distributions The equiv alen t bandwidth based algorithm found in Floa  is
inheren tly conserv ativ e In general while it is clear that admission con trol algorithm
for con trolledload service should ha v e a utilization target it is still not clear ho w
to compute this bound from observ ed trac c haracteristics Computing equiv alen t
bandwidth or admissible region taking in to accoun t only the sources p eak rate and
tok en buc k et lter parameters do es not seem sucien t One m ust also tak e in to
accoun t the sources burst lengths and idle times distributions The Simple Sum
metho d used in conjunction with wf q sc heduling discipline fa v ored b y router v en
dors for its implemen tation simplicit y giv es the w orst p erformance in terms of link
utilization Ho w ev er w e ha v e not studied the implemen tation and op erational costs
of the v arious admission con trol algorithms when these are tak en in to accoun t one
mightnot be able to implementan ything more complicated than the Simple Sum
algorithm giv en curren t hardw are tec hnology  
Chapter
Summary and Extensions
In this dissertation w e presen ted a measuremen tbased admission con trol algorithm
that consists of t w o logically distinct pieces the criteria and the estimator The ad
mission con trol criteria are based on an equiv alen t tok en buc k et lter mo del where
eac h predictiv e class aggregate trac is mo deled as conforming to a single tok en
buc k et lter This enables us to calculate w orst case dela ys in a straigh tforw ard
manner The estimator pro duces measured v alues w e use in the equations repre
sen ting our admission con trol criteria W e ha v e sho wn that ev en with the simplest
measuremen t estimator it is p ossible to pro vide a reliable dela y bound for predic
tiv e service using our measuremen tbased admission con trol algorithm Weha v e also
sho wn that our measuremen tbased admission con trol can be used with con trolled
load service to pro vide the illusion of ligh tly loaded net w ork Th us w e conclude that
for those applications willing to tolerate dela y violations services with more relaxed
commitmen ts than those pro vided b y guaran teed service are viable alternativ es F or
burst y sources in particular measuremen tbased admission con trol algorithm with
the more relaxed services can ac hievea lev el of net w ork utilization signican tly higher
than those ac hiev able under guaran teed service Finallyw enowiden tify three broad
categories of p ossible extensions to our w ork

A Better Estimator
It is essen tial for an admission con trol algorithm to set aside some slac k bandwidth
to accommo date sudden increases in trac o w The amoun t of bandwidth set aside
for suc h purp ose could b e decided based on historical data suchas weha v e done with
our utilization target A less adho c metho d w ould be to compute the equiv alen t
bandwidth of the aggregate trac as prop osed b y the authors cited in Section  Unfortunately  b ecause of the assumptions made b y the dieren t approac hes to com
pute equiv alen t bandwidth the resulting n um b ers are either to o conserv ativ e for
certain t yp es of o w or to o optimistic for other t yp es of o w Or the approachw ould
be to o restrictiv e and supp ort only sp ecic t yp es of o w Recen t w orks on sp ectral
analysis of net w ork trac suc h as LCH ha v e iden tied the lo w frequency of traf
c as a go o d indicator of bandwidth requiremen t and the high frequency as indicator
of buer space requiremen t Ho w ev er other researc hers ha v e also called in to question
the reliabilit y of trac auto correlation in predicting queueing b eha vior HH It is
in teresting to pursue ho w and when one migh t b e able to p eruse the sp ectral densit y
of trac in estimating adequate resource pro visioning
Another approac h to a b etter estimator is to b ound the error rates of the estimates
Reference DJM con tains suc h an approac h Giv en the reliance of estimating error
rates on trac c haracteristics w e doubt that this w ould b e a promising approac h Of
more in terest to us is a fast implemen tation of the estimator either in hardw are or in
soft w are References C
  W CK G  con tain p ossible hardw are implemen tations
of the estimator Finallyw e w ould lik e to implementan higher order mec hanism to
automatically tune the parameters of our algorithm o v er large timescales
Other Admission Criteria
In Chapter  w e iden tify t w o kinds of o w underrepresen tation problem  o ws
with large resource requiremen ts are discriminated at admission time and  o ws
with m ultiple hops run a larger c hance of being rejected b y the net w ork The rst
of these discriminations is lo cal to the decision of a switc h the second requires co op
eration bet w een switc hes W e sho w ed in Chapter  that these problems are alw a ys

presen t when service violation prev en tion is the only criterion used in making admis
sion decisions b oth parameterbased and measuremen tbased T o address the rst
kind of discrimination w e adopted in Chapter  another criterion wherein dieren t
kinds of o w are alloted their o wn quota W e also in tro duced a measuremen tbased
quota mec hanism that allo ws net w ork administrators to con trol the trac mix on
their links This mec hanism relies on a o w opp ortunit y cost metric to compare the
resource requiremen t of one o w against that of others Both a more accurate es
timate of o ws actual opp ortunit y cost and a more sophisticated quota mec hanism
w ould be in teresting extensions to our w ork W e ha v e not begun to address the
second discrimination problem T o explore it is of of immediate in terest to us
Additional Issues
In this section w e presen t three additional issues that could eect a measuremen t
based admission con trol algorithm
Stabilit y of adaptiv e pla ybac k p oin t Guaran teed service pro vides an absolute
dela y b ound from whic h one can compute the b ound on a pac k ets endtoend dela y  Predictiv e and con trolledload services do not pro vide suc h bound While adaptiv e
applications can adjust their pla ybac k poin t to accommo date v ariations in pac k ets
endtoend dela y  one w ould still prefer a stable pla ybac k poin t An in teresting re
searc h pro ject w ould be to study the stabilit y of pla ybac k poin ts for applications
receiving predictiv e and con trolledload services W ould one be able to compute a
stable endtoend dela y distribution giv en dela y distributions at the switc hes along a
o ws path
Link sharing In references FJ SCZ the authors iden tify the need to parti
tion link bandwidth in to p ortions that are then sold to separate en tities This service
is called linksharing in the literature Topro vide this service the admission con trol
algorithm m ust ensure that realtime trac from eac h en titydoes not o v ero w its al
loted p ortion As wemen tioned in this dissertation a measuremen tbased admission
con trol algorithm can deliv er high degree of utilization gain only when there is an

high degree of statistical m ultiplexing The reliabilit y of trac estimates also dep end
on high degree of statistical m ultiplexing Linksharing lo w ers the degree of statistical
m ultiplexing b y segregating trac in to dieren t partitions One p ossible approac h
to regain an higher degree of statistical m ultiplexing is for the sc heduler and trac
estimators to ignore link partitioning once a realtime o w has b een determined bythe
admission con trol algorithm to conform to its en tit ys share W e plan to exp erimen t
with this arc hitecture
Preemptible Service In Chapter  w e men tioned sources that can transmit at
v ariable bandwidth either b y c hanging their compression ratio or b y transmitting
few er lev els of their hierarc hically enco ded data In reference HS eac hlev el of hi
erarc hically enco ded data is sen t as a separate o w with resource reserv ation T o sup
port v ariable bandwidth sources requires reconsideration of our measuremen tbased
admission con trol algorithm In the case where a source can adjust its transmission
rate based on congestion feedbac k our trac estimates m ust ignore the extra trac
generated b y the source when net w ork is not congested In the case where sources re
serv e bandwidth for eac h of their hierarc hically enco ded data and adjust the n um ber
of lev els they transmit based on congestion feedbac k w e m ust prioritize our drop
ping p olicy  One p ossible solution is to givelo w er sc heduling priorities to higher lev els
trac Ho w ev er this could cause massiv e pac k et reordering if the dieren t lev els of
priorit y are sc heduled b y strict priorit y  W e think the righ t approac h is to transmit
trac from all hierarc hies in the same lev el of sc heduling priorit y and rely on pac k et
dropping p olicy to drop the highest la y er trac rst
T o facilitate prioritized dropping policy  w e in tend to in tro duce a meta service
mo del the preemptible service mo del It is a meta service mo del in that it m ust
be used in conjunction with one of the other service mo dels men tioned previously
whic h w e will call the base service P ac k ets of a preemptible o w will be dropp ed
rst before pac k ets from nonpreemptible o ws of the same sc heduling priorit y  A
preemptible o w ma y also be completely dropp ed from service W e can supp ort
m ultiple lev els of preemptible service with decreasing dropping priorities An extra
benet of preemptible service is that one can admit preemptible o ws that w ould

otherwise b e rejected b ecause of quota or link share violation Preemptible o ws could
also be dropp ed up on sudden surges of trac or arriv als of an adv ance reserv ation
start time Note that when net w ork is not congested preemptible o ws receiv e
the same service as nonpreemptible o ws requesting the same base service Hence
preemptible service is not b esteort service It is an in teresting problem to study
ho w a measuremen t mec hanism m ust be designed to supp ort preemptible o ws Do
w e include pac k ets from preemptible o ws in our measuremen t If not ho w shall
w e subtract them out esp ecially when measuring dela y If so ho w do w e recognize
whether w e can admit more nonpreemptible o ws giv en curren t load of preemptible
trac

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and Vide o WorkshopNo v  URL h ttpnet w ebuscedujaminadmctlnossda vpsZ
Kel FP  Kelly  Eectiv e Bandwidths at MultiClass Queues Queueing
Systems #  KM SM Kliv ansky and A Mukherjee On longrange dep endence in nsfnet
trac T ec hnical Rep ort GITCC Gerogia Insititue of T ec hnology  Decem b er  KMR H Kanakia P P  Mishra and A Reibman An Adaptiv e Congestion
Con trol Sc heme for RealTime P ac k et Video T ransp ort Pr o c of A CM
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Strategies in In tegrated Service Net w orks IEEE T r ansactions on Com
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for an a tm Net w ork Considering Fluctuations in Cell Loss Rate Pr o c
of IEEE GLOBECOMM   pages #  KU YH Kim and CK Un Analysis of Bandwidth Allo cation Strategies
with Access Con trol Restrictions in Broadband isdn IEEE T r ansac
tions on Communic ations # Ma y  Kur J Kurose On Computing P ersession P erformance Bounds in High
Sp eed Multihop Computer Net w orks Pr o c of A CM SIGMET
RICS  pages # Jun  KW C G Kesidis J W alrand and CS Chang Eectiv e Bandwidths for
Multiclass Mark o v Fluids and Other a tm Sources A CMIEEE T r ans
actions on Networking # Aug  
LCH SQ Li S Chong and CL Hw ang Link Capacit y Allo cation and
Net w ork Con trol b y Filtered Input Rate in HighSp eed Net w orks
A CMIEEE T r ansactions on Networking # F eb  URL
h ttpmo c haeceutexasedu sanqipap erslinkcapps
LPP A Lom bardo S P alazzo and D P anno A F ramew ork for Sharing
Bandwidth Resources Among Connectionless and ConnectionOrien ted
Services in bisdns  th International T eletr ac Congr ess Sept
L TWW WE Leland MS T aqqu W Willinger and DV Wilson On the Self
Similar Nature of Ethernet T rac Extended V ersion A CMIEEE
T r ansactions on Networking # F eb  L V SH Lo w and P P  V araiy a A New Approac h to Service Pro visioning
in A TM Net w orks A CMIEEE T r ansactions on Networking #
Oct  L W WE Leland and DV Wilson High TimeResolution Measuremen t
and Analysis of LAN T rac Implications for LAN In terconnection
Pr o c of IEEE INF OCOM    MH
 K MeierHellstren et al T rac Mo dels for ISDN Data Users Oce
Automation Applications International T eletr ac Congr essth  pages
# Jun
Mit D Mitra Sto c hastic Theory of a Fluid Mo del of Pro ducers and Con
sumers Coupled b y a Buer A dvanc e Applie d Pr ob ability #
MJV S McCanne V Jacobson and M V etterli Receiv erdriv en La y
ered Multicast Pr o c of A CM SIGCOMM   Sep  URL
ftpftpeelblgo vpap ersmccannesigcommpsgz
Mol EC Molina Application of the Theory of Probabilit y to T elephone
T runking Problems The Bel l System T e chnic al Journal #
MP NM Mitrou and DE P endarakis CellLev el Statistical Multiplexing
in a tm Net w orks Analysis Dimensioning and CallAcceptance Con trol
wrt qos Criteria th International T eletr ac Congr ess Sept  MSST T Murase H Suzuki S Sato and T T ak euc hi A Call Admission
Con trol Sc heme for a tm Net w orks Using a Simple Qualit y Estimate

IEEE Journal of Sele ctedA r e as in Communic ation # Dec
NK R Nagara jan and J Kurose On Dening Computing and Guar
an teeing Qualit yofService in HighSp eed Net w orks Pr o c of IEEE
INF OCOM    NRSV I Norros JW Rob erts A Simonian and JT Virtamo The Sup er
p osition of V ariable Bit Rate Sources in an a tm Multiplexer IEEE
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Dela yLoss T radeo in a tm Net w orks IEEE Journal of Sele ctedA r e as
in Communic ation # Dec  OST S Oh ta KI Sato and I T okiza w a A Dynamically Con trollable a tm
T ransp ort Net w ork Based on the Virtual P ath Concept Pr o c of IEEE
GLOBECOMM   pages #  P ar AK P arekh A Gener alizedPr o c essor Sharing Appr o ach to Flow Contr ol
in Inte gr ate d Servic es Networks PhD thesis MIT Lab for Information
and Decision Systems T ec h Rep ort LIDSTR  P arts of this
thesis w ere also published with RG Gallager in the A CMIEEE T r ans
actions on Networking  and  PF V P axson and S Flo yd WideArea T rac The F ailure of P ois
son Mo deling Pr o c of A CM SIGCOMM   pages # Aug
An extended v ersion of this pap er is a v ailable as URL
ftpftpeelblgo vpap ersp oissonpsZ
PG AK P arekh and RG Gallager A Generalized Pro cessor Sharing Ap
proac h to Flo w Con trol in In tegrated Services Net w orks The Single
No de Case A CMIEEE T r ansactions on Networking #
PK C K P ark G Kim and M Cro v ella On the relationship be t w een le sizes transp ort proto cols and selfsimilar net w ork traf
c T ec hnical rep ort Boston Univ ersit y  Mar  URL h ttpcs
wwwbuedufacult ycro v ellapap erarc hiv elesproto colsps
RD G Ramam urth y and RS Dighe Distributed Source Con trol A Net
w ork Access Con trol for In tegrated Broadband P ac k et Net w orks IEEE
Journal of Sele cte d A r e as in Communic ation # Sep  
Rob JW Rob erts T rac Con trol in bisdn  Computer Networks and
ISDN Systems #  RS C Rasm ussen and J Sorensen A Simple Call Acceptance Pro cedure in
an a tm Net w ork Computer Networks and ISDN Systems #
RSKJ C Rasm ussen J Sorensen KS Kv ols and SB Jacobsen Source Inde
p enden t Call Acceptance Pro cedures in a tm Net w orks IEEE Journal
of Sele cte d A r e as in Communic ation # Apr  Sai H Saito Call Admission Con trol in an a tm Net w ork Using Upp er
Bound of Cell Loss Probabilit y IEEE T r ansactions on Communic a
tions # Sept  SCZ SJ Shenk er DD Clark and L Zhang A Sche duling Servic e Mo del
and a Sche duling A r chite ctur e for an Inte gr ate d Servic es Packet Network URL ftpparcftpparcxero xcompubnetresearc harc hnps  She S Shenk er F undamen tal Design Issues for the F uture In ternet IEEE
Journal of Sele cte d A r e as in Communic ation # Sep
SRLL C Shim I Ry oo J Lee and SB Lee Mo deling and Call Admission
Con trol Algorithm of V ariable Bit Rate Video in a tm Net w orks IEEE
Journal of Sele cte d A r e as in Communic ation # F eb  SS H Saito and K Shiomoto Dynamic Call Admission Con trol in
a tm Net w orks IEEE Journal of Sele cte d A r e as in Communic ation # Sept
V C M Visw anath and PChou An ecien t algorithm for hierarc hical com
pression of video preprin t  VPV W V erbiest L Pinno o and B V o eten The Impact of the a tm Concept
on Video Co ding IEEE Journal of Sele cte d A r e as in Communic ation # Dec  W C I W ak eman and J Cro w croft A Com bined Admission and Congestion
Con trol Sc heme for V ariable Bit Rate Video The Journal of Distribute d
Systems Engine ering

W CK G R W areld S Chan A Konheim and A Guillaume RealTime T raf
c Esitmation in A TM Net w orks International T eletr ac Congr ess June  WKFR G W o o dru R Kositpaib o on G Fitzpatric k and P Ric hards Con trol
of a tm Statistical Multiplexing P erformance Computer Networks and
ISDN Systems #  WKZL DE W rege EW Knigh tly  H Zhang and J Lieb eherr Deterministic
Dela y Bounds for VBR Video in P ac k etSwitc hing Net w orks F undamen
tal Limits and T radeOs A CMIEEE T r ansactions on Networking # Jun
W ro J W ro cla wski Sp e cic ation of the Contr ol le dL o ad Network Element
Servic e In ternetDraft No v  WTSW W Willinger MS T aqqu R Sherman and DV Wilson Self
Similarit y Through HighV ariabilit y Statistical Analysis of Ethernet
LAN T rac at the Source Lev el Pr o c of A CM SIGCOMM   pages
# Aug
YH N Yin and MG Hluc h yj A Dynamic Rate Con trol Mec hanism for
Source Co ded T rac in a F ast P ac k et Net w ork IEEE Journal of Se
le cte d A r e as in Communic ation # Sept  Z
 L Zhang et al R esour c e R eSerV ation Pr oto c ol  rsvp In ternetDraft
URL ftpdsin ternicnetin ternetdrafts Oct  ZF H Zhang and D F errari Impro ving Utilization for Deterministic Ser
vice in Multimedia Comm unication IEEE International Confer enceon
Multime dia Computing and Systems
ZK H Zhang and EW Knigh tly  Pro viding EndtoEnd Statistical P erfor
mance Guaran tee with Bounding In terv al Dep enden t Sto c hastic Mo d
els Pr o c of A CM SIGMETRICS  pages # Ma y 
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Description
Sugih Jamin. "A measurement-based admission control algorithm for integrated services packet networks." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 639 (1996). 
Asset Metadata
Creator Jamin, Sugih (author) 
Core Title USC Computer Science Technical Reports, no. 639 (1996) 
Alternative Title A measurement-based admission control algorithm for integrated services packet networks (title) 
Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher) 
Tag OAI-PMH Harvest 
Format 116 pages (extent), technical reports (aat) 
Language English
Unique identifier UC16270838 
Identifier 96-639 A Measurement-Based Admission Control Algorithm for Integrated Services Packet Networks (filename) 
Legacy Identifier usc-cstr-96-639 
Format 116 pages (extent),technical reports (aat) 
Rights Department of Computer Science (University of Southern California) and the author(s). 
Internet Media Type application/pdf 
Copyright In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/ 
Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series) 
Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. 
Repository Name USC Viterbi School of Engineering Department of Computer Science
Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Repository Email csdept@usc.edu
Inherited Values
Title Computer Science Technical Report Archive 
Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017. 
Coverage Temporal 1991/2017 
Repository Email csdept@usc.edu
Repository Name USC Viterbi School of Engineering Department of Computer Science
Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher) 
Copyright In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/