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Congestion pricing with an unpriced time period and with heterogeneous user groups

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Congestion pricing with an unpriced time period and with heterogeneous user groups

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CONGESTION PRICING WITH AN UNPRICED TIME PERIOD AND
WITH HETEROGENEOUS USER GROUPS

by

Jiangping Zhou

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(POLICY, PLANNING AND DEVELOPMENT)

August 2010

Copyright 2010 Jiangping Zhou
ii

DEDICATION

I dedicate this dissertation to all my family members in China and in the US.
Without their patience, understanding, support, and most of all, love, the completion of
this work would have been impossible.

iii

ACKNOWLEDGEMENTS

I wish I could find better words than “thank you so much” to describe my gratitude
for Professor Genevieve Giuliano, my research advisor. For the past several years, she has
provided me with so many wonderful opportunities to execute intriguing research projects
and to network with leading figures in the fields of transportation and planning. She has
released me from worry about financial and logistic burdens while pursuing my research
and studies. She has given me constant encouragement and unwavering support each time I
felt tired or frustrated.
I would like to acknowledge Professor James E. Moore, II for his insightful
guidance and timely support as an outside member on my doctoral committee. I will not
forget how responsive he was to almost every email I sent him or to the various questions I
posed to him about research or professional development. He constantly demonstrated to
me how dedicated and warm-hearted a professor can be for his students. I will miss the
days of going to local academic events in his car with fellow students— and all the humor
and joy.
I am also very thankful to Professor Lisa Schweitzer, who has given me chances to
contribute to several research projects and to benefit from her unconditional trust and
timely encouragement. I enjoyed those short but fruitful meetings with her. In those
meetings, we not only talked about how to link our research with the well-being of the
disadvantaged but also how to upgrade oneself to be a first-rate researcher and a
responsible citizen. I learned so much from her emails, which dealt with a variety of topics
iv

on academic research and beyond. She showed me how one could have insight into both
academic research and daily life. Her thoughtful essays helped me see the fun and wit of
life and the beauty of the English language.
In addition, I would like to express my gratitude to Professors Kenneth Small, from
University of California, Irvine, Erik V erhoef from Free University in Holland, and Jose A.
Gomez-Ibanez from Harvard University. Through a series of emails, Professor Small
kindly helped me translate sporadic congestion pricing phenomena in the real-world
setting into coherent research questions within a context one could scientifically and
seriously explore in a doctoral dissertation. He also kindly reviewed multiple versions of
my models and provided me with suggestions regarding how I could improve them.
Professor Verhoef carefully explained every question I had about his papers on congestion
pricing, which are important references for this dissertation. Professor Gomez-Ibanez,
during his half-day stay at USC, spent hours with me, sharing his research experience and
going over my original doctoral research proposal. I can never forget how quickly he was
able to grasp the essence of the proposal and how responsive he was in providing me with
insightful feedback on— and useful references for— enhancing the proposal.
Last, but not least, I would like to thank the classmates and research colleagues I
met at USC. I know you will not blame me if I do not provide a full list of your names here,
because there so many of your names I could have listed, among them: Tom O’Brien,
Lianqian (Ivy) Hu, Sylvia He, Keith Naughton, and Xian Zhang. I could not believe how
much one can learn from fellow students and colleagues until I met you and interacted with
you.
v

TABLE OF CONTENTS
Dedication

Acknowledgments

List of Tables

List of Figures

Abbreviations

Notations

Abstract

Chapter 1. INTRODUCTION
1.1 Overview
1.2 Research Questions
1.3 Research Design
1.4 Policy Implications of the Disseration
1.5 Organization of the Dissertation

Chapter 2. RELEV ANT LITERATURE
2.1 Congestion, Congestion Pricing, and Planning/Public Policy
2.2 First-, Second-, and Third-best Regimes: Definitions
2.3 Existing Studies of Different Regimes: Taxonomy
2.4 The Second- and Third-best Regimes: User Heterogeneity
2.5 The Second- and Third-Best Regimes: Policy Constraints
2.6 The Second- and Third-best Regimes: Unpriced Alternative and Heterogeneity
2.7 Implications from Existing Literature

Chapter 3. MODEL DEVELOPED AND DATA USED
3.1 The Model of General Form
3.2 Solutions to the Model
3.3 The Expanded Wardrop’s Principle
3.4 Constrained Iterations
3.5 Numerical Models

Chapter 4. QUANTITATIVE RESULTS: CASES
4.1 First-best Toll Is Not a Must
4.2 User Group Exemption Can Be Made
4.3 Tradeoff Has to Be Made
4.4 Toll Structures and Distributional Effects
4.5 Consideration of User Group Differences

Chapter 5. QUANTITATIVE RESULTS: POLICY SCENARIOS
5.1 Efficiency Underestimated When User Group Differences Ignored
5.2 Demand Elasticity and the Representative Regime
5.3 User Group Differences that Could Be Ignored
5.4 Value of Time and the Representative Regime
5.5 Commute Distance and the Representative Regime
ii

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ix

x

xi
1
1
6
7
14
17

19
19
24
26
32
53
56
59

64
64
68
72
79
81

100
103
104
105
106
107

109
112
112
113
114
116
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5.6 Totally Ignoring User Group Differences Lead to Many Biases

Chapter 6. CONCLUSIONS AND FUTURE DIRECTIONS

REFERENCES

117

119

125
vii

LIST OF TABLES

Table 1: Cases Constructed for the Representative Regime
Table 2: Values of Time for Truckers in Existing Studies
Table 3: Values of Time for Motorists in Existing Studies
Table 4: Existing Estimated Values of Truckers’ Demand Elasticity
Table 5: Existing Estimated Values of Motorists’ Demand Elasticity
Table 6: The Simplified Literature of Relevance
Table 7: Literature Using the Static Model
Table 8: Constraints Considered in Existing Studies
Table 9: Literature on Heterogeneity and Unpriced Alternative
Table 10: Economic Properties of a Simplified Congestion Pricing Program
Table 11: Cases Constructed and Studied
Table 12: Policy Scenarios Under the First-best Case
Table 13: No-toll Baseline Traffic V olumes
Table 14: Parameters Used in the Model
Table 15: Quantitative Results about Different Cases Constructed
Table 16: Quantitative Results of Policy Scenarios

11

35

35

38

39

48

50

53

57

74

82

84

88

91

101

110

viii

LIST OF FIGURES

Figure 1: Map of the Toll Freeway Segment
Figure 2: Hours Delay per Traveler by Population Area Size in America
Figure 3: The Basic Model for Congestion Pricing
Figure 4: Congestion Pricing’s Impacts on the Poor and the Rich
Figure 5: The Network Considered

13

19

29

42

64

ix

ABBREVIATIONS

ACD Average Commute Distance

AGC Average Group-specific Costs

GAO Government Accountability Office

FHWA Federal Highway Administration

MEC Marginal External Costs

MSC Marginal Social Costs

SCAG Southern California Association of Governments

SW Social Welfare

PCEs Passenger Car Equilibrants

Rel. SW Relative Social Welfare gains of one congestion pricing case as
compared to the first-best case

TT link-base Travel Times

UCD Unobserved Costs of Diversion for a user who switches from one time
period to another

VOT Value of Time

x

NOTATIONS

τ A toll charged in a congestion pricing regime

η Generalized cost-demand elasticity

ω Relative efficiency of a congest pricing case, ω = (welfare gain from
case)/(welfare gain from first-best case)

M User group such as motorists in a congestion pricing regime

L Length of a link in a transportation network

N Number of user in absolute vehicle counts or in PCEs

D Inclusive price, which equals to AGC plus τ and UCD, if applicable

T User group such as truckers in a congestion pricing regime

t
1
or t1 Tolling period or peak hour in a congestion pricing regime

t
2
or t2 Non-tolling period or shoulder hour(s) in a congestion pricing regime
xi

ABSTRACT

Congestion pricing has received increased attention from planners and policy
analysts as a cost-effective strategy to optimize the economic efficiency of congestible
facilities like roads. In the real-world setting, the implementation of congestion pricing
often involves heterogeneous user groups, unpriced alternatives for some users or user
groups, and/or policy constraints such as the toll revenue collected must be at least equal
to the costs of implementation. This dissertation focuses on a representative category of
congestion pricing regimes (called “the representative regime” in the text) that has an
unpriced time period, heterogeneous user groups, and/or has to meet certain policy
constraints. Internet-based search and a literature review indicate that the representative
regime has not been well studied; however, the regime has great relevance to planners
and policy analysts interested in congestion pricing. This dissertation reviews existing
literature related to the regime, develops a model of general form for the regime, devises
numerical cases about the regime, and examines the economic properties of the regime
based on the case findings.
This dissertation finds that treating users as homogeneous may cause biased
estimations of the economic properties of the representative regime. But results of
different cases in this dissertation show that there is no silver bullet regarding how to
differentiate users in the regime. For planners and policy analysts interested in congestion
pricing, nevertheless, it is probably worthwhile to categorize users into two user groups:
truckers and motorists, focusing on user group differences in value of time, demand
elasticity, commute distance, and road space requirements.
This dissertation also finds that as long as heterogeneous users are categorized
xii

into reasonable user groups and group-specific data are used in relevant models, the
economic efficiency of the representative regime based on the models will remain stable
whether first-, second-, or third-best tolls are charged. Ignoring user group differences in
value of time, demand elasticity, road space requirement, and commute distance all affect
the economic properties of the representative regime disclosed by the models. Relatively
speaking, ignoring the difference in road space requirement results in fewer biases in the
estimated indicator values of the regime.
This dissertation argues that offering unpriced alternatives and/or meeting certain
policy constraints— such as exempting certain user groups all the time— reduces the
economic efficiency of the representative regime. But the reduction does not necessarily
remove most of the optimal value of the regime. For instance, the case results of this
dissertation indicate that exempting all truckers from paying any tolls all the time only
reduces 7-10% of the maximum economic efficiency of the representative regime that the
first-best tolls can achieve. Of course, the overall economic efficiency ignores the fact
that different numbers of users by group could be priced off or on the toll road in
question. Results of different cases in this dissertation will allow planners and policy
analysts to know better who would be priced off and on, and how the first-, second-, or
third-best tolls would affect who would be priced off and on.
Despite the above findings, this dissertation could still be improved upon in the
future. Possible improvements relate to the limitations of the numerical approach
developed and employed, the assumptions made in the cases and policy scenarios
constructed, and the data used to construct these cases and policy scenarios.
1

CHAPTER 1. INTRODUCTION
1.1 Overview
Increasing the economic efficiency of transportation systems or the public
infrastructure has long been central to the work of urban and transportation
planners. Pricing in general and congestion pricing in particular are a policy option or
strategy to increase the economic efficiency of the public infrastructure. Recently,
congestion pricing has received increased attention in the transportation and public policy
arenas. The latest regional transportation plans in metropolitan areas such as New York
and Los Angeles have proposed congestion pricing or its analogues as a strategy to
increase the transportation system’s efficiency.
In addition to the above plans, quite a few high-profile congestion pricing
programs have emerged in the United States and abroad. Outside the US, for instance,
London and Stockholm, the capitals of their respective countries, launched congestion
pricing programs in 2003 and in 2007, respectively. During this time, in the US, the Ports
of Los Angeles and Long Beach, the nation’s two busiest seaports, started a
peak-load/congestion pricing program to divert peak-hour port-bound truck traffic to
off-peak hours. More recently, the City of New York successfully advanced a congestion
pricing proposal to the state legislature for approval but narrowly lost the legislators’
endorsement.
Beyond specific metropolises, the US federal government initiated an
$853-million Urban Partnerships program in 2007. The purpose of the program was to
encourage US cities to try different aggressive congestion-relief programs, including but

2
not limited to congestion pricing and HOT lanes.
The popularity of the congestion pricing programs highlighted above has its
economic, policy, political, and financial explanations. Firstly, road spaces or other
congestible facilities in peak hours are as scarce as other economic resources and thus
road users should pay tolls correctly reflecting the marginal congestion/social costs they
impose on others during those hours. Economists have long argued that marginal-cost
pricing increases the economic efficiency of roads and this belief is extremely evident
during peak hours and/or on congested roads where there is relatively high demand for
very limited roads (Vickrey 1969, 1973; Walters 1961). Partially enlightened by the
economists’ arguments, decision-makers, policy analysts, and planners have gradually
recognized that pricing is one of the most effective ways— and probably the only
practical way— of coping with negative transportation externalities such as congestion
and emissions (Cambridge Systematic Inc. 2009; Congressional Budget Office 2009;
FHWA 2006; GAO 2009; Lewis 2008).
Secondly, empirical evidence has shown that road expansions have rarely kept up
with motorists’ ever-increasing demand for more roads, especially when the motorists do
not pay the full costs for their trips (Downs 1992, 2004). There is a need for the
government to use congestion pricing as a strategy to correct the lower-than-MSC prices
that motorists pay for their trips, as well as to manage travel demand, curb traffic
congestion, and reduce related emissions, noises, and vibrations.
Thirdly, in many countries, including the US, the public funding collected from
various transportation-related fees and taxes have begun to fall short of the actual
financial needs of keeping existing transportation systems in good shape (Goldman and

3
Wachs 2004). From the government’s perspective, toll revenues from congestion pricing
may provide supplemental sources of funding for various transportation projects or
improvements, as reflected by real-world cases (Ieromonachou et al. 2006; Kristiansen
2004; Larsen 1995), and as indicated in the literature (Liu 2004).
In formulating efficient, equitable, and effective congestion pricing policies or
proposals in the real-world setting, however, policy analysts, decision-makers, and
planners often need to address these basic questions:
 What happens to the efficiency and effectiveness of congestion pricing when certain
users, routes, or time periods have to be exempted from congestion pricing charges
due to political considerations, prohibitive levying and enforcement costs or
technical constraints? That is, would congestion pricing still be an efficient policy
tool or strategy to optimize road usage when the marginal-cost pricing principle is
not implemented at its full swing or when the first-best tolls are not adopted as
dictated by the principle?
 Given that user groups are often heterogeneous in terms of value of time,
toll-demand elasticity, marginal social costs produced, road space requirement, and
so forth, how should between-user-group differences, that is, user group
heterogeneity, be accounted for when planners and policy analysts design or
evaluate congestion pricing policies or proposals?
 If planners and policy analysts do not differentiate user groups, that is, neglect user
group heterogeneity when formulating and evaluating congestion pricing policies, do
their policy proposals or evaluation results deviate or go wrong?
More interestingly, what happens to the efficiency and effectiveness of congestion

4
pricing regimes where extremes of special interest to planners and policy analysts
are simultaneously present? The regimes cannot charge certain users or user groups
all of the time; for example, there is always an unpriced alternative for some users or
user groups due to equity considerations; there are significant differences among
user groups, but due to cost and time constraints policy analysts and planners cannot
take them into account when determining the levels of optimal tolls.

It is important that policy analysts and planners appropriately answer the above
questions if their ultimate goal is to formulate an economically efficient congestion
pricing program or proposal. Even if their goal is not economic efficiency but rather
political feasibility, planners and policy analysts may still have to address some of the
above questions. For instance, because of issues such as high data collection costs and an
unwillingness to share private and proprietary information among certain user groups,
policy analysts and planners may have to design or evaluate congestion pricing regimes
with what limited user group information is available. They must gauge how much
efficiency or social welfare gains a congestion regime will sacrifice if certain information
about user groups goes unused or ignored. On the other hand, if policy analysts and
planners decide to collect more user data than usual, they need to know the range of
potential gains or benefits that more data would provide to the policy design and proposal
evaluation to justify the extra data collection costs or efforts.
In light of the popularity of congestion pricing and the common questions
highlighted above, this dissertation focuses on congestion pricing regimes or proposals
where an unpriced alternative, policy constraints, and user group heterogeneity are

5
simultaneously under consideration. Specifically, this dissertation investigates optimal
tolls, social welfare, relative efficiency, and distributional effects of a category of
congestion regimes or proposals (“the representative regime” for shorthand hereafter) that
epitomize three characteristics of congestion pricing regimes commonly found in the
real-world setting:
 Not all users are guided by the marginal-cost principle due to political considerations,
implementation or enforcement costs, and/or technical limitations. In other words,
this dissertation considers congestion pricing cases where there is always an
unpriced alternative or a discounted toll for some users, which is not uncommon in
the real-world setting
 There are at least two user groups that differ in value of time, demand elasticity,
marginal social costs imposed on others, road space requirements, and commute
distance. For transportation policy analyst and planners, two often-seen
heterogeneous user groups are truckers/truck traffic and motorists/automobile traffic.
This dissertation considers cases and policy scenarios where these two user groups
are always present, unless otherwise stated.
 To increase its feasibility, the representative regime could have several equally
weighted but sometimes mutually contradictory goals: maximum possible toll
revenue, simplest toll structure, and optimal economic efficiency, depending on the
specific policy context.

As will be discussed in Chapter Two, the representative regime has not been
studied in depth before and quite a few analogues exist for it in the real-world setting.

6
Therefore, this dissertation may be able to fill the gap in existing studies, as well as shed
light on the above-mentioned common issues facing policy analysts and planners
advocating congestion pricing.
1.2 Research Questions
To provide general knowledge and policy recommendations for planners and
policy analysts advocating the representative regime as a strategy to increase the
economic efficiency of roads, this dissertation strives to answer the following research
and policy questions:
 It is often more practical for planners and policy analysts implementing a congestion
pricing regime to adopt second-best or even third-best tolls rather than first-best tolls
(Rouwendal and Verhoef 2006; Small and Verhoef 2007; Verholf et al. 1995;
Verhoef et al. 1996; Verhoef 2007). We know that in general the former achieves a
lower economic efficiency than the latter (e.g., Liu and McDonald 1999). But
precisely how much economic efficiency would second- or third-best tolls typically
lose as compared to their first-best counterparts in the representative regime in
particular?
We know user groups such as motorists and truckers differ significantly in aspects
such as value of time, demand elasticity, road space requirement, and external costs
imposed on others (de Palma et al. 2007; Parry 2008; Steimetz et al., 2008). But
planners and policy analysts who design and evaluate the representative regime do
not always have the data about these differences. What would happen to the
properties of the representative regime if certain data from one user group were used
as proxy for another when designing and evaluating the representative regime? In

7
other words, what would happen to the properties of the representative regime if
planners and policy analysts chose to ignore certain aspect(s) of user group
differences?
 Given that secondary user groups such as truckers often account for a relatively
small percentage of all users, what would happen to the properties of the
representative regime if all user groups were treated as identical to the dominant user
groups such as motorists?
 Given that data collection and processing are expensive and/or time-consuming, if
planners and policy analysts had options, which data about user group
heterogeneity could be ignored and cause the fewest, if not negligible, effects when
designing or evaluating the representative regime?
1.3 Research Design
1.3.1 Research method
This dissertation relies heavily on numerical simulations or approaches to finding
answers to the research and policy questions highlighted above. A series of
semi-hypothetical cases and policy scenarios were constructed for the representative
regime in the first-, second-, and third best contexts. They are “tools” for one to find
underlying relationships of relative efficiency, distributional effects, and user group
heterogeneity in the representative regime. As described in Chapter Four, these tools
probably take or derive the most reliable data about traffic or users on an actual freeway
segment from all sorts of sources, including peer-reviewed literature, local regional travel
models, and official reports. It is based on these tools that the research and policy
questions posed are answered. Judging from the network’s set-up, the number of user

8
groups, and the dimensions of user group heterogeneity considered, these tools may be
relatively simple. But this simplicity does not necessarily decrease their effectiveness in
terms of producing useful insights or policy implications for planners and policy analysts
advocating pricing in general and the representative regime in particular. In studying
congestion pricing and its usefulness, researchers have long argued that models (i.e., tools)
“need not be complex to provide useful insights” (Arnott et al. 1994).
Three reasons justify choosing the numerical approach. First, existing studies
provided no solutions to optimal toll(s) for the representative regime, which suggests that
a new cost-effective solution has to be developed anyway if more insights into the
representative regime are desired. The numerical approach was also chosen because of its
cost-effectiveness and operationalibility, as compared to alternative methods such as
complex mathematical derivation, agent-based simulation, and social experiment. The
latter requires either advanced mathematical knowledge/skills or appreciably more
monetary and time investment.
Second, compared to conventional methods such as Newton and Lagrangian
methods used to derive optimal tolls for congestion pricing regimes, the numerical
method developed for this dissertation requires fewer mathematical operations to derive
optimal tolls. For instance, existing studies have provided formulae and algorithms to
derive optimal tolls for congestion pricing cases with two user groups differing in only
one dimension (e.g., Small and Yan, 2001). In those studies, general knowledge of
differentiation, derivative, integration, and other intermediate variables (i.e., Lagrangian
multipliers) and formulae are indispensable. Deriving general formulae for optimal tolls
for the representative regime where more dimensions of user group differences are

9
considered, requires incrementally more knowledge of differentiation, derivative and
integration, as well as more intermediate variables or formulae. Gaining this additional
information could be formidable for economists who lack trainings in those aspects, let
alone for noneconomists who rarely use quantitative models and advanced mathematical
knowledge routinely. To avoid this challenge, alternative methods are desirable, at least
for planners and policy analysts advocating the representative regime. The numerical
approach offers one such alternative. As will be shown in Chapter Three, this approach
requires only general knowledge of differentiation, derivative, and integration. Further,
the approach does not require any intermediate variables and formulae to identify optimal
tolls.
Third, the numerical approach has been commonly used in the study of
congestion pricing regimes (e.g., Liu and McDonald 1998; Small and Yan 2001; Verhoef
and Small 2004). This usage indicates that even though it may not directly prove
anything, the numerical approach is still useful for providing bounded knowledge of, or
insights into, congestion pricing regimes. Similar to earlier studies, this dissertation
attempts to obtain some bounded knowledge of, or insights into, the representative
regime in particular. Therefore, the numerical approach may be appropriate as well.
1.3.2 Cases constructed
To answer the questions posed and to test the hypotheses relevant to these
questions, this study constructs one first-best, one second-best, and two three-best cases
about the representative regime. These cases cover most if not all forms by which the
representative regime could take in the real-world setting. Therefore, planners and policy
analysts may learn about the applicability and characteristics of the representative regime

10
of various practical forms from these cases. Each of these cases would always have two
distinct user groups: motorists and truckers, two user groups that many planners and
policy analysts, especially transportation planners and analysts in Metropolitan Planning
Organizations (MPOs), often deal with in their daily work. As mentioned latter in the text,
these groups differ from each other in multiple dimensions: demand elasticity, road space
requirement, value of time, and commute distance. This dissertation uses these
differences interchangeably with “user group heterogeneity.” It is probably due to these
differences that planners and policy analysts often treat motorists and truckers separately.
For instance, MPOs have related but relatively independent passenger and freight flow
models without which there may not be strong theoretical foundations about the need for
such separated models for passenger transportation and freight transportation. Indeed,
planners and policy analysts have learned from experience that if they do not have these
models, that is, do not differentiate motorists from truckers, they could get biased
estimated values of indicators of their interest. As such, the five cases constructed in this
dissertation all have truckers and motorists as two distinct user groups. Specifically,
Table 1, below, summarizes the set-up of these cases, variables or constants used to
measure the user group heterogeneity, and how each case relates to research and policy
question(s) posed by this dissertation. More details about the parameterization of the
cases are described in Chapter Three.

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Table 1: Cases Constructed for the Representative Regime

Case User Group
Heterogeneity
Considered
Toll Structure and Duration Relationship to
Research Questions
First-best Tolls are differentiated by user group
and by time period; these tolls are based
on group-based characteristics
(including marginal social costs
imposed), which in theory would
generate maximum Rel. SW.

The first-best case
results are used as
baselines to measure
results for other cases
or policy scenarios

Second-best Tolls are not differentiated by user
group but by time period

How much economic
efficiency that the
second-best tolls could
lose as compared to
the first-best ones?
Third-best
(1)
In the peak hour, user groups pay
differentiated tolls;
In the off-peak hour, both user groups
are exempted from the tolls.

Third-best
(2)
Only the secondary user group pays
tolls; the dominant user group is
exempted all the times.

Third-best
(3)
VOT,
η,
road space
requirement,
relative group
size,
demand
function,
generalized cost
function

Only the predominant user group pays
tolls; the secondary user group is
exempted all the times.

How much economic
efficiency that the
third-best tolls could
lose as compared to
the first-best ones?
How would different
types of exemptions
affect the properties of
the representation
regime?

1.3.3 Policy scenarios constructed under the first-best case
Results and findings from the above cases may have provided planners and policy
analysts with general knowledge about the applicability and design of the representative
regime in the real-world setting. But planners and policy analysts may still face concrete
questions, such as:
 What happens to the properties of the representative regime when there are not full
data about both user groups and certain data about one user group has to be used as
proxy for the other in the design or evaluation of the regime?

12
 What happens if for some reasons truckers have to be treated identically to motorists,
that is, if most, if not all, commonly seen dimensions of user group
heterogeneity—such as value of time, demand elasticity, and road space
requirement— are ignored?
 Given the high costs of data, if one has options, which data about user group
heterogeneity can be ignored and cause the fewest, if not negligible, effects on the
evaluation and design of the representative regime?

To help planners and policy analysts address the above questions, this dissertation
also constructs five policy scenarios under the first-best base case, which is specified in
Table 1. In each policy scenario, one or several input parameters in the baseline case will
be manipulated to see to the affect on output variables such as levels of optimal tolls, ω,
and SW per trucker or per motorist. Each policy scenario mimics a real-world situation in
which people ignore one or several aspects of between-user-group differences when
designing or evaluating the representative regime.
1.3.4 Charging site for cases and policy scenarios
A segment of the Interstate 710 (I-710) freeway in Los Angeles, California is the
facility where hypothetical congestion pricing cases or policy scenarios takes place for all
cases and policy scenarios constructed in this dissertation. A map of I-710, the cordon
location, and other landmarks in Los Angeles are shown in Figure 1.
Designating the I-710 as the congestion pricing site is not random. Subsection 4.5
in Chapter 4 provides detailed explanations for this choice. With a congestion pricing
regime, members from one or both user groups passing a cordon on the I-710 freeway

13
just north of Del Amo Boulevard would be charged during the designated peak hour, t1.
Users passing the cordon outside t
1
may or may not pay tolls, depending on toll structure
or duration features of different cases purposively assigned by the modeler.
Algorithms and procedures used to identify optimal tolls of different cases are
detailed in Chapter Four. These algorithms and procedures are specially developed for
this dissertation and could be implemented with minimal human intervention on most
desktop computers available nowadays. They do not replicate or emulate any algorithms
and procedures in existing studies of congestion pricing. In light of the needs and
knowledge bases of most planners and policy analysts, the algorithms and procedures do
not require advanced programming, mathematical, or knowledge of economics to be
understood.

Figure 1: Map of the Toll Freeway Segment

Toll Segment
Cordon

14
1.4 Policy Implications of the Dissertation
Efficiency in general and efficiency of transportation and land use in particular
have long been one of the overarching goals pursued by urban planners, policy analysts,
and the like. For instance, at the core of both the jobs-housing advocacy and urban
sprawl-compact development debate among planners, policy analysts, and the like is the
efficiency or inefficiency of land use and transportation systems. Underlying many
Transit-Oriented Development (TOD) proposals or plans is the energy efficiency required
to meet peoples’ mobility demands. One reason for infill development and downtown
renewal is to optimize the efficiency of available funding, existing visible physical basic
infrastructure, and invisible social fabrics.
Various strategies have served to increase the efficiency that planners and policy
analysts care about: integrated land use-transportation planning, smart growth or land use
regulations, Travel Demand Management (TDM), and pricing, to name a few. Recently,
pricing in general and congestion pricing in particular have received increased attention
in the planning and public policy fields. This spike in interest may be due to the
following reasons:
(a) Pricing could increase the efficiency of congestible facilities, as shown in theories
presented by various researchers (Pigou 1920; Small 1992; Smeed 1968; Vickrey 1969;
Walters 1961).
(b) Implementations of congestion pricing in a few places have proved to be effective
(Congressional Budget Office 2009; Eliasson et al. 2009; Goh 2002; Olszewski and Xie
2005; Santos 2008).
(c) High-level public agencies have started showing concern about congestion pricing as

15
a strategy to increase overall economic efficiency, curb traffic congestion, and improve
mobility (Congressional Budget Office 2009; Committee on Transportation and
Infrastructure 2001; FHWA 2006; GAO 2009; Subcommittee on Highways and Transit
2002; USDOT et al. 1995).
This dissertation will not rehearse the argument that pricing would be one of the
best ways to achieve efficiency goals that are of particular interest to planners or policy
analysts. Rather, it will show the underlying relationships among pricing structure,
relative efficiency, distributional effects, policy constraints, and user group heterogeneity
within congestion pricing using the representative regime as an example.
Semi-hypothetical numerical cases and policy scenarios are constructed to quantify the
relationships or to provide qualitative statements about the relationships. Knowledge of
these relationships will enable planners and policy analysts to conduct better evaluations
of congestion pricing regimes or alternatives that they are fighting for or against.
Specifically, this dissertation is intended to convey to planners and policy analysts
the following:
 Congestion is a commonly seen phenomenon facing cities and metropolitan areas.
 Congestion pricing could be an efficient way to curb congestion and has received
increased attention in the public policy domain home and abroad.
 Congestion pricing could be categorized into different regimes or groups, depending
on toll structure and duration, policy constraints considered, and user group
heterogeneity accounted for by analysts. Each congestion pricing regime has some
unique features, which are discussed in Chapter Two of this dissertation.

16
 Of all congestion pricing regimes, the second- and third-best ones may be of greater
relevance to planners and policy analysts.
 It is important to differentiate users in the study of the representative regime. Not
differentiating users could cause bias in estimated values of indicators about the
regime.
 The economic efficiency of the representative regime is relatively stable whether the
first-, second-, or third-best tolls are charged, as long as the following premises are
met: users are reasonably categorized into groups, accurate group-specific data are
used when deriving the optimal tolls, and the predominant user group in terms of size
is not exempted from paying tolls
 Meeting policy constraints such as offering free hours for users or user groups in the
representative regime does not necessarily remove most of the economic value of the
representative regime.
 To conduct a good evaluation for the representative regime, planners and policy
analysts do not need to collect and use as many data as possible. In short, planners
and policy analysts can perform a reasonable evaluation of the regime even if they
use the same PCE factor for both truckers and motorists.
 Despite the fact that studies of congestion pricing regimes often require advanced
mathematical knowledge and skills, planners and policy analysts can still use
well-designed cases and numerical tools to grasp the underlying relationships of
pricing structures, relative efficiency, distributional effects, policy constraints, and
user group heterogeneity in congestion pricing. This dissertation will exemplify such
cases and tools.

17
1.5 Organization of the Dissertation
This dissertation is broken into six chapters. This chapter (Chapter One) is an
introduction, which describes the background, research questions, and research design of
this dissertation.
Chapter Two categorizes and reviews literature of relevance to this dissertation.
The first category of literature focuses on congestion pricing as a strategy to achieve
efficiency goals in the planning and public policy fields. The second and third categories
are on the first-, second-, and third-best regimes and their respective characteristics. The
remaining categories study subjects such as user heterogeneity, policy constraints, and/or
unpriced alternatives, and how they affect the design and assessment of congestion
pricing regimes. As described above, these subjects are all present for the representative
regime, thus making this study of the representative regime as informative as possible.
On the one hand, a review of different categories of the existing literature helps situate
this dissertation in the fields of urban planning and public policy and within the ongoing
dialogues on congestion pricing in these fields and beyond; on the other hand, the review
helps highlight the dissertation’s relevance to existing congestion pricing studies and
practices.
Chapter Three describes the model developed, and numerical cases and policy
scenarios constructed to answer the research questions posed. I evaluate and discuss the
properties of the representative regime and their determinants based on the quantitative
results of these cases and policy scenarios.
Chapters Four and Five are the core of the dissertation, presenting the quantitative
results of different cases and policy scenarios. Based on a synthesis of these results and

18
linkage of these results to findings in existing studies, discussions of the policy and
planning implications of the results are presented in Chapters Four and Five.
Chapter Six concludes the dissertation and discusses the limitations of the study
and future research directions.

19
CHAPTER 2. RELEVANT LITERATURE
2.1 Congestion, Congestion Pricing, and Planning/Public Policy
Traffic congestion has plagued many metropolitan areas in the US for decades and
tends to be increasingly severe in these areas. According to the Texas Transportation
Institute (TTI), American metropolitan areas of various population area sizes have seen a
steady growth in hours of delay per traveler since 1982, as shown in Figure 2, below.
Figure 2: Hours Delay per Traveler by Population Area Size in America

Source: (Schrank and Lomax 2005).

In very large American metropolitan areas such as Los Angeles, Chicago, and Atlanta,
congestion has had notable growth in three dimensions between 1982 and 2003. As such,
there have been longer delays during peak hours resulting from congestion, extra hours
spent on travel due to congestion, and a larger percentage of freeway mileage that is
congested (Cambridge Systematics and Texas Transportation Institute 2005). Since 2003,

20
congestion in these areas has seen some relief but is still very severe overall— if overall
level of congestion is measured in hours wasted in congestion per traveler per year. In the
Los Angeles metropolitan area, for instance, each commuter wasted 72 hours and 70
hours behind the wheels due to congestion in 2006 and 2007, respectively (Schrank and
Lomax 2009).
The costs of traffic congestion have been high. Commuters stuck in congestion
could have used those wasted hours for other purposes such as work, entertainment, or
being with their families. In addition, congestion results in extra fuel consumption and
emissions, which add to private and social costs. An estimated $63 billion dollars is lost
in the U.S. each year from fuel consumption due to congestion (FHWA 2006). The
economic loss caused by congestion would be even more substantial if costs other than
fuel consumption such as lost productivity, environmental costs, and travel time
unreliability—were taken into consideration.
Despite what is highlighted above about traffic congestion and its many costs,
most if not all transportation planners and policy analysts working in US metropolitan
areas cannot overlook the subject of traffic congestion. On the one hand, the general
public may expect them to figure out strategies to cope with traffic congestion; on the
other hand, the planners and policy analysts themselves are unable to solve the pressing
issue of traffic congestion and are likely to be victims of it themselves.
To cope with traffic congestion, the first thing that planners and policy analysts
can do is to identify its contributors or determinants. There are multiple contributors or
determinants to traffic congestion. Among them, simply that too many motorists
commute on a given route or bridge simultaneously. Road supply has lagged greatly

21
behind travel demand. A large number of people in vehicles simultaneously rush into or
out of a few spots, such as downtowns, airports, and stadiums, producing bottlenecks on
roads leading toward and away from those sites. Transit systems do not offer services in
the quantity or quality desired by commuters, a lack that forces them to drive everywhere.
Accidents at strategic locations block traffic that has to pass through, generating
temporary choke points in the transportation network.
Auto-oriented development makes alternative modes of transportation, such as
biking, transit, and walking, impossible. The geographic distances between jobs,
shopping, and housing increases Vehicle Miles Traveled (VMT) and make the costs of
building sufficient roads more expensive. Probably most importantly, motorists do not
fully cover the costs that their own trips impose on others and on the environment. In
other words, motorists are not held responsible for the negative external costs they
produce. Thus there could be a public policy or market failure underlying traffic
congestion that planners and policy analysts have to deal with.
Existing studies offer an array of strategies for planners and policy analysts to
address traffic congestion while pursuing other policy goals such as conserving
nonrenewable energy, raising productivities, and increasing mobility options for travelers
of all types. At the overarching level, planning or land use regulations could be viewed as
a primary strategy for increasing accessibility, reducing the need for travel, shortening
trips, and curtailing motorized trips. In theory, a well-thought-out land use plan or
reasonable land use regulations could reduce or at least control the intensity, duration,
and frequency of traffic congestion.
Within the fields of land use planning and public policy, TOD, infill development,

22
and mixed-use development are just some of the common strategies offered to curb traffic
congestion while fulfilling other planning and policy goals. Extensive literature has
addressed these strategies and various executions of them in specific contexts. Robert
Cervero, for instance, has published four books and numerous papers systematically
discussing topics such as the role of transit, TOD, mixed-use development, and infill
development in America, Hong Kong, Europe, and China (UC Regent 2006). The
National Smart Growth Center, since its inception in 2000, has produced numerous
reports on the topics of infill development or “smart growth” within the US.
Relatively speaking, TDM in general, and pricing in particular are strategies that
have received less attention from planners and policy analysts than the strategies
highlighted above, a distinction that is likely explained by the fact that these strategies
directly deal with travel behavior changes. TDM measures sometimes even force those
changes to happen with the assistance of pricing or regulations (Victoria Transport Policy
Institute 2010). There has been strong political objection among the general public to
cohesive behavioral changes and economic disincentives in general and to congestion
pricing in particular, especially when the general public have no unpriced alternatives.
Strategies such as TOD and infill development, in contrast, seem to be more popular
politically perhaps because they largely provide only necessary infrastructure or
conditions to facilitate voluntary travel behavior changes. Nevertheless, as highlighted
already, congestion pricing has recently received increased attention in the public policy
domain. In America, for instance, the federal government set aside one billion dollars for
the Urban Partnership program to encourage different metropolitan areas to test
transportation pricing strategies in various forms in 2007. Multiple reports on, or

23
proposals about transportation pricing, have also been published by government agencies,
think tanks, research institutions, and the like since 2006. In the past five years or so, the
number of academic books and journal articles on transportation pricing has also rapidly
increased. For instance, only four papers have words such as “congestion pricing,”
“congestion charging,” or “road pricing” in the title in Transport Policy between 2002
and 2004; however, since 2005, two issues of the journal have been completely dedicated
to the study of congestion pricing. Since 2005, there have been at least 12 papers with
key words such as “congestion pricing,” “congestion charging,” or “road pricing” in their
titles. Similar trends may be found in other journals such as Transport Research Record,
Transport Review, and Transportation Research Part A. In addition, nine academic books
published between January 2008 and March 2010, as listed in Amazon’s on-line
bookstore, contain key words such as “congestion pricing” and “road pricing” in their
titles. Such a surge in book publications was not seen in the bookstore before 2008.
Due to their complex methodologies, the models they construct, and the formulae
they use to derive optimal solutions, however, many if not most existing studies of
congestion pricing are outside the purview of most analysts and researchers. For instance,
the nonlinear optimization model and the Lagrangian method are often used to derive
optimal tolls for congestion pricing regimes in existing studies (e.g., Liu and McDonald
1998; Small and Yan 2001; Verhoef and Small 2004). Such model and method are often,
if not always, too complicated for most researchers and analysts. From the perspective of
planners and policy analysts who advocate congestion pricing, less complicated tools or
models that are usable to evaluate or design congestion pricing proposals or regimes are
necessary. There is also a need for models or tools that simultaneously examine topics

24
such as efficiency, pricing structures, user group heterogeneity, and the distributional
effects of different congestion pricing regimes. More often than not, existing studies,
models, or tools address these topics separately, as discussed below.
2.2 First-, Second-, and Third-best Regimes: Definitions
Before reviewing existing studies, redefining important terms such as first-best,
second-best, and third-best congestion regimes, which planners and policy analysts
interested in congestion pricing come across from time to time, is worthwhile. These
terms are frequently used in existing studies but their meanings may vary from one study
to another. Therefore, redefining the terms will help reduce some of the confusion that
planners and policy analysts may have about different types of congestion pricing.
Redefining the terms will also facilitate this dissertation’s categorizing and review of
specific existing studies by providing consistent terms from the outset.
2.2.1 First-best regimes
This example assumes that there is a congestible facility, F, that allows M users
simultaneous use without any congestion, that is, so that no user imposes negative
externality costs on others. So when number M+1 user J starts using F, he or she would
impose extra costs of delay to all M users that are on F. The extra costs are called
“Marginal External Costs (MEC)” by economists. A toll that equals MEC is a “first-best”
one. A regime or a policy charging a first-best toll to all users who produce MEC is
called the first-best regime. The consensus among theorists has been that charging
first-best tolls will maximize the efficiency and the overall social welfare of a congestible
facility or system (Yang and Huang 1998); however, first-best tolls or first-best regimes
are often infeasible in the real-world setting. The infeasibility could be attributed to one

25
or a combination of the following reasons:
 The implementation and enforcement costs to charge users whenever and wherever
there is congestion are prohibitively expensive unless the congestible system is
extremely simple (Yang and Huang 2005)
 Charging users tolls whenever and wherever there is congestion is politically
unpopular, at least in the current political climate (Yang and Huang 2005)
 Our real-world market is not perfect and MEC such as congestion are not the only
distortion we must deal with in the market (Small and Verhoef 2007)
 Where there are heterogeneous user groups, the first-best tolls may require
differentiation of group-specific MEC and setting toll levels according to
group-specific MEC, which are difficult if not impossible efforts in most real-world
applications.
2.2.2 Second- and third-best regimes
The constraints highlighted above regarding the first-best regime tend to displace
people’s interest onto second-best or third-best regimes or policies, which accommodate
more of the real-world constraints that planners and policy analysts must face. Compared
to its first-best counterpart, the second-best regime has at least one of these attributes:
 Even though the heterogeneous user groups and MEC that these groups produce
differ from one group to the other, a uniform or non-differentiated toll is charged to
all user groups regardless of the MEC differences.
 Not all user groups of a congestible facility that produce MEC are charged a
first-best toll; in other words, some or all user groups only partially pay for the MEC
that they produce.

26

In cases where the second-best regime has one of the following attributes, the regime
becomes a third-best one:
 Toll levels are set according to goals such as maximizing overall toll revenue,
curbing congestion, and covering implementation costs rather than according to
optimal economic efficiency. In other words, the ultimate or primary policy goal of
the congestion pricing regime is not optimizing economic efficiency and social
welfare gains may be a byproduct of the materialization of other goals
 There is always an unpriced temporal or spatial alternative for a number of users or
user groups despite the fact that they impose MEC on others.

The cases and policy scenarios constructed in this dissertation about the
representative regime could be first-best, second-best, or third-best in nature, depending
on the feature(s) they are purposively assigned. Therefore, a review of existing studies on
the first-best, second-best, or third-best regimes is helpful for obtaining sufficient
background information about the representative regime and about the different cases and
policy scenarios built to mimic the regime. In addition, because the second- and
third-best regimes are often tied to subjects such as user heterogeneity, unpriced
alternative, and policy constraints, reviewing how existing studies on congestion pricing
deal with these subjects is also helpful.
2.3 Existing Studies of Different Regimes: Taxonomy
2.3.1 The first-best regime
Simplified network: Existing studies of the first-best regime are closely related to a

27
simplified network and to assumptions about user homogeneity. In the “basic model”
(Lindsey 2006:304) for the first-best regime, for instance, a simplified network (a
network with only two nodes and one or two links) is considered when authors examine
the properties of the congestion pricing regime. In the same model, “unrealistic”
assumptions about user homogeneity are also made to facilitate “the theoretical
development and the empirical tests” (Walters 1961). After an intensive survey of
existing literature, Lindsey (2006:307) summarizes the commonly made homogeneity
assumptions in the first-best regime as follows:
 One individual per vehicle;
 Vehicles contribute equally to congestion;
 Individuals are identical except for their reservation price to make a trip;
 Traffic flow, speed, and density are uniform along the road, and are independent of
time.

Researchers often evaluate or measure economic properties of the first-best
regime based on the above assumptions and a simplified network. For instance, in a
simplified network where MSC can be easily estimated, one measurement for congestion
pricing’s efficiency is the degree to which MSC could be recovered from the user toll
charged (Lindsey 2006). In other words, assuming that τ is the user toll charged in a
congestion pricing regime, the ratio of τ to the corresponding MEC that a user produces
will be a good indicator for measuring the efficiency of the regime.
In a mathematical form, MEC and related variables are expressed as (Walters
1961):

28
MSC(Q)=C(Q)+ ∂C(Q)/ ∂Q*Q

where
MSC(Q) is the marginal social costs that a user J generates when there are Q users on a
congestible facility such as a road;
C(Q) is the private costs such as fuel, licensing fees, and insurance that J usually pays;
∂C(Q)/ ∂Q*Q is the MEC that J imposes on other users of the facility when his or her
entry triggers congestion or aggravates it.
When no congestion toll exists, users do not pay for the MEC they produce. Thus,
assuming that they are rational, users, especially peak-hour users, would keep using the
facility to a congestion level where their private costs equal their perceived benefits. At
this level, the MSC that a typical user produced has already exceeded his private costs by
a magnitude of MEC. Or, in other words, market failure occurs where users do not fully
compensate for the costs they impose on others. One of the economists’ recommended
remedies for this failure is “congestion pricing,” that is, charging users of a congestible
facility a toll ( τ
0
) equal to the MEC they impose on others. The economists further
substantiated that if τ
0
equals ∂C(Q)/ ∂Q*Q it would optimize social welfare for all users.
In Figure 3, below, which shows the relationship between demand for trips and cost per
trip for a given congestible facility, τ
0
should cut down the demand for using the facility
to such a point that only Q
0
users who pay a toll are using the facility. At this point, the
social welfare for all users is optimized, because there is no deadweight loss, that is, area
FDG equals zero.

29

Figure 3: The Basic Model for Congestion Pricing

Source: Lindsey 2006.

However, the underlying relationship of τ
0
and social welfare, depicted in Figure 3,
would change if either of these two assumptions is violated (Lindsey 2006):
 Congestion is the only market failure, i.e., there are no other negative externalities
or distortions elsewhere in the economy;
 There are no shocks due to accidents, bad weather, special events, etc.
General network: In a general traffic network with homogeneous users, the first-best
regime should also achieve a system-optimizing flow pattern should users pay a toll fee
that equals the MEC they generate at each congested link (Beckmann 1965; Dafermos
and Sparrow 1969, 1971; Smith 1979). In other words, the marginal-cost pricing
principle always applies whether it deals with homogeneous users on a simplified
network or homogeneous users on a general network (Yang and Huang 2005).
In a general traffic network with heterogeneous users, however, the marginal-cost

30
pricing principle needs to be adapted or revised in order to be useful. Studies on
adaptations and revisions are underway. For instance, levels of first-best tolls for a
general traffic network with heterogeneous users could be different, depending on where
and how the tolls are charged. If the tolls are charged at the link level, the
marginal-pricing cost principle still applies. If the tolls are charged at the path level, the
principle may or may not apply. Some cases even require negative tolls (subsidies to
users) in order to realize the system-optimizing flow pattern (Dafermos 1973). Negative
tolls are rarely seen for cases in a simplified network with homogeneous users. The above
cases indicate that the marginal-cost principle has to be adapted where there are user
groups heterogeneous in their route choices and MEC are produced. In addition, even
locations where user groups pay tolls could affect the optimal tolls and associated user
equilibria (Dafermos 1972, 1973).
2.3.2 The second- and third-best regimes
As mentioned above, two predominant features of second- and third-best regimes
are that:
 They regard users as heterogeneous rather than homogeneous, and
 They allow some users to be exempted from tolling in view of various policy or
real-world constraints.
These features mean that the second- and third-best regimes sacrifice at least one of the
assumptions that the first-best regime upholds. This situation makes the second- and
third-best regimes closer to the real-world circumstances and significantly increases their
practicability (Small and Verhoef 2007; Verhoef 2002b; Yang and Huang 2005). Given
this practicability, planners and policy analysts going for congestion pricing should

31
probably pay more attention to the second- and third-best regimes than to the first-best
regime.

The following three subsections (Subsections 2.4 to 2.6) provide a survey of
existing studies on the second- and third-best regimes by categorizing the literature into
several streams. The criteria used for categorizing are closely related to recurrent subjects
such as user heterogeneity, unpriced alternatives, and policy constraints in the study of
the second- and third-best regime. Linking these subjects to the actual implementation of
a congestion pricing regime, one arrives at several questions that may be of special
interest to planners and policy analysts; they include:
 Whether and how users are considered as a user group, that is, whether and how
user group heterogeneity is considered, which could affect how optimal tolls are
determined as well as who would benefit from, and suffer as a result of, congestion
pricing;
 Whether there have to be an unpriced alternative for selected users or user groups,
which could influence the political acceptance of a congestion pricing proposal or
regime;
 Whether there are policy or real-world constraints and how they are considered in a
regime. Examples of these constraints include, but are not limited to: only
non-differentiated tolls could be charged, only peak-hour tolls are allowed, and tolls
can only be charged to certain users or user groups.

Though they seem comprehensive, the above criteria do not produce the kind of

32
mutually exclusive streams of literature or publications about the second- and third-best
regimes that one would like. There are cases in which some publications could be
classified into more than one stream simply because they address several subjects or
questions simultaneously. For instance, a publication could simultaneously deal with a
congestion pricing regime with heterogeneous user groups and with an unpriced
alternative.
2.4 The Second- and Third-best Regimes: User Heterogeneity
2.4.1 Overview
Users or user groups of a transportation system are often heterogeneous, that is, they
vary in multiple dimensions: road space requirement (size of vehicle used), value of time,
cost demand elasticity, route choice, schedule delay cost, preferred arrival time at work,
extraneous support needed, and so forth. On the one hand, these above variations make
congestion pricing regimes in general feasible, effective, and efficient; on the other hand,
they pose challenges for the design of specific regimes. For instance, commuters’ preferred
arrival time heterogeneity makes it possible to sort commuters in some sequence through
pricing that optimizes social welfare. Because some commuters who value their time more
than others, allowing the former to be tolled onto a road while incentivizing the latter to
utilize other modes or to travel at non-peak hours sometimes makes economic sense. But
dealing with heterogeneous users also means that setting tolls and evaluating the efficiency
of the tolls could be more complicated than when there are only homogeneous users, as
reflected in Verheof and Small (2004). More importantly, the marginal-cost principle
specifies that the optimal toll for a user equals the marginal external costs he or she imposes
on others. Heterogeneous users or user groups may mean that one has to find user- or

33
user-group-specific marginal external costs in order to derive optimal tolls.
Given the above impacts of user or user heterogeneity on congestion pricing,
planners and policy analysts interested in congestion pricing should not ignore user or
user group heterogeneity. Specifically, different dimensions of user or user group

heterogeneity and their relationships to congestion pricing could be briefly summarized
as follows:
Road space requirements and marginal external costs: Vehicles such as
sedans, trucks, buses, SUVs, and pickups have different physical and operational
attributes. Different vehicles contribute differently to congestion or impose different
MEC than others. Truckers as a user group, for instance, despite being relatively small
compared to the user group for passenger cars, generate proportionally higher marginal
external costs than the latter (Parry 2008). On a specific freeway, a truck imposes more
significant external costs on other users as well (de Palma et al 2007; Steimetz et al.
2008). Based on the marginal-cost pricing principle, therefore, truckers should pay a
higher toll than motorists do. But how to determine optimal tolls by user group in
congestion pricing cases where there are heterogeneous users? Meyer et al. (1971, p.48)
recommend that “the tolls charged to different users should be proportional to their
capacity requirements: if one bus requires twice as much capacity as one car, the bus tolls
should be twice as the car tolls.” In the same vein, other authors have estimated a range
of optimal tolls organized by vehicle group and/or marginal social costs by vehicle group.
Based on hypothetical cases on a freeway segment and a bridge, Walters (1961) estimates
that the optimal toll for a passenger car is $0.62/mile to $0.95/mile (1961$) at the peak.

34
Based on a survey of existing studies, Lemp and Kockelman (2008) found that the
marginal external costs imposed by a passenger car range from $0.015/mile to $0.3/mile.
Using existing value of time, speed, and flow data, Steimetz et al. (2008) arrive at
marginal external costs per roundtrip per truck to and from two seaports in Los Angeles.
Their estimated marginal external costs per roundtrip per truck across routes are $19.75
(2007$) in peak hours and $3.63 (2007$) in off-peak hours. By synthesizing information
provided by others, de Palma et al. (2007) estimate that the marginal congestion cost for a
passenger car is $0.1/mile (2007$).
Value of time: Different trip-makers have different perceived values of time.
Each trip-maker can place different values of time on her or his trip, depending on the
time the trip occurs, the route the trip takes, the mode of the trip, and the primary purpose
the trip serves. It is trip-makers’ heterogeneity in value of time that congestion pricing
increases overall social welfare by allocating peak-time road resources to those who
value the resources the most. It is also partially because of this value of time
heterogeneity that planners and policy analysts sometimes separate different users or user
groups spatially, using strategies such as truck-only or HOT lanes to increase overall
social welfare.
Tables 2 and 3, below, list some of the representative values of time for truckers
and for motorists found in existing studies.

35

Table 2: Values of Time for Truckers in Existing Studies

Source
Mean Value of Time per Hour
(Adjusted to 2007 $)**
1.Texas Transportation Institute 1997 57.58
2. Kawamura 1999 33.39
3. de Jong 2000 50.09
4. Oregon Department of Transportation 2004 34.30
5. Smalkoski and Levinson 2005 55.15
6. Steimetz et al. 2008* 49.05
8. USDOT 1997 19.00
7. de Palma et al 2007 50.00
Mean of 1-5, 7, 8 46.59
Standard Deviation of 1-5,7, 8 9.49
*The average of 1 to 5.
**Inflation adjustment used this on-line tool: http://www.bls.gov/data/inflation_calculator.htm.

Table 3: Values of Time for Motorists in Existing Studies

Source
Mean Value of Time per Hour
(Adjusted to 2007 $)
1. NuStats 2005* 7.96
2. Brownstone and Small 2005** 25.98
3. Small, Winston, and Yan 2005 24.25
4. Lam and Small 2001 29.61
5. Steimetz and Brownstone 2005 27.72
6. Steimetz et al 2008*** 27.19
7. de Palma et al 2007 50.00
8. USDOT 1997 10.2
Mean of 1-5, 7, and 8 23.78
Standard deviation of 1-5 and 7 7.95
* Values identified through a stated preference survey
** Including values of time reported by other authors
*** The average of 2-5.

36
Route choice: Some commuters may prefer and be able to choose different routes
to travel. Route-shifting makes it possible that road resources underutilized before
congestion pricing are put to fuller use, in turn increasing the overall economic efficiency
of road resources and transportation investment. As indicated in Arnott et al. (1992) and
Braid (1996), route choice has been a recurrent subject in studies of congestion pricing.
Extraneous support: Certain trip-makers require their companions’ co-presence
on the road. For instance, a trucker who picks up a container at a seaport needs crane
workers on duty when he arrives. Similarly, a trucker delivering commodities to a
superstore may need other persons to help unload commodities and to sign off on certain
documents. To summarize, without some exogenous support, many truckers would have
to spend extra time waiting at a destinations and even have to cancel or postpone their
trips (Holguín-Veras 2008). Thus planners and policy analysts must take into
consideration the need for extraneous support among drivers; charging drivers while
ignoring their extraneous support might make these drivers, and perhaps all drivers as a
whole, worse-off.
Trip-timing preferences: Commuters often have heterogeneous trip-timing
preferences and attach different values to travel time relibility or disbenefits to delay or
lateness (Arnott et al. 1988; Brownstone and Small 2005; Chang and Hsueh 2006; de
Palma et al. 2005; Friesz et al. 2004; Lam and Small 2001; Verhoef 2001). The
effectiveness of a congestion pricing regime sometimes depends largely on the above
heteogeneity and differences. For instance, in extreme cases where most commuters
cannot spread their trips over time, that is, where their trip-timing preferences are
homogeneous, providing alternative modes of transportation is necessary to win support

37
for congestion tolls. For planners and public policy analyts, then, pricing as a strategy to
increase effiency works better when there are alternatives to which the tolled-off can turn.
Demand elasticity: Users and user groups of transportation facilities are not
equally sensitive to price changes. When prices change, some users or user groups may
be better able to absorb additional costs than others; in other words, some users or user
groups may have rather inelastic demands. Authors have studied demand elasticity for
passenger transport (motorists) and freight transport (truckers). Their studies indicate that
on the one hand, two user groups may have demand elasticities that vary greatly in size;
on the other hand, factors that influence demand elasticity differ from one group to the
other. In terms of demand for trucking services, for instance, the commodities transported
rather than the timing of the trip may be the primary determinant of demand. For
motorists, the purpose of the trip may be the primary determinant. Specifically, Tables 4
and 5, below, highlight some of the estimates of demand elasticties that truckers and
motorists identified in existing studies.

38

Source Context
Geographic
Level
Short-term or
Long-term
Mode
Demand
Measurement
Type of
Elasticity
Estimated Values of
Elasticities
Comments
Oum 1979 Canadian data 1945-1974 Inter-city
Long-term(five-year
time interval)
Highway freight
Share of raod in total
freight Own-price
1.11 in 1950 and -0.16
in 1970
-
Freiedlaender
and Spady
1980
US data 1972 for 96
manufacturing industries Regional Short-term Trucking
Share of trucking in
total freight transport
Own-price -0.956 to -1.230
-
Lewis and
Widup
Shipment data for assembled
autos in US 1955-1975 National Long-term Trucking
Share of trucking in
total freight transport Own-price -0.52 to -0.67
-
Machinery goods movements
National Short-term Highway freight Truck volume Own-price -0.04
-
Leather rubber&plastic
products National Short-term Highway freight Truck volume Own-price -2.97
-
Winston et al
1988
US grain(wheat) movements
via road National Short-term Highway freight Truck volume Own-price -0.73
-
Short-term Highway freight
Truck volume (All
Coomodities) Own-price -0.692 Translog method
Short-term Highway freight
(fruit vegetables and
edible foods) Own-price -0.652 Translog method
Oum et al
1992 Literature review - -
Trucking for
commodities Truck volume Own-price
-0.52 to -1.55,
depending on
commodity group
Translog method
Abedelwahab
1998
US(contains a summary of
elasticities by other authors) National Short-term
Trucking for
commodities Truck volume Own-price
-0.74 to -2.52 depending
on region and
commodity group
Binary probit functions; differences in
estimated elasticity values caused by: type of
model; type of data(aggregate or
disaggregate); definition and grouping of
commodities; market coverage; demand
dfi ii
Freight transport -0.47
Traffic -0.81
National Short-term Tons -0.58 to -0.63
Tons for short distance and long distance
respectively
National Short-term Ton-KMs -1.06 to -1.31
Ton-KMs for short distance and long
distance respectively
Graham and
Glaister 2002 Literature review - - All modes Freight Services Mixed -2.79
Based on 143 elasticities reported in 11
studies, mean value: -0.84
Beuthe et al
2001 All modes
Generalised
cost elasticity
Belgium: shippers
generalised costs
Long-term Trucking Own-price
Traffic as an input in the shippers' production
of output while transport demand is derived
from firms' production of output; large
elasticity for traffic than for transport
Evaluation of Four aggregate
models for calculating freight
demand elasticities;
Interregional freight flows in
Canada in 1979 National
Bjorner 1999
Denmark quartly time series
data 1980-1993 National
Winston 1981
Oum 1989
Table 4: Existing Estimated Values of Truckers’ Demand Elasticity

39

Source Context Geographic
Level
Short-term or
Long-term
Mode Demand
measurement
Type of
elasticity
Estimated
Values of
Elasticities
Comments
Oum et al 1992 Overall
elasticities
Across
countries
Both Driving Trips Own-price -0.23 (Short-
term) and -0.28
(long-term)
-
Button 1993 Elasticities by
trip purpose
Urban and
inter-urban
Unspecified Driving Trips Own-price -0.3 to -3.2 Shopping trips are
found to be most
elastic to price
changes.
NHI 1995 Recommended
values for
modelers
Metropolitan
Areas
Unspecified Driving Trips Own-price -0.5 -
Oum et al 1996 Netherland National Short-term Driving Trips Own-price -0.3 -
Burris 2003 A toll bridge in
Florida
A route Short-term Driving Traffic volumes Toll-elasticity 0.021 to -0.362 Elasticities vary by
time of a day; toll-
demand elasticities
are more elastic than
other components of
travel costs.
Off-peak elasticity is
found to be higher
Ingram and Liu
1999
Literature
review
Across
countries
Unspecified Driving Trips Own=price -0.06 to -0.28 -
Driving Trips Own-price 0.384 for peak
hours
DeBorger et al
1997
Belgium Urban Short-term
Table 5: Existing Estimated Values of Motorists’ Demand Elasticity

40
2.4.2 Categorizing existing studies based on how heterogeneity is considered
Possible criteria: Given the importance of user group heterogeneity, as
highlighted above, quite a few authors have considered user or user group heterogeneity
in congestion pricing (e.g., Arnott et al. 1988, 1992, 1994; de Palma and Lindsey 2004;
Small, Winston, and Yan 2006; Small and Yan 2001; Verhoef and Small 2004; Yang et al.
2002). These studies provide useful references for planners and policy analysts
advocating congestion pricing. Based on these studies, for instance, one could use the
following criteria to categorize the existing literature on congestion pricing, depending on
what and how user or user group heterogeneity is considered:
 Whether individual or group differences in departure time, scheduled delay cost, and
route choice is considered or overlooked in the congestion pricing models that are
used or developed;
 Whether users or user groups are treated as heterogeneous in terms of perceived
values of time, road space requirement, occupancy rate per vehicle, and marginal
social/congestion externalities generated;
 Whether users or user groups have different functions for the generalized costs;
 Whether different demand functions for two or more user groups are introduced;
 Whether within-group or across-group cost externalities are considered;
 Whether demand elasticities across user groups are taken into account.

Existing criteria: If the existing congestion pricing literature focusing on user or
user group heterogeneity is called “the heterogeneity literature” then authors have already

41
started classifying this literature. For instance, de Palma and Lindsey (2004) identify four
streams in the heterogeneity literature. Built on their work, the first stream in the
heterogeneity literature is represented by Glazer (1981), Layard (1977), and Niskanen
(1987). This stream is built on the static model by Walters (1961) and considers users’
heterogeneity in value of time, income, and/or demand elasticity, while ignoring
trip-timing heterogeneity in the models employed. Authors of this stream have long
argued that congestion pricing may have different effects on the social welfare gains of
heterogeneous user groups, a point that planners and policy analysts may care very much
about. For instance, Figure 4, below, adapted from Niskanen (1987), shows how a
uniform toll (t) in congestion pricing can make the poor or the low-income worse off.
As the figure indicates, when t is introduced into a market consisting of a flexible number
of commuters, the market generates (X
0
-X’) fewer trips as a response, resulting in less
congestion on the toll road. The reduced congestion compels additional rich people to
travel on the toll road—people who perceive benefits in the time savings net of t and
other private costs. Thus the perceived benefits are generated more or less because some
poor users have been tolled off the road (see the inverse demand curves of the poor in the
middle). Furthermore, the number “tolled-off” (the poor) is usually greater than the
number “tolled-on” (the rich). Without appropriate revenue recycling mechanisms,
therefore, the poor at large are worse off after t is introduced. In this sense, congestion
pricing in general or congestion pricing with common tolls in particular could be
regressive in benefitting the rich more than the poor. This issue is probably one of the
primary reasons why congestion pricing is not popular, despite the fact that there have
been continuous discussions of the topic, as also partially indicated in Morrison (1986),

42
Niskanen and Nash (2008), Pahaut and Sikow (2006), and Verhoef et al. (1997).

Figure 4: Congestion Pricing’s Impacts on the Poor and the Rich

Source: Adapted from Niskanen (1987).

Recent work on this stream presents a more sophisticated picture of congestion
pricing’s impact on heterogeneous users, who cannot simply be classified as “the poor”
or “the rich.” This stream sheds new lights on the applicability and evaluation of
congestion pricing. For instance, Verhoef and Small (2004) study how congestion pricing
influences users who are heterogeneous in value of time. Their studies demonstrate that
accounting for user heterogeneity and providing price differentiation may increase the
efficiency of congestion pricing. Moreover, de Palma et al. (2007), Fischer et al. (2003),
Holguin-Veras et al. (2006), and Kawamura (2003) examine the impact of congestion
pricing on truckers and motorists as two distinct user groups. Their work as a whole
indicates that an efficient congestion pricing regime should consider temporal as well as
spatial separations of heterogeneous user groups.
The second stream of the heterogeneity literature takes into account the route
Trips with toll
Trips with toll
Trips without toll Trips without toll
Trips without toll
Trips with toll

43
choice heterogeneity in the static model but assumes that all trips occur at a uniform peak
time period (Beckmann 1956; Dafermos 1973). This stream more or less expands
Walters’ (1961) model at the corridor level to the general network level. By ignoring trip
timings’ effects on the social welfare of road users, this stream focuses on the
interrelationships among tolls, aggregate travel demand, route choices, or spatial
distribution of trips and corresponding social welfare gains. The primary implication of
this stream for planners and policy analysts is that pricing could be as important as
designing a well-balanced multi-modal transportation system in terms of curbing traffic
congestion and minimizing social costs. Pricing could incentivize users to allocate
themselves among different routes/modes in a way that increases overall social welfare
without adding new capacity to the system. Without pricing, users choose whichever
routes and/or modes at will and ignore the MEC they impose on others, which can
diminish overall social welfare.
The third stream of the heterogeneity literature accounts for trip-timing
heterogeneity among travelers and frequently uses the dynamic model and/or bottleneck
congestion model or function to estimate the travel disutility (time and monetary costs)
(Arnott, de Palma, and Lindsey 1994; Cohen 1987; Henderson 1974; 1977; 1981;
Vickrey 1969, 1973). One of the primary insights from this stream is that the overall
social welfare of users of a congestible facility or system can be optimized if tolls or
subsidies allot staggered time slots to heterogeneous users in the uniform peak hours. The
dimensions of user or user group heterogeneity emphasized in this stream are value of
time, travel time cost, route choice, schedule delay cost, and/or preferred arrival time.
Based on this stream, planners and policy makers may see that managing the temporal

44
distribution of traffic is as important as supplying sufficient roads or allocating users
along different routes. This dissertation focuses on such temporal distribution of traffic
through pricing.
The fourth stream of the heterogeneity literature emphasizes the network
environment where congestion pricing regimes take place. Compared to the other three
streams, this stream often considers user or user group heterogeneity in a general network
rather than in a simplified network. The fourth stream also often assumes that there are
multiclass vehicles (users) who can choose from multiple routes and/or multiple modes of
travel. According to de Palma and Lindsey (2004), this stream is still under development,
primarily because with more heterogeneous user classes or groups, models for congestion
pricing become increasingly complicated, as partially indicated in Han and Yang (2008),
Yang and Huang (1998, 2005). For planners and policy analysts, this stream could be of
direct policy relevance, since it addresses issues that resemble ones in the real-world. Due
to the underdeveloped status of this stream at this time, however, planners and policy
analysts may not be able to gain many insights from it.
2.4.3 Heterogeneity and congestion pricing models
Based on the specific models used or developed, the heterogeneity literature can
be grouped in a way that is slightly different from the way described above. These
models include the “bottleneck model,” “dynamic model,” “static model,” “hybrid
model,” and “aggregate model.” Depending on which of these four models is used, the
heterogeneity literature could be divided into four groups, each group focusing on certain
dimensions of user or user group heterogeneity and on how these dimensions are related
to, or considered in, congestion pricing. As a whole, models of all four groups imply that

45
as long as some dimensions of user or user group heterogeneity are present, planners and
policy analysts oftentimes can consider congestion pricing a strategy to increase the
efficiency of congestible facilities such as roads and bridges. Each group of models
provides a specific framework in which planners and policy analysts can consider certain
dimensions of user or user group heterogeneity when evaluating or designing a specific
congestion pricing regime or proposal.
The bottleneck model deals with user or user group heterogeneity through
preferred arrival time, departure time, schedule delay cost, and route choice. The model
shows planners and policy analysts how pricing can allocate users to commute in a
sequence that increases the economic efficiency of facilities such as roads and bridges.
The static model addresses user or user group heterogeneity through dimensions
such as marginal congestion/environmental costs, fixed travel cost, value of time, and
toll-demand elasticity. Unlike the dynamic model, the static model focuses on trips
occurring in a uniform period and on the spatial separation of trips rather than on their
temporal sequence or separation. Thus, the static model sheds light on how planners and
policy analysts could charge peak-time users so that they efficiently use available
facilities or routes across space.
The hybrid model simultaneously accounts for dimensions of user or user group
heterogeneity that the dynamic and static models consider separately. Therefore, the
hybrid model provides planners and policy analysts with a tool for understanding how
pricing could or should be used to efficiently distribute or separate heterogeneous users
or traffic simultaneously across space and over time.
If the models highlighted above more or less only deal with what happens to

46
heterogeneous users in congestion pricing and efficiency of congestion pricing within the
transportation sector, the aggregate model studies heterogeneous users and efficiency of
congestion pricing at the societal or cross-sectoral level, that is, how congestion pricing
influences the operations and efficiency of sectors beyond transportation. Thus the
aggregate model may help planners and policy analysts link congestion pricing to the
economic efficiency of the whole economic system.
More characteristics about the above four models in congestion pricing and their
implications for planners and policy analysts are summarized as follows:
Bottleneck/dynamic models: Henderson (1974, 1977, 1981) and Vickrey (1969) are
among the pioneers who developed and employed dynamic/bottleneck models. They
introduce trip timing or trip sequences into the earlier models of congestion pricing. Prior
to the Henderson and Vickrey, most authors or researchers only considered aggregate
traffic flows in a uniform time period. For Henderson and Vickrey, however, the uniform
period above could still be divided into smaller staggered time slots. Different time slots
will be of different value to heterogeneous commuters with different/heterogeneous
values of travel time and schedule delay costs. With a time-varying toll or subsidy,
commuters will change their starting times or trip sequences and allot themselves into
different time slots or trip sequences, according to the respective values of their travel
time or schedule delay costs. Commuters with higher values of travel time or schedule
delay costs would be priced into time slots that previously had greater demand and longer
travel delays. Other commuters are subsidized or priced into time slots that were not
highly utilized before tolling. As a whole, most commuters experience less congestion
after tolling and aggregated social welfare for all commuters increases as a result.

47
Based on the pioneering work described above, authors recently have developed
more sophisticated dynamic/bottleneck models of congestion pricing. In these models,
users or user groups are heterogeneous not only in travel time value or schedule delay
cost but also in cost interdependence. For instance, Arnott et al. (1992) and de Palma et al.
(2007) have applied “own-cost coefficients” and “cross-cost coefficients” to address
within-group and between-group congestion externalities by different heterogeneous user
groups. Roughly speaking, the own-congestion coefficient indicates the within-group
effect of one additional driver from a specific user group on the generalized cost of all
other users in the same group. The cross-congestion coefficient reflects the average
impedance costs that one group impose on users from the other group. Consideration of
such own-cost coefficients and cross-cost coefficients allows researchers to determine
when it is economically efficient to segregate, separate, or mix different user groups of a
congestible facility through pricing and other measures.
Depending on the network complexity being considered, existing literature
employing or developing dynamic models could be further divided into two subgroups:
“the simplified literature,” which uses the dynamic model for users within a simplified
network, and “the general literature,” which uses the model for users on a general
network. Probably due to its tractability, the former is much more developed than the
latter. Table 6, below, summarizes some of the simplified literature of relevance to this
dissertation.
48
Table 6: The Simplified Literature of Relevance

Source
Scenario
Studied
Heterogeneity
Addressed
Main Findings
Vickrey 1969
Henderson
1974
Henderson
1977
One routes;
fixed travel
demand; two
user groups
Users’ trip-making
decisions regarding and
when to travel to
minimize the sum of
travel time and schedule
delay costs

Workers’ earlier arrival increases
waiting costs but lowers travel
costs, congestion tolls can help
increase social welfare as compared
to the no-toll scenario
Workers’ earlier arrival increases
waiting costs but lowers travel costs

Henderson
1981
Fixed demand;
no carpooling
behaviors; two
groups
Staggered Work
Hours(SWH); preferred
schedules; workers’
wage; workers’ skills
SWH may increase social welfare.
Taxing firms can facilitate SWH.
SWH is not always efficient.
Efficient SWH requires identical
skill workers’ wages vary by
starting time

Cohen 1987 Two groups;
fixed demand;
one route
Value of time; preferred
arrival time at work
Motorists with high value of time
and high income are never worse
off by paying an efficient toll
Arnott et al.
1988
Fixed demand;
one route
Travel time costs; starting
time at work; the costs
incurred from early and
late arrival
A time-varying congestion toll can
be constructed to eliminate queuing
in peak hours and to induce the
optimal order of departure.
Estimated benefits from the toll are
biased if user heterogeneity is not
considered

Arnott et al.
1992
Two routes;
fixed demand
Travel time costs;
schedule delay costs;
route Choice; own- and
cross-group congestion
costs
In the bottleneck case, separated
usage may be optimal if one group
has both higher travel time and
schedule delay costs
Arnott et al.
1994
One route;
fixed demand
Unit travel time costs;
schedule delay costs;
relative costs of late to
early arrival times; timing
of trips

Optimal tolls with rebates to
travelers are likely to benefit every
traveler

49
Table 6, Continued

Bernstein and
Sanhouri 1994

Two route;
two modes;
elastic demand

Tolls’ impacts on
decision to travel,
origin/destination choice,
mode choice, route
choice, and
departure-time choice

It may be impossible to properly
price more than one choice process
when one alternative is left
untolled
Huang et al.
2007
One route; two
modes
Mode choice When there are two modes of
travel, the arrival rates of
commuters at workplace may be
different from that at bottleneck

de Palma et al.
2007
Two routes;
fixed demand
by vehicle
type
Vehicle types; value of
time; congestion delay
and safety hazards
Value of time, congestion delay
and safety hazards, ratio of
different vehicles and lane
capacity indivisibilities are
important factors determining
whether truck-only lanes are
economically efficient

In terms of the general literature, the work of Yang and Huang (2005) contains a
concise review of the limited literature that has been published so far. It regards the
general literature as an extension of the literature on the first-best congestion pricing
model, arguing that the latter initially only modeled congestion pricing on a simple
network with homogeneous or nearly identical users. The general literature introduces
various dimensions of heterogeneity into first-best models, for instance, multiple
vehicle types (Dafermos 1972, 1973), multiple vehicle types and link flow
interactions (Smith 1979), and multiple time periods (Liu and Boyce 2002). In
addition, the paper contends that the rise of the general literature contributes to the
methodological development of the dynamic traffic assignment.
The static model: Unlike the dynamic model, the static model usually
exogenises the heterogeneity that the former attempts to endogenise. The static model
focuses on users’ or user groups’ heterogeneity in one or several of these aspects:
marginal congestion/environmental costs, fixed travel costs, value of time, and
toll-demand elasticity (Evans 1992; Small, Winston, and Yan 2006; Small and Yan

50
2001; Verhoef, Nijkamp, and Rietveld 1995; Verhoef and Small 2004; Yang and
Huang 1999). Table 7, below, summarizes selected literature of relevance to this
dissertation that develops or applies a static model.
Table 7: Literature Using the Static Model
Source Scenario Studied
Heterogeneity
Addressed
Main Findings
Evans 1992 Two groups,
elastic demand,
one route, two
modes (transit vs.
car)
Value of time;
travel costs
Congestion pricing tends to favor traffic
with higher value of time
Verhoef et al.
1995
Multiple groups,
demand and
network info
unspecified
Marginal
External Costs
(MEC)
General formulae showing how much
weight should be given to different users
when deriving a common fee
Yang and Huang
1999

Two groups, one
route with multiple
lanes, elastic
demand
MEC; vehicle
occupancy
The optimal uniform toll for the
second-best solution in the presence of
HOV lanes is a weighted average of the
MEC between non-carpooling and
carpooling commuters
Small and Yan
2001
Two groups,
elastic demand,
two routes
Value of time Accounting for user heterogeneity is
important in evaluating constrained
policies and improves the performance of
the policies
Verhoef and
Small 2004
Multiple groups,
elastic demand, a
three-link network
Value of time Second-best pricing policies would lose
their effectiveness if user heterogeneity in
value of time and demand elasticity is
ignored when setting tolls
Small et al. 2006

Two groups, a
two-route
network , inelastic
demand
Vehicle
occupancy;
user
preference;
travel choice
Accounting for user heterogeneity in value
of time and ride-sharing preference is
important in assessing road pricing’s
efficiency and HOT policies

51
The literature listed in Table 7 indicates that the static model often hypothesizes a
fixed number of trips occurring simultaneously or in one uniform period. This
uniform period means that the heterogeneity of users or groups in dimensions such as
departure time and schedule delay costs are neglected.
The hybrid model: So far, few papers have applied or developed the hybrid
model. In a piece by Yang et al. (2002), a good example of these few papers, the
authors categorize users into multiple groups by value of time, simultaneously
considering user group heterogeneity in travel demand elasticity and route choice.
However, unlike other papers that apply the dynamic model, the authors do not take
into account user group heterogeneity in departure time and schedule delay cost.
Another paper that develops and applies the hybrid model is by Arnott et al. (1992).
In this paper, the authors account for the user heterogeneity in values of time and
route choice simultaneously. Usually, route choice is not considered in a dynamic
model.
The aggregate model: In literature that applies or develops the aggregate
model, user or user group heterogeneity, optimal tolls, fiscal effects, and equity
concerns beyond the transportation sector are considered systematically. For instance,
de Palma and Lindsey (2004) use a “general-equilibrium” framework to study how
congestion pricing regimes affect the whole economic system. In their framework,
user heterogeneity is linked to issues at the societal level or at the economic system
level, such as:
 How to spend the revenues of congestion pricing among heterogeneous users or
user groups in the whole society;
 How to set the levels of tolls to achieve optimum welfare for the system or the
society in which congestion pricing takes place;

52
 How to quantify effects of congestion pricing on overall employment for all
sectors and on the efficiency of these sectors as whole.

2.5 The Second- and Third-Best Regimes: Policy Constraints
One or more the assumptions underlying the first-best congestion pricing
regime is always violated in the world of planners and policy analysts, for instance,
despite imposing MEC on others, some users cannot be charged due to political
considerations or technical constraints. To win the political support of the majority of
users, tolling authorities have offered free general-purpose lanes parallel to a HOT
lane. In other words, like user or user group heterogeneity, unpriced alternatives and
policy constraints are an unavoidable and recurrent subject for planners and policy
analysts advocating congestion pricing. Specifically, what would happen to a
congestion pricing regime where there are policy constraints or an unpriced
alternative? Also, what would happen to a congestion pricing regime where there are
policy constraints or an unpriced alternative tied to heterogeneous user groups? These
are some of the important questions that planners and policy analysts have to answer
when proposing or advocating a congestion pricing regime.
Depending on the policy constraints being considered and/or whether an
unpriced alternative is offered for users, existing studies of congestion pricing could
be categorized and summarized in a different way from above. But authors have
rarely studied the policy constraints in congestion pricing per se. Rather, if they touch
on the constraints, authors are actually more interested in the impacts of these
constraints on different aspects of congestion pricing. The aspects that have been
examined in existing studies include, but not are limited to: political feasibility,
optimal toll, relative efficiency, social welfare, and distributional effect, as indicated

53
in Table 8, below. Some of these aspects of congestion pricing are probably
unavoidable for planners and policy analysts advocating congestion pricing, for
instance, political feasibility and distributional effects.
Table 8: Constraints Considered in Existing Studies
Source
Constraints
Considered
Impacts of the
Constraints Studied
Main Conclusions
Levy-Lambert 1968
One route in a
two-route network
cannot be charged
Untolled alternative;
second-best tolls
Marchand 1968
One route in a
two-route network
cannot be charged;
individuals' budget
has to be balanced
Untolled alternative;
second-best tolls
Models used to arrive at second-best
tolls, given there is an untolled
alternative in a simplified network
Borins 1988
Evans 1992
Giuliano 1992
Lave 1994
Verhoef 1994
Political acceptability
or resistance
(networks vary)
Unpriced alternatives
for users; second-best
tolls; equity issues;
redistribution of the
toll revenue,
government's role, etc
Political resistance could make
congestion pricing politically
infeasible
Infeasibility to
charged
differentiated tolls
among different
types of vehicles
(network
unspecified)
Sizes of second-best
common tolls
Second-best common tolls equal to
the weighted average of optimal
first-best differentiated tolls; the
group-specific weights are related to
corresponding toll-demand
elasticities and cost functions.
One user group is not
charged (network
unspecified)
Sizes of the
second-best toll for the
group that is charged
Demand elasticity, cost independence
between groups and cost function all
affect sizes of second-best tolls
Verhoef et al 1995
One route in a two
-route network is not
charged due to
"political or admin-
istration reasons"; all
users are assumed to
be homogeneous in
schedule delay cost
Efficiency/Overall
social gains of
congestion pricing
Efficiency gain is determined by the
relative capacity of two routes, which
are substitutes to each other in a
dynamic model and

54

Table 8, Continued.

Small and Yan 2001
One lane in a
two-lane network has
to be free due to
political
considerations
Efficiency/Overall
social gains of
congestion pricing
Accounting for heterogeneity in
value of time is important in
evaluating congestion pricing;
unpriced alternatives or second-best
tolls decrease the efficiency of
congestion pricing;
profit-maximizing or third-best tolls
could bring about negative overall
social welfare gains
Verhoef and Small
2004
One or two links in a
three-link network is
untolled
Efficiency/Overall
social gains of
congestion pricing
Second-best policies would lose
effectiveness if heterogeneity is
ignored when setting toll levels
Liu 2004
Some portions of the
urban road network
are not subject to
tolls due to technical
and political
constraints
Sizes of second-best
tolls, efficiency of
congestion pricing in a
two-route network
Increased coverage of the network
with toll increases percentage of
welfare in a nonlinear way; the
network with faster tolled route
yields higher percentage of overall
welfare gains
de Palma et al 2007
Non-differentiated
tolls in a two-lane or
two-route network
Optimal assignment of
different types of
vehicles and efficiency
of congestion pricing
Differentiated tolls could lead to
optimal assignment of different types
of vehicles

As a whole, Table 8 indicates that:
 Unlike the first-best regimes, the second- or third best regimes often have
unpriced alternatives for selected users, due to political, enforcement,
administrative, or technical reasons (Braid 1996; Levy-Lambert 1968; Liu 2004;
Marchand 1968; Verhoef et al. 1995; Verhoef and Small 2004).
 Unpriced alternatives are often tied to the political acceptability of congestion
pricing (Borins 1988; Evans 1992; Giuliano 1992; Lave 1994); in other words,
choosing or providing appropriate unpriced alternatives may help increase the
feasibility of congestion pricing.
 An unpriced alternative for users rather than an unpriced alternative for user
groups has received more attention in existing studies. Of the multiple studies
highlighted in Table 8, above, only one deals with an unpriced alternative for
user groups (Verhoef et al 1995).
 Unpriced alternative and policy constraints influence optimal toll size, economic

55
efficiency, social welfare gain, and the distributional effects of a congestion
pricing regime (Braid 1996; Liu 2004; Small and Yan 2001; Verholf et al 1995).
 In existing studies, a non-differentiated toll across users or user groups has been
more intensively studied than have differentiated tolls that consider various
dimensions of user group heterogeneity. In the literature listed, only de Palma et
al. (2007) and Verhoef et al. (1995) specifically study differentiated tolls.

For planners and policy analysts considering congestion pricing, the above
findings based on existing studies may have important implications. These findings
pose to planners and policy analysts these unavoidable questions:
 If an unpriced alternative has to be offered, is it more efficient to offer a spatial
unpriced alternative such as a free general-purpose lane parallel to toll lanes, or
to offer an unpriced or discounted temporal alternative such as free hours before
or after the peak?
 If some user groups have to be exempted in a congestion pricing regime, is it
more efficient to provide group-specific exemption or to offer limited-time or
limited-route exemption?
 If certain forms of unpriced alternatives have to be offered, how much do they
change the economic efficiency and distributional effects of a congestion pricing
regime?

This dissertation does not address all the above questions. Rather, it examines
the relationships among a temporal unpriced alternative for user groups, distributional
effects, economic efficiency, and user group heterogeneity in the representative
regime. The representative regime epitomizes many if not most congestion pricing

56
regimes in place as well as their analogues. The above survey of existing literature
shows that few studies have been conducted on these relationships, which may be of
special interest to planners and policy analysts who pursue congestion pricing as a
strategy to increase economic efficiency and who want simultaneously to address
equity issues and to improve economic efficiency.
2.6 The Second- and Third-best Regimes: Unpriced Alternative and
Heterogeneity
As highlighted above, unpriced alternative and user or user heterogeneity are
important topics to examine in congestion pricing. They are of special interest to
planners and policy analysts. Nevertheless, a survey of existing studies indicates that
few authors have studied congestion pricing cases that have heterogeneous users or
user groups and an unpriced alternative for all or selected users or user groups. Even
fewer authors have examined how the distributional effects and economic efficiency
of a congestion pricing case would change if there were both heterogeneous users or
user groups and an unpriced temporal alternative. Table 9, below, summarizes a
handful of studies on cases where there are both heterogeneous user groups or users
and an unpriced alternative.
57
Table 9: Literature on Heterogeneity and Unpriced Alternative
Source
Heterogeneity
Considered
Unpriced Alternative
Characteristics
Model Used
Bernstein
and
Sanhouri
1994
Mode choice, route
choice, departure time
choice
Mode-, route- and
time-specific in a two-link
network

Static model
Braid 1996 Arrival time preference,
schedule delay cost
One link in a two-link
network is untolled
Dynamic model
Verhoef et al
1996
Marginal private cost,
demand function
One of two links is
untolled
Static model
Liu and
McDonald
1998
Departure time choice
(peak vs. off-peak
hours), users’ demand
function in peak and
off-peak hours

Four lanes of a six-lane
highway are untolled
Static model that considers
two time periods: peak and
off-peak
Small and
Yan 2001
Value of time One lane of a two-lane
highway is untolled
Static model
Verhoef and
Small 2004
Value of time One link of a three-link
network is untolled
Static model
Verhoef
2007
n.a. Partial capacity of a single
road or one link in a
two-link are untolled

Static model

As a whole, the literature listed in Table 9 indicates that:
First, even though user group heterogeneity is an important topic in congestion
pricing, existing studies have only considered certain dimensions of it. User group
heterogeneity in dimensions such as road space requirement and commute distance
has not been explicitly accounted for. Also, if motorists and truckers are treated as two
distinct user groups, truckers as a group have not been studied in any of the identified
literature. In other words, most authors have used the parameters of motorists as a
proxy for all users in relevant models. Such a substitute is reasonable if motorists
dominate the cases studied or the model being developed. When there is a heavy
presence of truckers or users of multiple modes of travel, however, using parameters
of motorists as a proxy could be problematic, as partially indicated in de Palma et al

58
(2007). Planners and policy analysts who need to evaluate or design a congestion
pricing regime may need to differentiate users or user groups to arrive at better
evaluation results or to obtain sound policy proposals.
Second, the literature listed has explored the characteristics of the second- or
third-best regimes with an unpriced temporal alternative for certain users or user
groups. In other words, planners and policy analysts who want to take advantage of
roads’ underutilized capacity in off-peak hours through congestion pricing may find
little useful information in existing studies. In the literature listed in Table 9, for
instance, authors have only focused on:
 Where there is an unpriced spatial alternative (Bernstein and Sanhouri 1994;
Verhoef et al 1996; Liu and McDonald 1998; Verhoef 2007);
 Where there are staggered time slots in a uniform time period (Braid 1996).

Notably, Liu and McDonald (1998) consider cases where there are peak and
off-peak periods but do not study cases where all users are exempted from tolls in the
off-peak period. Due to the above characteristics, the literature listed in Table 9 also
does not contain any operational algorithms or formulae that could be used to derive
optimal tolls and social welfare gains for the representative regime. Therefore,
planners and policy analysts who advocate the representative regime in particular also
need to develop new algorithms or formulae for the regime.
Third, trucks or truckers as a user group distinct from automobiles or motorists
are not explicitly discussed in the literature listed above. This absence indicates that
few authors have studied congestion pricing cases where there are heterogeneous user
groups such as trucks and cars as well as cases where there is an unpriced alternative
for certain members of heterogeneous user groups. Planners and policy analysts

59
looking at congestion pricing in metropolitan areas such as Los Angeles and New
York, where trucks consist of a significant share of road traffic, however, need more
information about these cases to better address the congestion issue where trucks
contribute significantly to it. As partially indicated by the PierPASS and E-ZPass
programs in Los Angeles and New York, respectively, treating truckers as a separate
user group in congestion pricing could help people curb truck-related congestion and
emission issues.
2.7 Implications from Existing Literature
The above classification and survey of existing literature are by no means
exhaustive; however, they provide several implications for this dissertation; they also
justify the dissertation’s relevance to planners and policy analysts who advocate the
representative regime. Specifically, the implications of existing studies and the
relevance of this dissertation in tandem with these implications are highlighted below.
First, user heterogeneity, on the one hand, makes congestion pricing possible,
as different users and user groups value their time differently and some are more
willing to pay out of congestion than others; on the other hand, user heterogeneity
poses challenges to setting optimal tolls across users or user groups given that
different users and user groups impose different marginal external/congestion costs on
others. Planners and policy analysts advocating congestion pricing in general and the
representative regime in particular cannot avoid the issues of user differentiated and
differentiated tolls across users or user groups.
Second, in addition to user or user group heterogeneity, unpriced alternatives
and policy constraints are recurrent subjects in the second- or third-best congestion
pricing regimes. Planners and policy analysts who are interested in these regimes
cannot totally avoid these subjects. Existing studies have provided useful references

60
for these planners and policy analysts. Based on information from these studies, the
second- or third-best regimes can be further divided into the following different
subgroups:
 Subgroup #1: Regimes with homogeneous users and an unpriced alternative;
 Subgroup #2: Regimes with heterogeneous users and no unpriced alternative;
 Subgroup #3: Regimes with heterogeneous users and an unpriced temporal
alternative;
 Subgroup #4: Regimes with heterogeneous users and an unpriced spatial
alternative.

A survey of existing studies indicates that user group heterogeneity, unpriced
alternatives, and policy constraints all affect relative efficiency, social welfare gains,
toll settings, and evaluations of the second- or third-best regimes, especially for
Subgroups # 1 and 2. Existing studies have paid little attention to Subgroup #3, that is,
the representative regime. But in the real-world setting, many if not most cases belong
to the representative regime or its variants, for instance, the London Congestion
Pricing program, the Stockholm congestion pricing program, and the PierPASS
program in Los Angeles (for more details of these programs, see Eliasson et al. 2009;
Giuliano et al. 2008; Steimetz et al. 2008; Santos 2008). There is a gap between
research on the representative regime and its real-world applications and popularity.
This dissertation is intended to fill the gap.
Third, few authors have studied truckers and motorists as two distinct user
groups in congestion pricing. Therefore, we know little about the differences between
how truckers and motorists affect the design and properties of the second- or
third-best regimes. In other words, planners and policy analysts who have to deal with

61
congestion pricing cases involving a large number of trucks may gain few insights
from existing studies. In view of this dearth of information, this dissertation constructs
and studies policy scenarios and cases where truckers and motorists are two
heterogeneous user groups, differing in dimensions such as toll-demand elasticity,
value of time, commute distance, generalized cost function, demand function, relative
group size, commute distance, and road space requirement. Relevant results from the
dissertation should help planners and policy analysts better evaluate and design
congestion pricing regimes or proposals where there are heterogeneous user groups in
general and truckers and motorists as two dominant user groups in particular.
Fourth, several authors have developed general algorithms or formulae to
derive optimal toll(s) for— and evaluate social welfare gains and distributional effects
of— regimes belonging to Subgroups # 1, 2, and 4, as mentioned above. The
algorithms or formulae developed provide useful references for this dissertation, as
they show elegant ways to derive optimal tolls for regimes that resemble the
representative regime in certain aspects. For instance, selected users are exempted
from the toll, there is an unpriced alternative, and/or there are heterogeneous user
groups. Nonetheless, there are still notable differences between the representative
regime (Subgroup #3) and other regimes (Subgroups #1, 2, and 4). Notably, the
representative regime deals with the temporal allocation of users, temporal unpriced
alternatives, and heterogeneous user groups simultaneously, which means that new
algorithms or models are needed to derive optimal tolls and relative social welfare
gains for the representative regime. These new algorithms or models will be a focus
of this dissertation. To develop algorithms and models that are amenable to planners
and policy analysts, this dissertation avoids using existing Lagrange multiplier and
Newton methods. As discussed below, this dissertation develops a combination of

62
constrained iteration and exhaustive search methods to derive optimal tolls and
associated social welfare gains for the representative regime. The methods developed
are simple enough for most planners and policy analysts to comprehend.
Fifth, existing studies indicate that when there is an unpriced spatial
alternative on a simplified network, economic efficiency of congestion pricing will be
lost (Liu and McDonald 1998; Small and Yan 2001). When costs of tolling are
ignored, the social welfare gains from the second- or third-best cases only account for
50-75% of those from the corresponding first-best cases (Verhoef et al 1996). The
existing studies reviewed above, however, only consider user heterogeneity in
dimensions such as values of time, demand function, generalized cost function, and/or
route choices. In addition, users in existing studies are often implicitly treated as
motorists or commuters. When there are two distinct user groups such as motorists
and truckers and an unpriced temporal alternative, conclusions and insights from
existing studies may vary. For planners and policy analysts interested in congestion
pricing, motorists are not the only user group they need to consider (e.g., de Palma et
al. 2007; Fischer et al. 2003; Holguin-Veras et al. 2006; Kawamura 2003). Plus,
peak-load pricing with an unpriced or discounted time period has been present in the
real-world setting (Giuliano and O’Brien 2008; Holguin-Veras et al. 2006). To better
evaluate all of the congestion pricing alternatives available, planners and policy
analysts need additional insights into regimes where there are both heterogeneous user
groups and an unpriced temporal alternative. These regimes, according to the above
survey of existing literature, have not been well studied before.
Last but certainly not least, existing studies have highlighted the importance of
user group heterogeneity and an unpriced alternative in the study of congestion
pricing. Also, existing studies have provided interesting insights about how ignoring

63
user heterogeneity may influence the evaluation or design of congestion pricing
regimes. For instance, Small and Yan (2001) demonstrate that when user
heterogeneity in value of time is overlooked, the economic efficiency of a congestion
pricing regime may be underestimated. Cases where there are two routes and users
differing in value of time (Arnott et al 1992; Shmanske 1991, 1993) indicate that tolls
differentiated by route are more efficient than non-differentiated tolls. What’s more,
the more different users are in terms of value of time, the more efficient differentiated
tolls will be (Shmanske, 1993). For planners and policy analysts interested in
congestion pricing, the above findings are useful but still insufficient. For them, some
important questions have still been unanswered. For instance, would the above
findings still be upheld if an unpriced temporal— rather than spatial— alternative is
offered? Also, in the real-world setting, user groups often differ not only in value of
time but also in toll-demand elasticity and road space requirement. Would the
findings in existing studies still be valid if between-group differences in demand
elasticity and road space requirement were considered? This dissertation explores
such questions of special interest to planners and policy analysts—questions that have
not been well examined— using the representative regime as an example.

64

CHAPTER 3. MODEL DEVELOPED AND DATA USED
3.1 The Model of General Form
The representative regime could be modeled in an abstract manner, as
suggested by existing studies (Verhoef and Small 2004; Verhoef et al 1996). In the
spirit of these studies, this dissertation assumes that the representative regime and
relevant cases or policy scenarios constructed take place in a simplified network, as
shown in Figure 5, below.

Figure 5: The Network Considered

This network has two origins (O1, O2), one destination (D), and three links (A, B, C).
E is the point where Links A and B intersect. When a congestion pricing regime is in
place, all or some eastbound users passing E will be subject to a toll, depending on the
policy goal of the program/example. Links A and B can have different lengths,
indicating that users starting from O1 or O2 have traveled different distances before
they reach E. Travel distances could have an impact on a user group’s generalized
cost-demand elasticity, as indicated in Salas et al. (2008):

η'= η
0
* d
(-0.1)
(F0),
where
O1
D
B
A
2
E
O2
F

65
η' is the generalized cost-demand elasticity, which takes into account commute
distance differences between user groups;
η
0
is the generalized cost-demand elasticity, which ignores commute distance
differences between user groups;
d is the user-group-specific travel distance.
The average speeds of traffic on Links A or B can be the same or different, depending
on vehicle types and heterogeneous traffic interactions captured in the model. A
real-world example can better explain the above network’s set-up. For instance, due to
great demands for land, an increasing scale of warehousing and distribution activities,
and the costs of rent/land, freight facilities such as warehouses and intermodal hubs
are often located at peripheral areas of a region. This location gives relevant truck
traffic an origin (or destination) at O2, which is further away from E, to the east of
which is the core area of the region. O1 is closer to E and the core area, and has less
pollution and a better school district. Some residents living at O1 commute to work at
D, an employment and business center of the region. East of E, both commuting
traffic and freight traffic have to share Link F, which can be thought as an arterial
road in the core area.
To introduce user group heterogeneity, that is, between-group differences, into
the model but still keep the model manageable, it is assumed that there are two user
groups, M and T, commuting between O1/O2 and D. M and T can be heterogeneous in
multiple dimensions, depending on specific research questions the model is
attempting to explore. In this dissertation, the dimensions of special interest are:
toll-demand elasticity, value of time, commute distance, and road space requirements.
In the representative regime and hypothetical cases constructed, a time
duration TR is artificially divided into two equal time periods t
1
and t
2
for traffic

66
management purposes, whereas t
1
covers the peak time, say 7am to 8am, and has
more traffic or users than t
2
. t
2
is the hour right before or after t
1
. Prior to the tolling, t
2

has significantly underutilized road capacities. The underutilized capacities are what
policymakers attempt to take advantage of via tolling.
Users from M and T t
1
and t
2
are elastic to cost/price changes. That is, users
from either group could switch modes of transportation, move their trips from one
time period to another, and travel outside the study time periods, and/or reduce trips.
The vehicle volumes by user group by time period on Link F are M
ik

and
T
ik
respectively, where i=t
1
or t
2
and k=0,1,2…n. Different values of k indicate
different congestion pricing cases. These cases sometimes can be almost identical
except one or two input parameters about user groups are different. k =0 in the no-toll
base case where there are no tolls to any user groups at all.
The average generalized costs by user group by time period are captured by
the following cost functions:
AGC
i
M
=AFC
i
M
*(L
a
+L
f
)+VOT
i
M
*(TT
i
Ma
+TT
i
M
) (1)
AGC
i
T
= AFC
i
T
*(L
b
+L
f
)+VOT
T
*(TT
i
Tb
+TT
i
T
) (2),
where AGC is the group-specific average generalized cost by time period, subscripts
“M” and “T” and superscript “i” are the same as above, AFC is the average
group-specific fixed cost by time period, L is the length of a specific link, subscripts
“a,” “b,” and “f” denote three links in Figure 5, VOT is group-specific values of time,
by time period, subscripts and superscripts of VOT are the same as above, TT is
link-based travel time, by time period by link, which can be calculated using the BPR
volume-delay function when free-flow travel time, carrying capacity and traffic
volumes by user group of a link are known. The function is written as:

67
TT=TT
0
*(1+0.15*N/K
4
),
where
TT
0
is the free-flow travel time,
N is traffic volumes and K is the capacity, N and K should be in the same unit of
measurement in terms of measuring traffic volume.
The BPR volume-delay function has also been used by several authors (Small
and Yan 2001; Liu and McDonald 1998; Verhoef and Small 2004). Subscripts and
superscripts of TT are the same as above. Since M and T share Link F thus
TT
i
T
=TT
i
M
.
The group-specific demand functions on Link F by time period have a linear form:
D
i
M
=R
i
M
-S
i
M
*N
i
M

(3)
D
i
T
=R
i
T
-S
i
T
*N
i
T

(4)

where
R and S are time-period- and group-specific parameters, D is time period- and
group-specific “inclusive price,” which equals to AGC plus a group-specific toll (  )
when applicable.
The aggregate social welfare function is defined as the total areas under the
inverse demand curves defined by D
i
C
and D
i
T
, less total generalized costs:
SW=
i
T
t
t i
i
T
i
M
t
t i
N
t
t i
i
M
t
t i
N
i
T
i
M
AGC N AGC N dt t D dt t D
i
c
i
T
* * ) ( ) (
2
1
2
1
0
2
1
2
1
0
 

 

  
   (5)
Equation (5) could be looked as an extension of a similar equation by Small and Yan
(2001).
Relative efficiency ( ω) of a pricing program in terms of social welfare gains is
evaluated using the following equation:

68
 = SW
(t)
/SW
(0)
(6)

where
SW
(t)
is the overall social welfare of a regime, and SW
(0)
is the overall social welfare
in the first-best regime where user group-specific and time-specific tolls are charged
to all user groups.
Given the above equation, the

value for the first-best regime will be 1. For
other regimes, their

values will range from 0 to 1. Within this range, the higher
the

value is, the more efficient the regime will be.
3.2 Solutions to the Model
Existing studies such as Small and Yan (2001), Verhoef et al. (1996), and Verhoef
and Small (2004) have derived or illustrated algorithms to obtain the optimal tolls and
corresponding social welfare gains of the pricing cases with heterogeneous users and/or
an untolled spatial alternative. These algorithms provide a useful framework and
procedures for considering the economic efficiency of the representative regime. The
algorithms in existing studies, however, cannot be used to derive optimal tolls for the
representative regime. The representative regime is different from regimes examined in
existing studies in at least three aspects:
 It deals with an unpriced temporal alternative whereas the latter deal with an
unpriced spatial alternative.
 It has two user groups that differ in multiple dimensions such as value of time,
demand elasticity, road space requirements, and commute distance whereas the
latter has individual users that differ only in value of time and/or demand
elasticity.
 It explicitly categorizes users into two user groups and considers
between-user-group differences (user group heterogeneity) whereas the later

69
implicitly assume that all users are motorists and focus on within-group
differences (user heterogeneity), if any.

In theory, one could still adapt algorithms such as Lagrangian and Newton
methods employed in existing studies for the representative regime. When more
dimensions of user group differences are considered in the representative regime,
however, the derivation of optimal tolls will be much more complicated than they are
in existing studies. For instance, in a case that has two user groups differing only in
values of time, eight equations are constructed to derive Lagrangian multipliers, the
intermediate parameters required to obtain optimal tolls for the case (Small and Yan,
2001). When there are two user groups, two time periods, and several dimensions of
user group heterogeneity, the number of Lagrangian multipliers at least doubles. Thus,
the derivation of Lagrangian multipliers requires significantly more equations and
computation time. In light of this fact, this dissertation proposes an alternative method
for deriving optimal tolls for the representative regime— one less complicated than
the adapted Lagrangain and Newton methods. This method does not require users to
have advanced economy and mathematical knowledge, but still provides reasonable
estimations of indicators about the representative regime, such as optimal toll, overall
social welfare gains, social welfare gains by user group, and economic efficiency.
This quality would appeal to planners and policy analysts who are interested in the
representative regime but do not want to adopt a complicated and time-consuming
method to dissect the regime.
Take the model of general form as an example to explain the method
developed and used in this dissertation. When there are user-group-specific tolls

70
introduced on Link F in t
1
, D
1 t
c
and D
1 t
T
increase. This increase then may cause a
decrease or increase in the quantity of M and T in t
1
, as Button and Pearman (1981)
qualitatively highlighted. Once M and T varies TT on Link F for t
1
would change. The
changed TT makes values of D’s unstable. Depending on values of D’s, users in t2
could switch into t1 or vice versa. Unless we know how D’s, TT, M, and T are
quantitatively interdependent on each other we cannot be exact about how many users
from different groups in t1 or t2 there would be after tolling. In other words, if we use
a computer program to find the numbers of M and T where there are tolls, we can
never find the equilibrium where values of M, T, TT and D’s are comparatively stable
unless there are some rules guide the relationships of the variables. What do we mean
by “stable” in the foregoing sentence? Stable means that if there are two sets of values
for M, T, TT or D’s, S1 and S2, meeting the rules that specify the relationships of M,
T, TT or D’s and S1 can be used as input for S2 in the computer program simulating
the above relationships where there are tolls, the numerical differences between
comparable elements of S1 and S2 are smaller than some predetermined thresholds.
An algorithm called “constrained iteration” could be used to find the above
two sets of M, T, TT or D’s. This algorithm has been commonly used to find user
equilibrium or traffic convergence in the travel demand model (Boyce et al 2004).
Let there be a network with two routes R1, R2, two nodes O1, O2, and a flow
of quantity S between O1 and O2. The costs (CS) to users using R1 and R2 are an
increasing function of flows and other constants such as road capacity and free flow
speed: CS=f(S). A modeler could implement constrained iteration as follows:

Step 1: He loads 1% or 5% of S onto R1 or R2.

71
Step 2: He calculates costs by route with function CS=f(S).
Step 3: He assumes that users would choose the route that has the fewest costs to them
and assign all 5% or 10% of S to that route. This step completes the first iteration. At
this time, either route now should have a revised cost to users.
Step 4: He loads another 1% or 5% of S onto the network and repeats Steps 1 to 3,
assuming that costs to users now would be revised costs from Steps 1 to 3. At this
time, the second iteration is finished.
Step 5: He repeats Steps 1-4 up to 100 or 20 times or cuts down the percentage of S
incrementally allocated until the cost differences of the two routes are smaller than a
predetermined criterion, say, the costs of one route is only 1% or 5% smaller or bigger
than those of the other route. At this time, user equilibrium is identified. By ignoring
the relatively small cost differences, the equilibrium that the modeler identified
conforms to Wardrop’s principle. Wardrop’s principle specifies that users of a
transportation network reach user equilibrium when no users can unilaterally switch
routes to obtain cost savings (Wardrop 1952).
Nowadays, computer programs are often used to execute the above procedures
about constrained iteration. For this dissertation, the above constrained iteration
algorithm provides useful enlightenments but has to be adapted to identify user
equilibrium for different cases constructed to mimic the representative regime, where
there are:
 Two heterogeneous user groups that differ in value of time, road space
requirement, commute distance, and demand elasticity;
 Two time periods that users from either group could allocate themselves to,
depending on the costs faced by user groups in each time period;
 Tolls imposed on both user groups or one groups;

72
 Tolls imposed on one or both time periods;
 Tolls can be (a) differentiated by user group and by time period (first-best); (b)
differentiated by time period but not by user group (second-best); or, (c) zero for
a time period or for a user group or both (third-best).

Dafermos (1973) sets the foundation for the algorithm used to find
system-optimizing multi-class traffic equilibrium where there is only one uniform
time period that all user groups share. Thus, finding user equilibrium where there are
two heterogeneous user groups but only one time period is not a big issue should one
follow Dafermos (1973) and Wardrop’s principle highlighted above. But finding user
equilibrium in congestion pricing regimes where there are two heterogeneous user
groups and two time periods into which users from either group could allocate
themselves is a different story. This dissertation argues that such a scenario involves
an expansion of Wardrop’s principle. This expanded Wardrop’s principle is
substantiated and described below.
3.3 The Expanded Wardrop’s Principle
3.3.1 User equilibrium across time periods
Let there be two equal time periods t
1
and t
2
in a day next to each other and
t
1
=t
2
. DR is a continuous duration and DR=t
1
+t
2
. For DR, two groups of users U1 and
U2 travel on route R. Without losing generality, the length of R is assumed to be 1. To
simplify, users have no preference for t
1
over t
2
and vice versa so long as the
perceived costs in t
1
and t
2
are the same for users. Before tolling, not all users have
full information of the costs and travel times on R on matter if they choose to travel in
t
1
and t
2
. The time-independent fixed costs per unit of length per user are $1 and $2
for U1 and U2, respectively. It is assumed that time costs are the only variable costs

73
that users encounter. Values of time per unit of time per user for U1 and U2 are $1
and $2, respectively. The total numbers of U1 and U2 in DR are n1 and n2,
respectively. To simplify calculations, it is assumed that n1=n2=2. It is also assumed
that U2 travel in bigger vehicles and each U2 user causes exactly twice as much delay
as his or her U1 counterpart. Travel Times (TT) for t
1
and t
2
on R is a linear form like
this following (Arnott et al. 1992):
TT
i
M
=N
i
M
+2*N
i
M
,
where N is the number of users by time period by group,
i=t1 or t2
M=U1 or U2.
Total Costs (TC) per user by group by time then are:
TC
i
U1
=1+ N
i
U1
+2*N
i
U 2

TC
i
U 2
=2+2*(N
i
U1
+2*N
i
U 2
)
At this point, if we assume that N
i
M
≥ 0, there can be five different scenarios of user
allocation. Of these scenarios, only one is stable in terms of providing a no cost
saving incentive for any users to switch between t
1
and t
2
. Table 10, below,
summarizes cost and allocation properties of these scenarios. Since t
1
=t
2
, columns 2
and 3 from the left in Table 10 can actually be switched without changing the
properties of the scenarios.

74

Table 10: Economic Properties of a Simplified Congestion Pricing Program

t
1
or t
2
t
2
or t
1
Total Costs per User ($)
Scenario
Number U1 in t
1

U1 in
t
2

U2 in
t
1

U2 in t
2

Total Costs
for All
Users($)
1
1 U1
user + 0
U2 users
2 U2
users + 1
U1 users
2 6 - 12 32
2
2 U1
user + 0
U2 users
2 U2
users + 0
U1 users
3 - - 10 26
3
1 U1
user + 1
U2 users
1 U2
users + 1
U1 users
4 4 8 8 24
4
1 U2
users +
2 U1
user
1 U2
users + 0
U1 users
5 - 10 6 26
5
2 U2
users +
2 U1
user
0 U2
users + 0
U1 users
7 - 14 - 42

As Table 10 indicates, only Scenario 3 reflects a stable user allocation state, that is,
reaches a user equilibrium that can be explained by an expanded Wardrop’s principle.
In Scenario 3, users from either group in both time periods have no incentive to
switch from one time period to another because they will not be better off
economically in doing so. The other four scenarios always have some users that can
move to another time period and be better off for doing so. Therefore, the user
allocation in these scenarios is not stable or does not reach user equilibrium. In terms
of total costs (which, when being minimized will be the maximum social welfare) for
all users, Scenario 3 is superior to all other four scenarios as well. In other words,
Scenario 3 is also a Pareto optimum, where it is impossible to make one user better
off without making other users worse off. When initial user allocation is not the same
as Scenario 3, it is possible to use exogenous tolls to incentivize users to divert from t
1

to t
2
or vice versa, as is somewhat demonstrated in Shmanske (1991). When the toll
revenue is channeled back to users in an appropriate manner, the users as a whole are

75
equally better off as they are in Scenario 3, while external costs such as congestion are
minimized.
When there are Unobserved Costs of Diversion (UCD) such as schedule delay
costs in t
2
and early arrival costs in t
1
involved, the above equilibrium still applies, but
it is likely that:
N’
2 t
C
< N
2 t
C

(7)
N’
2 t
T
< N
2 t
T

(8)

P
1 t
C
> P’
2 t
C

(9)
P
1 t
T
> P’
2 t
T
(10),
where
P’
2 t
C
and P’
2 t
T
are observed generalized costs per user in t
2,
which exclude UCD,
N’
2 t
C
and N’
2 t
T
are observed numbers of users by group in t
2
. A real-world example of
this equation is when fewer commuters travel in the shoulders of the peak if there are
no tolls on commuters. In terms of travel time costs that can be observed, commuters
in the shoulders are economically better off than those in the peak. In this dissertation,
one could imagine that t
1
is the peak hour and t
2
will be the shoulder hour just before
or after t
1
. In the no-toll scenario, there are more users in t
1
(peak hour) than t
2

(shoulder hours) because:
 Users do not pay for the MEC that they impose on other users and thus there is a
market failure, as highlighted above;

 Not all users have full information of congestion, especially when and where
congestion may happen, thus they often could not choose the right departure time
or the right route that would minimize their overall travel costs;

76
 Many users are required to arrive at their destinations at a time point within t
1
,
traveling in t
2
would prevent them from arriving on time, that is, there are
schedule delay costs for these users if they choose to travel in t
2;

 Even though many users know that traveling in t
2
would save their travel costs,
traveling in t
2
may increase their other costs, for instance, postponed departure
time for home or work schedule changes.
3.3.2 Application of the principle to the cases constructed
In light of the above discussions of UCD, this dissertation assumes that when
members from user group K pay tolls only a certain number of them could switch to
another time and the rest simply reduce vehicle trips by using alternative modes and
rescheduling trips outside t
1
and t
2
. It is assumed that users of alternative modes
would not affect the level of congestion in either t
1
or t
2
. Of course, the trips outside t
1

and t
2
have no impact on the level of congestion in either t
1
or t
2
too. Without loss of
generality, let N
' 1 t
K
be users switching from t
1
to t
2
,

where K has to pay a toll in t
1
to t
2
,
N
' 1 t
K
could be calculated using the following equation:
N
' 1 t
K
= N
1 t
K
* η
K
* θ
t1
- (N
1 t
K
* η
K
* θ
t1
)* θ
t1-t2
* η
K
(11),
where
N
' 1 t
K
equals or is greater than zero. In any cases, for either user group, switching
between t
1
and t
2
is one-way. Both N
' 1 t
K
and the term N
1 t
K
* η
K
* θ
t1
are set to zero where
price inclusive of tolls and UCD that K faces in t
2
is greater than the price that K
originally paid before tolling in t
1
;
N
1 t
K
is the number of K in t
1
where there are no tolls;
η
K
is the toll demand elasticity of K with respective to price changes, which is

77
assumed to be constant over t
1
and t
2
;
θ
t1
is the percentage of price changes in t
1
where tolls are introduced, which takes into
account the demand-cost interdependence between user groups;
θ
t1-t2
is the percentage of price changes that users who switch from t
1
to t
2
would face,
which takes into account demand-cost interdependence between user groups in t
1
and
t
2
, tolls, and UCD that users who switch time periods would face.

In this dissertation, randomness is introduced into the UCD that users who
switch time periods would face. The means of the UCD by user group are calculated
based on no-toll baseline statistics. They are differences of generalized costs by user
group in t
1
and t
2
. It is assumed that the minimum of the UCD by user group will be
zero and that the universes of UCD follow a normal distribution. A computer is used
to generate two the same random UCD for truckers and motorists for each model run.
Given this status, even a same set of tolls could generate different modeling results,
which adds some randomness to the model. This randomness enables the modeler to
have quantitative results that fall into certain ranges but are not a set of fixed values.
The underlying reasoning for equation (12) above is that if there are tolls on K
in t
1
and t
2
, they would have two effects: reducing or increasing the number of K in t
1

and forcing a certain number of K into t
2
, if price inclusive of tolls and UCD that K
faces in t
2
is smaller than the price that K originally paid before tolling in t
1
. The
second term in (12) represents the maximum number of K members who could
potentially switch trips to t
2
, which is adapted from Salas et al. (2008). The third term
in (12) represents the number of K members who are priced out of t1 but are
unwilling to travel in t
2
due to perceived high costs. K members who would not switch
from t
1
to t
2
would choose other alternative modes, cancel, or reschedule trips outside

78
t
1
and t
2
. In this dissertation, the number of these K numbers are jointly determined by
average generalized costs in t
1
prior to tolling, tolls in t
1
and t
2
, revised travel times in
t
1
and t
2
, and UCD that a user who switch time periods would face. A method called
“constrained iteration” would be used to deal with interdependence of variables, if
any. Details about constrained iteration will be given later.
With equation (12) to identify the K members that switch to another time
period, we are ready to calculate N
1
) 1 (
t
K 

and N
1
) 2 (
t
K 
,
the numbers of the K in t
1
and t
2
,
respectively. These equations would work in light of the one-way switching condition
mentioned above:

τ1 and τ2 are tolls on K in t
1
and t
2
, respectively;
N
2 t
K
is the number of K in t
2
when there are no tolls;

N
' 2 t
K

is the number of K in t
2
that switches from t
2
to t
1
, N
' 2 t
K
equals to zero if

N
' 1 t
K

is
greater than zero, per the above one-way user switching condition. Other notations are
the same as above.
In Equations 11 to 13, θ’s are the key to find N’s, numbers of user by group at
new equilibrium after tolling. Estimation of θ’s could be a little complicated. It needs
to consider interdependence between variables of M, T, TT, and D’s as well as the
possible numbers of users who switch from one time period to another. Again, the

N
1 t
K
+ N
1 t
K
* η
K
* θ
t1
+ N
' 2 t
K
, if N 0
' 1

t
K

N
1 t
K
+ N
1 t
K
* η
K
* θ
t1
, if N 0
' 1

t
K

N
1
) 1 (
t
K 
=

(12)
N
1 t
K
+ N
1 t
K
* η
K
* θ
t1
+ N
' 1 t
K
, if N 0
' 2

t
K

N
2 t
K
+ N
2 t
K
* η
K
* θ
t2
, if N 0
' 2

t
K

N
2
) 2 (
t
K 
=

(13),

79
interdependence is accounted for using constrained iteration, which is described next.
3.4 Constrained Iterations
When commuter programs are used to find θ’s (more exactly D’s) by user
group given that user group-specific tolls in t
1
and t
2
are known, the interdependence
among M, T, TT, and D’s causes a problem called “circular references,
1
” which keeps
computer programs running indefinitely. In a mathematical form, the problem of
circular reference in the context of this dissertation can be simplified as:
M=f
1
(T, TT, D)
T=f
2
(M,TT,D)
TT=f
3
(M,T, D)
D=f
4
(M,T, TT).
Each time any single value of M, T, TT, and D changes, it triggers chained changes to
the values of all the others. For instance, if a toll is introduced in t
1
on trucks (T), it
will reduce trucks in t
1
, change the travel times (TT) in t
1
, decrease the inclusive price
(D) that motorists (M) face, and may increase M in t
1
by attracting some motorists
from t
2
. The attraction of motorists to t
1
could change the TT in t
1
, which could start
the chained changes described above again. A modeler needs to put some constraints
on the chained changes so that her or his computer program simulating the changes
can stop rather than running on and on. These constraints allow the modeler to find a
user equilibrium that complies with the expanded Wardrop’s principle described
above. In the context of this dissertation, and in addition to the above chained changes,
the constraints that the modeler considers in relevant computer programs include:
 Members from user groups would choose whichever time period minimizes their

1
More information about this can be found at: http://en.wikipedia.org/wiki/Circular_reference,
accessed August 10, 2009.

80
overall travel costs inclusive of tolls, if any;
 If members from the same user group switch from one time period to another, the
switching would only be one way, that is, from one time period to another but not
vice versa;
 If the number of one user group grows in one time period, the magnitude of
growth should not exceed the maximum number of users in that group that could
potentially switch to this time period;
 In all cases where there are nonnegative tolls, the total number by user group for
t
1
and t
2
combined should not exceed their counterparts in the non-toll scenario.

An algorithm called “constrained iteration” could overcome the chained
changes among variables mentioned above in the computer program developed to
study the representative regime. For instance, in Microsoft Excel 2007, users could
determine which rules in the program deal with cells filled with input variables that
cause circular references. For instance, users can force the program to stop after a
given number of executions or iterations, or when one of the input variables in two
iterations in sequence converge, that is, when the numerical differences between them
are very small, say, 0.01.
2
The above treatment of circular references is called
“constrained iteration.” In this dissertation, a computer program written in Visual
Basic for Applications (VBA) is developed to automatically complete customized
constrained iteration with respect to M, T, TT, and D’s when different levels of tolls
are introduced in t
1
and/or t
2
. At the same time, the logic and statistical functions in
Excel 2007 are used to ensure the other constraints highlighted above are obeyed.

2
For more details, please see: http://office.microsoft.com/en-us/excel/HP100662431033.aspx,
accessed August 10, 2009.

81
The customized constrained iteration could be comparable to the one
described above in travel demand models. In this dissertation, since one deals with
user equilibrium where there are two user groups and user diversions between two
time periods simultaneously; however, the constraints for iterations are different from
those in travel demand models, if one compares the constraints of the former
highlighted above to those in the travel demand model. Furthermore, the customized
constrained iteration in this dissertation has steps that differ from those in the travel
demand model. In Step 1 of the former, for instance, users have already been
“assigned” onto the network. Due to the existence of UCD, however, average costs by
user group in t
1
could be bigger than their counterparts in t
2
. In addition, once tolls are
introduced, Steps 2-4 could reduce or increase numbers of users in t
1
or t
2
, according
to Equations (11) to (13) and the constraints highlighted above. After a certain
number of iterations, results from Steps 2-4 are regarded as revised M, T, TT, and D’s
in t
1
and t
2
at new user equilibrium. In different cases, where different tolls are
introduced in t
1
and t
2
, the VBA computer program developed is used to find the
above revised M, T, TT, and D’s as well as θ’s.
3.5 Numerical Models
To show the usefulness of the above general-form model and to apply it to
answering the questions posed in this dissertation, it is necessary to construct some
policy scenarios and numerical cases that mimic the representative regime, as some
authors have done before (Liu and McDonald 1998; Small and Yan 2001; Verhoef
and Small 2004). These policy scenarios and cases would allow one to quantify and to
assess properties of the representative regime and the impacts of between-user-group
differences on the properties. As mentioned above, this dissertation constructs one
first-best case, one second-best case, and two third-best cases. Table 11, below, recaps

82
these cases, paying special attention to the toll structure and user group exempted.

Table 11: Cases Constructed and Studied

Differentiated
Tolls
User Group Exempted Time Period
Exempted
First-best
Yes No No
Second-best (1)
No No No
Third-best (1)
Yes (in t
1
only) All groups in t
2
Off-peak
Third-best (2)/(3)
Yes
One group
in t
1
and t
2

Peak and Off-peak

In the first-best case, differentiated tolls on user groups are charged in both
time periods. This case assumes that planners and policy analysts have most if not all
important data about user groups and could implement congestion pricing regimes by
taking into account the most important dimensions of user group heterogeneity.
Results of the first-best case are used as baselines for the assessment of all other
cases.
In the second-best case, a non-differentiated toll is charged to two user groups
in both time periods. This case mimics the real-world situation in which people accept
tolls but want the toll structure as simple as possible.
In the third-best case, at least one user group and at least one period are
simultaneously exempted from the tolling. This situation is not uncommon in reality.
For instance, in London congestion pricing case, all users can pass the cordon right
before or right after the designated peak hours without paying any tolls. In addition,
residents living in the charging area and certain vehicles such as ambulances, taxis,
and buses are exempted from tolls, or only pay a discounted toll.
In addition to the above cases, four policy scenarios are constructed under the

83
first-best case to help planners and policy analysts better understand the impacts of
between-user-group differences, that is, user group heterogeneity on design and
evaluation of the representative regime. Specifically, Table 12, below, highlights the
characteristics of the policy scenarios as compared to the first-best case described
above. Potential real-world situations or explanations for each policy scenario are also
presented in Table 12.

84

Table 12: Policy Scenarios Under the First-best Case
Input Parameters by User Group Used Case/Policy Scenario
Cars/Motorists Trucks/Truckers
Real-world
Situation/Explanation
Baseline Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)

Demand Elasticity
(-0.84)
PCE (2.72)
VOT ($19)
People use median or
average values by user
group available when
designing or evaluating
congestion regimes
Policy Scenario 1:
Ignoring
between-group
demand elasticity
differences
Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)

Demand Elasticity
(-0.5)
PCE (2.72)
VOT ($19)

People ignore the
differences in demand
elasticity between user
groups when designing or
evaluating congestion
regimes
Policy Scenario 2:
Ignoring
between-group road
space requirements
Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)
Demand Elasticity
(-0.84)
PCE (1.00)
VOT ($19)

People ignore the
differences in road space
requirement between user
groups when designing or
evaluating congestion
regimes
Policy Scenario 3:
Ignoring
between-group value
of time differences
Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)
Demand Elasticity
(-0.84)
PCE (2.72)
VOT ($10)
People ignore the
differences in VOT
between user groups
when designing or
evaluating congestion
regimes
Policy Scenario 5:
Considering/Ignoring
between-group
commute distance
differences
Demand Elasticity
(-0.38)
PCE (1.00)
VOT ($10)
Demand Elasticity
(-0.64)
PCE (2.72)
VOT ($19)
People ignore the fact
that for different user
groups length of the toll
road could account for a
different percentage of
total length traveled.
Policy Scenario 6:
Ignoring multiple
aspects of
between-group
differences
Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)
Demand Elasticity
(-0.5)
PCE (1.00)
VOT ($10)
People ignore several
aspects of differences
between user groups
when designing or
evaluating congestion
regimes

Together with the results of the four cases, the results of six different policy scenarios
in Table 12 could provide planners and policy analysts with many insights into the
design and evaluation of the representative regime. Details about the network settings,
sources of data, heterogeneity considered, assumptions, and toll structures of these
policy scenarios and cases are described next.

85
3.5.1 Network set-up
All the cases or policy scenarios described above take place on a segment of
I-710. When there is a pricing regime or policy, all or part of southbound vehicles or
users passing a cordon on the I-710 freeway just north of Del Amo Boulevard would
have to pay a toll during the AM or PM peak hours, for instance, 7-8 am or 6-7pm
each day. Vehicles passing the cordon outside the peak hour may or may not pay tolls,
depending on the case or policy scenario characteristics described in Tables 11 and
12.
Choosing I-710 as the charging facility for different policy scenarios and cases
is not random. The freeway has large volumes of heterogeneous traffic and a
peak-load pricing program for trucks called “PierPASS” is already in place. Further,
ongoing research on PierPASS has accumulated and compiled a large amount of
useful data for the dissertation. Details about PierPASS and reasons for choosing
I-710 as the site are as follows.
PierPASS: PierPASS is a peak-load pricing program undertaken by the marine
terminal operators in Los Angeles under public pressure to move container traffic out
of the daytime peak hours through peak-hour tolls (Steimetz et al. 2008). The policy
goal of PierPASS is to reduce truck traffic queues and related emissions on roads
enveloping the ports. The program has at least three features that resemble those of
the representative regime:
 It does not charge all container movements (all users) that impose MEC on others;
that is, not all users are charged;
 It offers an unpriced temporal alternative for container movements in the off-peak
hours;

86
 It treats truckers or trucks as a distinct user group when designing or evaluating
the program.
Heterogeneous traffic: I-710 predominantly serves the Ports of Long Beach and Los
Angeles, the busiest seaport complex in the US. Each day, the complex generates
35,000+ freight trips by a variety of trucks and another 19,000+ commuting trips by
different types of passenger cars on I-710 (Cambridge Systematic Inc. 2009). For
someone wanting to study congestion pricing regimes where there are two user groups,
such as trucks and cars, and the number of trucks is significant, I-710 is definitely one
of the best examples.
Data availability: To study PierPASS, a research team collected and compiled
various data before and after PierPASS implementation. The data collected and
compiled could be easily used for the construction of numerical cases for the
representative regime. As a member of the research team, the author fortunately has
full access to all the data. This access allows the author to quickly assemble necessary
input data for models constructed to study the representative regime.
3.5.2 Sources of baseline traffic data
The California Department of Transportation (Caltrans) has detective traffic
sensors on I-710 near Del Amo. These sensors automatically count and classify the
actual road traffic continuously passing the cordon. The sensors offer traffic data by
volume, by hour, and by vehicle type. In this dissertation, traffic data from Caltrans
on a typical weekday recorded by these sensors are used as baseline traffic volumes.
Details about the data are given in Subsection 3.5.5.

87
3.5.3 User group heterogeneity considered
To introduce user group heterogeneity, that is, between-group differences into
the five cases and four policy scenarios constructed, it is assumed in this dissertation
that there are two distinct user classes/groups: cars (motorists) and trucks (truckers).
To make the best use of the Caltrans traffic data and to simplify the data conversion,
vehicle Classes 1-4 recorded by Caltrans are treated as cars whereas Classes 5 and
above are regarded as trucks. The two user groups are heterogeneous in road space
requirement represented by PCEs, operating cost, commute distance, value of time,
and demand-toll elasticity. In each case unless otherwise stated, total demand for both
user classes/groups and the subtotal demand for either group in a given day are fixed.
Group-specific tolls can be differentiated or non-differentiated (anonymous),
depending on features of the policy scenarios or cases constructed in this dissertation.
Those scenarios or cases are purposively assigned certain features so as to answer
different questions posed in this dissertation.
3.5.4 Costs considered
To simplify the calculation, unless otherwise stated, it is assumed that costs of
time will be the only generalized costs faced by different user groups. In terms of
UCD, this dissertation does not use a fixed number. Instead, it is assumed that UCD
by user group both follow a normal distribution. This distribution has a mean that
equals the group-specific average generalized cost differences in t
1
and t
2
in the
no-toll baseline. In all cases, if a user switches from one time period to another where
there are tolls, she or he only do so when the generalized costs inclusive of UCD in
one time period are lower than or equal to what she or he paid in another time period
before tolling.

88
Here, as in the work of Liu and McDonald (1998), Small and Yan (2001),
Verhoef et al. (1996), and Verhoef and Small (2004), MEC such as environmental
costs, noises, and accidents other than congestion is ignored to simplify model
construction and associated computations.
3.5.5 Hour simulated
All of the cases and policy scenarios constructed simulate traffic allocation in
the most congested peak hour on a weekday and the shoulder hour after or before the
peak hour. The rationale for such a choice is that the potential benefits of a congestion
pricing policy would be optimized where there is extreme congestion in place. In the
mean time, if users do switch trips between two time periods due to tolling, they are
more likely to switch from the peak to the shoulder hours than to any other hours.
Table 13, below, presents the baseline traffic volumes used in the cases or
policy scenarios. The data are adapted from actual traffic data of I-710 recorded by
Caltrans, which classifies vehicles into fifteen classes. To simplify, Caltrans identifies
Classes 1-4 as cars whereas Classes 5-15 are regarded as trucks. This dissertation uses
the same designations. Traffic volumes of the most congested PM hour on a typical
weekday (Tuesday) are chosen as no-toll baseline traffic volumes in t
1
. No-toll
baseline traffic volumes in t
2
equal the hourly averages of all off-peak hours in the
day.

Table 13: No-toll Baseline Traffic Volumes

Time Period Car Volumes* Truck Volumes*
t
1
(5:00-6:00pm) 6,577 781
t
2
(Average of 0-6am and 7-12pm) 1,867 179
* Adapted from May 06, 2002 southbound traffic volume data on I-710 near Del Amo, which are
provided by Caltrans.

89

3.5.6 Initial input parameter values
Ideally, because the model in this dissertation is constructed around
congestion pricing policies on a specific freeway, as many parameter values as
possible are tailored to this freeway or to relevant subjects. It is even better if those
values are assembled in view of the research questions that the model attempts to
address. To acquire such values based on tailored surveys is costly, if not
prohibitively expensive. Emulating existing studies (Liu and McDonald 1998; Small
and Yan 2001; Verhoef and Small 2004), this dissertation borrows input parameter
values for the model from existing studies or surveys. Whenever possible, all values
are chosen from studies with a regional focus on Los Angeles or America. In addition
to existing studies or literature, this dissertation uses localized models to arrive at
input parameter values. For instance, commute distances by the user group in one
policy scenario were calculated using the SCAG 2003 Regional Transportation Model.
The model contains these data:
(a) Origin-destination (OD) data in PCEs by vehicle type in a day for 4,191 traffic
analysis zone (TAZ) in the SCAG region;
(b) The road network for the SCAG region in the TransCAD format;
(c) Centroids for all 4,191 TAZs in the TransCAD format.

Based on data (a), OD PCE flows by vehicle type between the Long Beach
Port TAZ and all other 4190 TAZs were identified. The shortest network distances
between the Long Beach Port TAZ and all other TAZs were calculated with data (b).
With flows and distances between the Long Beach Port and other TAZs known,

90
flow-weighted shortest-path network distances by vehicle type could be found. These
flow-weighted distances are used as Average Commute Distances (ACD) by the user
group for the policy scenario where impacts of ACD by user group are evaluated.
With ACD values, lengths of Links A and B in the model are calculated as:
L
a or b
=ACD
M or T
-L
f

where L
a, b or f
have been specified above.
More details about the input parameter values used in this dissertation are given in
Table 14, below, which describes parameters’ names, notations, raw and adjusted
values, values’ ranges, units of measurement, geographic attributes, and sources.

91

Name/Notation User Group
Unit of
measurement
Raw value
Raw value
time frame
Adjusted
values used
Geography Source(s)
Cars $/mile
0.1376
(1999$)
2007
0.152
( 2003 $)
Greater Los Angeles
Southern California Association of
Governments (SCAG), 2007
Trucks $/mile
1.11
(2003 $)
2003 - The State of Minnesota Levinson et al 2007
Cars - -0.5 2008 (-0.38) Unspecified
Estimated based on NHI,1995 and
Salas et al, 2008
Trucks - -0.5~-1.81 1999 -0.84 Unspecified
Small and Winston, 1999 and Graham
and Glaister, 2002
Cars PCE
1
-- - -
Trucks PCE 2~4.10 1994-2002 2.72 USA
Steimetz at al, 2008 (who summarized
values from other studies)
Cars $/hour
8.9
(1997 $)
2001-2005
10.2
(2003 $)
Greater Los Angeles USDOT 1997
Trucks $/hour
16.5
(1997 $)
1997-2005
19
(2003 $)
Multiple places Same as above
Cars 13.6 - 2003 - Greater Los Angeles
Trucks 15.2 - 2003 - Greater Los Angeles
Hourly Capacity of I-710
Southbound Lanes (K)
- PCEs/hour 5,400 2009 - I-710
Estimated based on I-710's engineering
characteristics and Highway Capacity
Manual 2000
Average Commute
Distance (ACD)
Estimated using the 2003 SCAG
Regional Transportation Model, flow-
weighted distance for all trips to and
from the Port
Average Fixed Costs
(AFC)
Generalized Costs-
Demand Elasticity ( η)
PCE Factor
Value of Time(VoT)
Table 14: Parameters Used in the Model
* Inflation adjustment using the inflation calculator at: http://www.bls.gov/data/inflation_calculator.htm, accessed June 08, 2009.

92

3.5.7 Demand functions
In ideal conditions, constants R’s and S’ in demand functions (3) and (4) are
calibrated with value of time data from the stated preference surveys of local drivers,
as indicated in Verhoef and Small (2004). Given the monetary and time constraints,
such surveys were not conducted for this dissertation. Instead, constants R’s and S’
for the cases constructed were calculated with two functions offered by Verhoef and
Small (2004):
Ri=50+VOTi (12)
Si=0.0434783/(-0.713714+0.705439*VOTi-0.095357*VOTi
2
+0.00468093*VOTi
3
-0.
00079*VOTi
4
) (13)
where VOTi is the average value of time for user group i based on stated preference
surveys.
Parameters in (12) and (13) are based on a stated preference survey of Dutch
drivers and have been calibrated by Verhoef et al. (1997) and Verhoef and Small
(2004). Functions similar to (12) and (13) in the American context were not found
based on a library search by the author as of March 2010. Given that the values of
time of all drivers revealed in most, if not all, stated preference surveys have a
log-normal distribution, it is defendable that one uses (12) and (13) across contexts or
locales, after using median VOT or average VOT matching methods to recalibrate
parameters in (12) and (13).
3
The procedures of these methods are rather
straightforward. For instance, let VOT
d
be VOT of a sample of Dutch drivers and
VOT
a
be VOT of a sample of American drivers. Both VOT
d
and VOT
a
follow

log-normal distribution. Equations (12) and (13) are then two functions calibrated

3
Professors Ken Small and Erik Verhoef recommended and described these methods in their emails to author
dated March 22, 2010 and March 24, 2010, respectively.

93
using VOT
d
. Let’s call these two functions f
1
(VOT
d,
) and f
2
(VOT
d,
), respectively.
Recalibrating parameters in (11) and (12) with the average matching method so that
they could be used in the American context means to find out f
1
(VOT
a,
) and f
2
(VOT
a,
),
given that for any comparable element of VOT
d
and VOT
a
,
VOT
d
/VOT
a
= β=VOT
dm,
/

VOT
am
(14),
where VOT
dm,
and VOT
am
are averages of VOT
d
and VOT
a
, respectively;
β is a constant once VOT
dm,
and VOT
am
are known.
In this dissertation, VOT
dm
equals 9.08 (DFl), which is from Verhoef and Small (2004)
and VOT
am
of equals 11.70 (2003 $), which is adapted from two USDOT’s VOT
values listed in Table 14, weighted by daily car and truck volumes on I-710 listed in
Table 13. That said, β= VOT
d
/VOT
a
=11.7/9.08. With known relationships in (14),
finding out the parameter values in f
1
(VOT
a,
) and f
2
(VOT
a,
) is not difficult. Given
f
1
(VOT
a,
) and f
2
(VOT
a,
) are known, if one assumes R’s and S’ vary by user group but
not time period,
R
M
= f
1
(VOT
aM,
)
S
M
=f
2
(VOT
aM,
)
Rt= f
1
(VOT
aT,
)
St= f
2
(VOT
aT
),
where VOT
aM
and VOT
aT
are the mean values of time for motorists and trucks used
for all cases or policy scenarios constructed in this dissertation, which are presented in
Table 14.
With R’s and S’ known, the demand functions used for motorists and truckers
in this dissertation are now:
D
M
=58-0.01N
M
(15)
D
T
=66-0.007N
T
(16).

94
Evidently, equations (15) and (16) indicate that the demand functions vary by user
group but do not vary by time period.
3.5.8 Generalized-cost-demand elasticity
When applying equations (11)-(13) above to a specific case, one must
calibrate η
K
. Ideally, η
K

are calibrated with data such as average inclusive costs for
K by time period and numbers of K where the above costs vary. In this dissertation,
η
M
=-0.50 and η
T
=-0.84 for most cases unless specifically stated. Those values are
means of demand elasticity values for motorists and truckers identified or
recommended in

existing studies (Graham and Glaister 2002; NHI 1995).

3.5.9 Traffic allocation and generalized costs
With the necessary input parameter values and functions known, one is
prepared to derive traffic allocation, overall social welfare gains, optimal toll(s), and
average generalized costs when there are tolls in t
1
and/or t
2
, using a customized Excel
2007 VBA program or analogue. The underlying rationales or relationships of this
program have already been highlighted above. In this dissertation, a customized Excel
2007 VBA program is developed to derive variables of interest mentioned above.
For each specific case, the Excel 2007 program fulfills three functions. The
first is to generate a matrix of reasonable toll sets like this:
Tn
t
T
t
T
t
1
2
1
1
1
...
...



Tn
t
T
t
T
t
2
2
2
1
2
...
...



Mn
t
M
t
M
t
1
2
1
1
1
...
...



Mn
t
M
t
M
t
2
2
2
1
2
...
...



,

where

95


is a reasonable toll by user group by time period. A reasonable 

meets these
two criteria:
a) It should not produce a negative number of users in a time period, and
b) It should not be negative in value.
Based on these criteria and Equations (11) to (13), this dissertation estimates
that 0  
T
 $15 and for motorists 0  
M
 $11 in t
1
and 0  
T
 $6 and for motorists
0  
M
$4 in t
2
.
Rows 1 to n represent n reasonable sets of  ’s. The maximum of n is manually
assigned for each case. In this dissertation, depending on a case’s set-up, toll structure,
the number of UCD generated, and decimal digits required for the optimal tolls,
maxima of n if different cases vary between 162 and 9,448. But as mentioned above,
to introduce randomness into the model, each individual set of tolls would be
accompanied by different sets of UCD by user group that are randomly generated by
the computer. Therefore, the actual number of runs or iterations of the Excel VBA
program for each case is greater than n and is n*X, where x is the number of UCD
sets assigned to each individual set of tolls. There is no ideal upper limit for X. But to
save computation time, X ranges from 3 to 10 for all cases in this dissertation.
Depending upon the horsepower of the computer used to run the program and the
purpose of the model, one can assign an increase or decrease in the value of X.
The second function of the program is to calculate the overall social welfare
gains for each individual set of ’s following the constrained iteration described
above.

96
The third function of the program is to identify the maximum of the overall
social welfare gains generated by different sets of  ’s and to single out the specific set
of  ’s that generates the maximum.
Once the matrix of reasonable toll sets is generated, user equilibrium for t
1
or
t
2
combined under each individual set of tolls ( 
K
n
) is identified through these
procedures which are automatically implemented by the Excel VBA program
developed:
Procedure 1: Calculate TT
) 0 (
, the initial travel time for all vehicles measured in
PCEs on Link F, using volumes by user group for the no-toll baseline presented in
Table 13. When applying the BPR function, it is assumed that TT
0
for Link F is 11
minutes. Length of Link F (L
f
) uses actual distance between Del Amo and the Port of
Long Beach, which is 11 miles.
For Links A and B, their travel times can be calculated with these equations
when needed in the policy scenario where ACD by user group is considered:
TT
a
= L
a
/AS
M

TT
b
=L
b
/AS
T
where AS’ are group-specific average speeds. In cases where fixed costs other than
the toll segment are considered, it is assumed that AS
M=
AS
T
=32 miles/hour. The AS
values are the average speed in the day reported by the local MPO (SCAG 2008).
Referring to Figure 5 and Table 13, L
b
=ACD
M
-L
f
=2.6 (miles) and L
a
=ACD
T
-L
f
=4.2
(miles).

97
Procedure 2: Calculate AGC’s
) 0 (
, the initial group-specific average generalized costs
on Link F in t
1
and t
2
when there are no tolls, using equation (1), TT
) 0 (
, and
appropriate parameter values highlighted in Table 13.
Procedure 3: Calculate AGC’s
) 1 (
for t
1
and t
2
, the user-group-specific average
generalized costs on Link F where there are tolls:
AGC
K
) 1 (
[t1 or t2]
=AGC
K
) 0 (
[t1 or t2]
+ 
K
n
[t1 or t2]

where
superscript K is used to differentiate different user groups. In all cases or policy
scenarios, there are only two user groups: motorists (M) and truckers (T). Thus, K=M
or T.
Subscripts indicate the number of iteration and time period.
Procedure 4: Calculate N
K
) 1 (
for

t
1
and t
2
, the intermediate volumes by user group
where there are tolls and UCD by user group that are randomly generated by the
computer program, using equation (3) and AGC
K
) 1 (
. N
K
) 1 (

obtained based on
AGC
K
) 1 (
simply would not be the volumes in t
1
or t
2
at user equilibrium unless a
coincidence occurs. As discussed above, because the values of TT, D, AGC, and N’s
are interdependent and would cause circular references, constrained iteration is
needed to overcome the circular references and to find the N
K
at user equilibrium.
Details about the constrained iteration and circular references have been given above.
Procedure 5: Repeat Procedures 1 to 4, ensuring that every iteration satisfies the
constraints highlighted in Subsection 3.4 and that

N
K
m) (
>0 (u1)

98
N
K
m ) 1 ( 
≥0 (u2)
The subscripts m (m ≥2) and m-1 are the number m and m-1 iterations of constrained
iteration, respectively. Inequalities u1 and u2 indicate that there cannot be a negative
number of users traveling in t
1
or t
2
when applying the constrained iteration on a
specific case. In the Excel VBA computer program developed for this dissertation, the
nonnegative nature of N
K
m) (
and

N
K
m ) 1 ( 

are automatically guarded. At the final step,
nonnegative N
K
m) (
’s

are regarded as the group-specific traffic volumes at user
equilibrium in t
1
or t
2
where there are 
K
n
. Correspondingly, D
K
m) (
’s would be the AG
Ｃ’s at user equilibrium in t
1
or

t
2
where there are 
K
n
.
Procedure 6: Calculate overall SW
(m)
for the case when there are N
K
t m 1 ) (
and N
K
t m 2 ) (

users in t
1
and t
2
, respectively, using Equations (5), (15), and (16). Once SW
(m)
for
all n sets of tolls have been calculated for a case, the computer program sorts n sets of
SW
(m)
according to their size of values and

treats SW
Max
m) (
, the maximum of these SW
(m)

as the optimal SW generated by the set of optimal tolls. Consequently, λ
K
O
, the set of
tolls that generate SW
Max
m) (
will be treated as the optimal tolls by user group and/or by
time period that for the case in question. In the case of this dissertation, there would
be three to five SW
(m)
as three to five sets of UCD are used for each individual set of
reasonable tolls. This dissertation also treats the top five SW
(m)
as the maxima and
uses the five SW
(m)
as indices to find other variables such as optimal tolls, user
allocation by time by group, etc.
The running time of the computer program developed to automatically
implement Procedures 1 to 6 above is largely determined by n and X and the

99
horsepower of the computer used to run the program. In this dissertation, the Excel
VBA programs customized for all cases or policy scenarios could be implemented in
36 hours on a Compaq desktop computer with a 2.6G Hz CPU and 4 GB RAM.
Source codes, input data, worksheets containing required formulae, and output data in
digital format for different cases or policy scenarios are available to interested readers
upon request.

100
CHAPTER 4. QUANTITATIVE RESULTS: CASES

Using the data, network set-up, procedures, and computer programs described
in Chapter 3, this dissertation came up with quantitative results about the cases
constructed to disclose the economic properties of the representative regime. These
results allow planners and policy analysts to obtain quite a few insights into the social
welfare, efficiency, and distributional effect characteristics of the regime. These
insights in turn should facilitate the design and evaluation of the representative regime
or congestion pricing programs or proposals that resemble it. This chapter discusses
results and insights of particular relevance to planners and policy analysts interested
in advocating the representative regime as a strategy to increase the efficiency of
roads.

101

No-toll First-best Second-best Third-best (1) Third-best (2) Third-best(3)
Rel. use t1 1 0.29-0.34 0.26-0.31 0.26-0.33 0.84-0.91 0.42
Rel. use t2 1 0.67-1.34 0.72-1.36 1.13-3.16 0.76-1.55 0.63-0.93
Cars in t1 6,577 1,437-1,540 1,294-1,624 1,314-1,701 6,577 1,539
Trucks in t1 781 391-505 355-386 156-690 230-506 781
Cars in t2 1,867 730-1,799 1,357-1,812 1,295-7,007 13,308-1,867 1,014-1,690
Trucks in t2 179 156-568 49-604 269-456 115-660 179
Total PCEs 11,055 4,482-5,847 4,179-5,477 5,221-9,726 8,986-11.055 5,164-5,708
Case PCE ratio as no-toll baseline 1 49-53% 37-49% 47-88% 81-100% 43-53%
Mean VOT motorists ($) 10 10 10 10 10 10
Mean VOT truckers ($) 19 19 19 19 19 19
Motorists' demand elasticity -0.5 -0.5 -0.5 -0.5 -0.5 -0.5
Truckers' demand elasticity -0.84 -0.84 -0.84 -0.84 -0.84 -0.84
Average schedule delay costs for motorists who switch to another time period -
Average schedule delay costs for truckers who switch to another time period -
Travel time in t1 (min) 26.1 14.5-15.0 14.0-14.7 14.0-14.9 22.8-24.4 16.2
Travel time in t2 (min) 14.2 12.7-14.7 12.9-15.4 13.0-22.6 13.8-16.0 12.8-13.9
Toll per truck t1 ($) 0 7-8.6 8.7-9.2 7.8-10.3 6.5-8 0
Toll per truck t2 ($) 0 0 0.25-1 0 0-1 0
Toll per car t1 ($) 0 8.7-8.9 8.6-9.2 8.5-9.1 0 8.5
Toll per car t2 ($) 0 1-2 0.25-1 0 0 1-2.5
Overall toll revenue in t1 and t2 combined ($) 0 16,324-19,193 15,649-18,867 15,514-17,877 2,020-2,316 14,638-16,198
SW per motorist remaining in t1 and t2* N 1.00 0.84-1.02 0.78-0.96 N 0.96-1.08
SW per trucker remaining in t1 and t2* 0.85 1.00 0.93-1.01 0.91-1.06 0.95-1.05 0.80-0.86
SW per user remaining in t1 and t2 N 1.00 0.87-1.01 0.83-0.99 N 0.88-1.02
ω (Rel. efficiency) 0 1 0.96-0.99 0.96-0.99 0.00-0.01 0.90-0.93
Follow a normal distribution, mean=$2.03**, standard deviation=0.66,min=0
Follow a normal distribution, mean=$3.79**, standard deviation=1.24,min=0
Table 15: Quantitative Results about Different Cases Constructed

102

Notes:
*Assuming toll revenue is differentiated by user group and is channeled back to user group which contributes it, “N” stands for a negative value
relative to its first-best counterpart. The maximum values are used for the first-best case when calculating SW per motorist, per trucker, and per
user.
**Estimates based on no-toll baseline statistics.
First-best case: differentiated tolls to all user groups in t1 and t2.
Second-best case: non-differentiated tolls charged to all user groups in both t1 and t2.
Third-best case (1): differentiated tolls to all user groups in t1, the peak hour/period only.
Third-best case (2): Exempt motorists, the dominant user group in both t1 and t2.
Third-best case (3): Exempt truckers, the secondary user group in both t1 and t2.
ω = (welfare gain from case)/(welfare gain from first-best case).
Table 16, Continued.

103

4.1 First-best Toll Is Not a Must
If efficiency is the primary goal of planners and policy analysts, they do not
necessarily need to charge first-best tolls in the representative regime. Based on the
quantitative results presented in Table 15, above, the first-best tolls only achieve 1 to
4% more social welfare gains than their second-best and third-best (1) counterparts
do.
In the context of this dissertation, as mentioned above, the first-best tolls are
differentiated by user group and time period. The second-best tolls are differentiated
by time period but not by user group. The third-best (1) tolls are differentiated by user
group in the peak time period but then they exempt all user groups in the off-peak
time period. The third-best (2) tolls are differentiated by time period for one user
group but totally exempt the other user groups all of the time. From the perspective of
simplifying tolling structure and saving enforcement and implementation costs, the
second-best tolls seem to be superior to first- and third-best tolls. But because the
sizes of the second-best tolls are on average slightly more than their first-best
counterparts, the second-best tolls would price more users off the toll road than their
first-best counterparts would. Thus, if increasing social welfare while keeping as
many users as possible on the toll road is a goal that planners and policy analysts
pursue, first-best tolls rather than second-best tolls are recommended. In one occasion,
first-best tolls could allow 15% more users on the toll road while still achieving
similar and even higher social welfare gains than their second-best counterparts.
If optimizing overall toll revenue is another goal that planners and policy
analysts pursue— besides social welfare gains or economic efficiency, planners and
policy analysts may want to adopt first-best tolls as well. According to the results
shown in Table 15, in one extreme case, the first-best tolls could produce as much as

104
22% more overall toll revenue than their second-best and third-best (1) counterparts.
In another extreme case, the first-best tolls could generate overall revenue at least
equal to the median of its counterpart that the third-best (1) tolls produce.
4.2 User Group Exemption Can Be Made
According to the marginal-cost pricing principle, for congestion pricing
regimes to be optimized, users should pay tolls whenever and wherever their entry
into roads or other congestible facilities impose additional costs on other users (Yang
and Huang 2005). That is, charging user groups or users a toll equal to the MSC they
impose on others produces the highest economic efficiency in congestion pricing.
Based on the results presented in Table 15, this principle still applies to the
representative regime. When first-best (differentiated) tolls are charged, the
representative regime has the biggest ω value. Despite this fact, planners and policy
analysts going for the representative regime as a strategy to increase economic
efficiency of roads are not required to stick to the marginal-cost principle all of the
time. The results of different cases shown in Table 15, for instance, indicate that even
the third-best (1) tolls would still enable planners and policy analysts to achieve the
bulk of the efficiency that the first-best tolls could possibly obtain. In other words,
when implementing the representative regime, planners and policy analysts could still
exempt some— even all— user groups from congestion tolls in the off-peak period
while still expecting a reasonably high ω value. This finding is generally consistent
with the findings of Safirova et al. (2004), who argue that one does not need to charge
all users in all places where there is congestion or to adopt a comprehensive
congestion pricing program in order to achieve the bulk of efficiency of congestion
pricing. Of course, user or user group exemption in the real-world setting is different
from arbitrarily exempting some users or user groups from paying tolls in a theoretic

105
model. The former requires that planners and policy analysts find evidence or grounds
for why some users or user groups receive special treatment. In addition, given that
there are multiple ways to realize user or user group exemptions in congestion pricing,
planners and policy analysts would also have to evaluate the policy implications for
different kinds of exemption. For instance, based on the results presented in Table 15,
planners and policy analysts could either exempt all users in t
2
or only exempt trucks
in t
2
to achieve a similar level of economic efficiency. But evidently, two exemptions
have different policy implications. One exemption tends to be fairer across all users or
user groups whereas the other strongly favors truckers as a user group. Plus, two
different exemptions result in different users remaining on the toll road.
Results in Table 15 also indicate that exempting dominant user groups from
paying tolls would reduce economic efficiency. Specifically, the results of the
third-best (2) case indicate that when the predominant user group is exempted from
tolling, the representative regime may lose most of the economic efficiency that the
first-best tolls could potentially achieve. When costs of implementation and
enforcement are considered in the same case, the regime could even make all user
groups worse off.
4.3 Tradeoff Has to Be Made
Because implementing and enforcing a congestion pricing regime is not free
from costs, planners and policy analysts need to consider the relationships among toll
structure (first-best vs. second-best vs. third-best tolls), toll revenue, and enforcement
and implementation costs. Based on the results presented in Table 15, despite the fact
that different toll structures can achieve similar levels of efficiency, they can also
generate overall toll revenue that varies notably in size. For instance, the second- and
third-best tolls sometimes generate a similar magnitude of overall toll revenue as their

106
first counterparts, but they never achieve the maximum that the latter can achieve.
These results mean that if planner and policy analysts want to optimize economic
efficiency and overall toll revenue at the same time, first-best tolls would be a better
choice. Implementing and enforcing first-best tolls, however, could be more
expensive than implementing and enforcing second- and third-best tolls, given that the
former requires differentiating user groups and/or a longer enforcement period. In
light of the above facts, planners and policy analysts advocating the representative
regime may need to better evaluate tradeoffs between toll structure,
enforcement/implementation costs, and toll revenue when evaluating the regime in a
specific context. Results presented in Table 15 should have provided some useful
information to them.
4.4 Toll Structures and Distributional Effects
Different toll structures can achieve a similar efficiency but have different
distributional impacts on user groups. Results presented in Table 15 indicate that the
third-best tolls (1) and second-best tolls can both achieve the bulk of efficiency that
the first-best tolls achieve. But different user groups, especially the members from
different user groups remaining on the toll road, can expect different levels of social
welfare gains when compared to the first-best case. Assumes that all toll revenue is
channeled back to the user groups who contribute to it; for instance, truckers tend to
achieve a relatively higher percentage of social welfare gains as compared to the
first-best case than motorists in the second- and third-best cases. Motorists, on the
other hand, could never expect a higher level of social welfare gains in the third-best
(1) case as compared to the first-base case.
What Table 15 does not show, however, is that the second-best or third-best
tolls allow one user group to obtain more social welfare gains than the first-best tolls.

107
But this gain always comes at the cost of shrinking the social welfare gains of the
other group in the same cases. In addition to the above tradeoffs, therefore, planners
and policy analysts may also need to consider the balance between toll
structures/contributions, numbers of users by group who are tolled on or off the toll
road, and social welfare gains across user groups.
The results presented in Table 15 indicate that, relatively speaking, the regime
as a whole makes truckers better off whether first-best, second-best, or third-best tolls
are adopted. Given that time values for truckers are on average higher than for
motorists, this finding is broadly consistent with the finding of Niskanen (1987),
which argues that congestion pricing could make the poor worse off. For planners and
policy analysts advocating congestion pricing in general and the representative regime
in particular, thus, appropriately classifying users into groups and comparing their
respective social welfare gains is important. Treating all users as homogeneous would
make it difficult to examine the impact of the representative regime on users who are
actually heterogeneous in value of time, demand elasticity, commute distance,
marginal external costs produced, and road space requirements.
4.5 Consideration of User Group Differences
The common assumptions underlying the findings in 4.1 to 4.4 about the
representative regime are that:
(a) Planners and policy analysts differentiate user groups when designing and
evaluating the regime;
(b) There are sufficient group-specific data such as demand toll elasticity, value of
time, and road space requirement available for planners and policy analysts to
differentiate user groups.
Without assumptions (a) and (b), that is, not considering between-user-group

108
differences could obscure the findings and even refute these findings. In other words,
planners and policy analysts interested in the regime may not be able to design and
evaluate the representative regime well if they choose to ignore certain differences
between user groups. The next chapter of this dissertation will discuss five policy
scenarios under the first-best case, where one or several aspects of
between-user-group differences are ignored, and how the quantitative results of these
scenarios differ from those of the first-best case (baseline) where between-user-group
differences in value of time, demand elasticity, commute distance, and road space
requirement are all accounted for.

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CHAPTER 5. QUANTITATIVE RESULTS: POLICY SCENARIOS
The above results about different cases constructed for the representative
regime can provide planners and policy analysts general knowledge about the regime
where first-, second-, or third-best tolls are adopted. The results, however, do not
show planners and policy analysts what consequences they can expect if they do not
differentiate user groups or if they ignore certain aspect(s) of between-user-group
differences when designing or evaluating the regime. To show these consequences, as
highlighted above, five policy scenarios under the first-best case (baseline) are
constructed. Details of these policy scenarios have been presented in Table 8. In each
policy scenario, it is assumed that planners and policy analysts either totally ignore
between-user-group differences in aspects such as demand elasticity, road space
requirement, and value of time, or ignore one of these differences when designing or
evaluating the representative regime. Using similar computer programs developed for
the cases, this dissertation came up with quantitative results about these five policy
scenarios. Table 16 summarizes some of these results, paying special attention to
levels of tolls, toll revenue, SW per user, SW per motorist, SW per trucker, and Rel.
efficiency of each policy scenario. Based on results presented in Table 16, there are at
least five findings that planners and policy analysts who want to advance the
representative regime may find helpful.

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No-toll First-best Ignore Elasticity Ignore PCE Ignore VOT Ignore ACD Ignore Multiple
Rel. use t1 1 0.29-0.34 0.28-0.31 0.23-0.34 0.27-0.30 0.26-0.33 0.17
Rel. use t2 1 0.67-1.34 0.77-1.12 0.42-1.41 0.49-0.70 0.78-1.23 0.54-0.70
Cars in t1 6,577 1,437-1,540 1,365-1,404 1,264-1,322 1,366-1424 1,464-1,542 1,498
Trucks in t1 781 391-505 391-481 261-607 343-479 286-512 -
Cars in t2 1,867 730-1,799 1,023-1,619 792-1,552 917-1,368 1,106-1,581 1,310-1,650
Trucks in t2 179 156-568 161-550 78-699 94-170 166-657 -
Total PCEs 11,055 4,482-5,847 4,334-5,109 3,707-5,457 3,525-4,347 4,564-5,413 2,778-3,149
Case PCE ratio as no-toll baseline 1 49-53% 39-46% 34-49% 31-39% 41-48% 25-48%
Mean VOT motorists ($) 101010 1010 10 10
Mean VOT truckers ($) 191919 1910 19 19
Motorists' demand elasticity -0.5 -0.5 -0.5 -0.5 -0.5 -0.38 -0.5
Truckers' demand elasticity -0.84 -0.84 -0.5 -0.84 -0.84 -0.64 -0.5
Motorists' commute distance (miles) n/a n/a n/a n/a n/a 13.6 n/a
Truckers' commute distance (miles) n/a n/a n/a n/a n/a 15.2 n/a
PCE per truck 2.72 2.72 2.72 1 2.72 2.72 1
PCE per car 1 1 1 1 1 1 1
Average schedule delay costs for motorists who switch to another time period
Average schedule delay costs for truckers who switch to another time period
Travel time in t1 (min) 26.1 14.5-15.0 14.3-14.7 13.0-13.5 14.2-14.6 14.1-14.7 12.94
Travel time in t2 (min) 14.2 12.7-14.7 13.2-14.1 11.6-13.3 12.3-15.4 13.2-15.6 12.15-13.84
Toll per truck t1 ($) 0 7-8.6 10-12 5-9 4-5 8-12 8
Toll per truck t2 ($) 0 0 0-1 0-1 0-1 1-2 0.5-2
Toll per car t1 ($) 0 8.7-8.9 9 8 9 11 8
Toll per car t2 ($) 0 1-2 1-2 0-3 1-2 1-2 0.5-2
Overall toll revenue in t1 and t2 combined ($) 0 16,324-19,193 18,641-20,172 1,2931-15,819 15,630-16,451 21,890-24,436 12,633-14,548
SW per motorist remaining in t1 and t2* N 1.00 0.89-1.11 0.96-1.12 0.85-1.22 0.82-0.97 0.79-0.93
SW per trucker remaining in t1 and t2* 0.85 1.00 0.94-1.07 0.90-0.97 0.88-0.96 0.95-0.97 0.50-0.59
SW per user remaining in t1 and t2 N 1.00 0.88-1.01 0.95-1.08 0.85-0.97 0.84-0.96 0.68-0.80
ω (Rel. efficiency) 0 1 0.82-0.96 0.89-0.97 0.94-0.95 0.95-0.96 0.63-0.64
Follow a normal distribution, mean=$2.03**, standard deviation=0.66,min=0
Follow a normal distribution, mean=$3.79**, standard deviation=1.24,min=0
Table 16: Quantitative Results of Policy Scenarios

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Notes:
*Assuming that revenue is differentiated by user type and is recycled by user type. The maximum values are used for the first-best case when calculating SW per
motorist, per trucker, and per user.
Ignore Elasticity: Use motorists’ toll demand elasticity as the proxy for truckers’.
Ignore PCE: Use motorists’ average PCE factor as the proxy for truckers’.
Ignore VOT: Use motorists’ average VOT as the proxy for truckers.
Ignore A VD: When designing or evaluating the regime, the modeler does not account for the Average Commute Distance (ACD) by user group, which could
affect demand elasticities by user group. The results of this policy scenario will be used as baseline while results of the first-best case will be the “treatment”
ones, where ACD is not explicitly considered.
Ignore Multiple: Use motorists’ toll-demand elasticity, PCE factor, and VOT as the proxies for truckers’ or simply put: “treat truckers and motorists as identical
users.”
Table 16, Continued.

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5.1 Efficiency Underestimated When User Group Differences Ignored
The results presented in Table 16 indicate that ignoring one or several aspects
of between-user-group differences can lead to underestimating the efficiency of the
representative regime. For instance, when the motorists’ demand elasticity value is
used as proxy for that of truckers, the efficiency of the representative regime can be
underestimated as much as 18%. When truckers are treated as identical to motorists in
terms of VOT, demand elasticity, and PCE, the efficiency of the representative regime
can be underestimated as much as 37%. Despite these underestimations, the results
across different policy scenarios never refute that the regime would increase social
welfare as compared to the no-toll baseline— as long as first-best tolls are charged.
This fact could be good news for planners and policy analysts who advocate the
representative regime. Given the characteristics of different policy scenarios, however,
planners and policy analysts should still be cautious about the scope of validity of the
information. The news is valid only when planners and policy analysts use reasonably
accurate data such as value of time, demand elasticity, and road space requirement
about motorists, the dominant user group, when designing or evaluating the regime. If
data about motorists are inaccurate and are used as proxy for those about truckers, the
secondary user group, the news may be invalid— that is, the economic efficiency of
the representative regime would be so significantly underestimated that the regime
would be regarded inefficient or not worthwhile.
5.2 Demand Elasticity and the Representative Regime
In the “Ignore Elasticity” policy scenario, it is assumed that designers or
evaluators of the representative regime ignore the fact that truckers may be more
sensitive to price changes than motorists and simply use motorists’ price demand
elasticity as proxy for that of truckers. In this scenario, in addition to an

113
underestimation of economic efficiency by a factor of 18%, planners and policy
analysts can expect biased estimations of first-best tolls, SW, and overall toll revenue.
Compared to the first-best case results, this policy scenario could overestimate the
first-best toll in t
1
for truckers by 42%, in the worse case. This policy scenario could
also overestimate overall toll revenue by 25%, or underestimate social welfare gains
for truckers and motorists by 11% and 6%, respectively. Based on the above, planners
and policy analysts responsible for designing or evaluating the representative regime
may have notable biases if they choose to ignore differences in demand elasticity
between user groups. They could either be a little pessimistic about the benefits that
the regime would bring to motorists and to truckers or be a little overoptimistic about
the overall toll revenue the regime would generate. The former attitude may not be
detrimental to the feasibility of the representative regime, however, the latter may be.
In cases where a large portion of overall toll revenue has to be used to offset the costs
of implementing and enforcing the representative regime, the planners and policy
analysts may have trouble if they were too optimistic about the overall revenue
produced by the regime while actual toll revenue generated by the regime is lower
than forecasted.
5.3 User Group Differences that Could Be Ignored
If planners and policy analysts have to ignore certain aspects of between-user-
group differences to save time and costs when designing or evaluating the
representative regime, road space requirement differences may be the one issue to
ignore. In the “Ignore PCE” policy scenario, planners and policy analysts overlook the
fact that truckers (one user group) are in bigger vehicles than motorists (the other user
group) and thus consume more road spaces when traveling. Therefore, they simply
assign one PCE factor, that is, the PCE factor of motorists to all user groups when

114
designing and evaluating the representative regime. Not surprisingly, then, the
“Ignore PCE” leads to various biases in the indicators about the regime, for instance,
underestimations in the overall toll revenue generated and the SW per truckers. What
is a little surprising, however, is that “Ignore PCE” still provides reasonably accurate
estimations for most indicators about the regime. This fact indicates that if planners
and policy analysts have to skip some data when designing or evaluating the
representative regime, they could probably skip data about PCE factors across user
groups.
Given the randomness in UCD across user groups, assigning one PCE factor
to different user groups may consistently lead to underestimating the overall toll
revenue that the first tolls can possibly produce. But this underestimation probably
does no harm because planners and policy analysts may be a little more conservative
when they expect a smaller amount of toll revenue from the regime than the revenue
the regime could possibly generate. More toll revenue being generated would be a
“windfall” for them.
5.4 Value of Time and the Representative Regime
In the “Ignore VOT” policy scenario, it is assumed that planners and policy
analysts neglect the fact that truckers may have a higher value of time than motorists
and designate the value of time of motorists as equal to that of truckers when
designing and evaluating the representative regime. Doing so could cause several
issues. The first notable issue is an underestimation in the economic efficiency of the
regime, which may not be surprising. One underlying purpose of congestion pricing is
to allow users or user groups who value their time the most to be priced onto roads at
peak hours and to divert users or user groups who value their time least to times,
routes, or mode of travel where there is less demand. When the value of time of one

115
user group is underestimated, all other things being equal, the economic efficiency of
the representative regime can decrease, as the average value of time of users who are
priced onto the roads decreases and so do their social welfare gains due to reduced
congestion.
The second notable issue is the underestimation in first-best tolls for truckers.
In the worse case, “Ignore VOT” could cause an underestimation in the toll by 115%.
This underestimation means that planners and policy analysts should be aware that
they could significantly underestimate the tolls for user groups with a higher value of
time if they treat all users groups identically in terms of value of time in the
representative regime. Such underestimated tolls, if adopted, could consistently
reduce the efficiency of the representative regime. For instance, if the optimal toll sets
identified in the “Ignore VOT” policy scenario are applied to the first-best case, the
toll sets could at most achieve 92% of the social welfare gains that first-best tolls can
potentially achieve. This finding is generally consistent with that of Small and Yan
(2001), who found that ignoring user heterogeneity in value of time could lead to
underestimations of the economic efficiency of congestion pricing regimes.
The third issue is underestimating the overall toll revenue that the regime
could generate, which may not be an issue if the costs of implementing and enforcing
the regime are extremely low. But if the costs are high and have to be covered by a
large portion of the toll revenue, then planners and policy analysts who propose the
regime would have abandoned— a proposal that could potentially generate more toll
revenue than forecasted.
The fourth issue is underestimating the benefits that the regime would bring to
truckers and all users. In the “Ignore VOT” policy scenario, truckers as a user group
and all users as a whole would see a reduction in social welfare gain as compared to

116
the first-best case. In two worse cases, the SW per trucker and the SW per user could
be underestimated by 12% and 16% in the policy scenario, respectively.
5.5 Commute Distance and the Representative Regime
In the “Ignore ACD” policy scenario, it is assumed that planners and policy
analysts going for the representative regime simply explicitly account for the
differences in commute distance between different user groups. Per the formula (F0)
in Subsection 3.1, considering the differences could change the demand elasticity by
user group. Thus, the results of the “Ignore ACD” policy scenario could be different
from those of the first-best case, where demand elasticity values by user group are
generic and which do not explicitly account for commute distance differences
between user groups. The differences between the former and the latter could be used
to explore how ignoring commute distance differences between user groups
influences the evaluation and design of the representative regime. Three general
points could be made here about the “Ignore ACD” policy scenario:
Firstly, the scenario tends to increase the size of the estimated optimal tolls.
Compared to the first-best case tolls, the scenario’s trucker toll and the motorist toll in
t
1
could increase as much as 30% and 26%, respectively. The increased tolls mean
that planners and policy analysts who are responsible for designing the representative
regime could have very biased optimal tolls if they ignore the differences in commute
distance by user group. Such biased tolls, when implemented, could notably reduce
the economic efficiency of the regime. Plugging one set of estimated optimal tolls into
the first-best case model, for instance, only generates a ω value between 0.61 and
0.71.
Secondly, the scenario would notably overestimate the overall toll revenue
that the representative regime could generate. Compared to its counterpart in the

117
first-best case, the scenario’s estimated overall toll revenue increases at least 14%. An
overestimated toll revenue can be good or bad for the planners and policy analysts
who are responsible for designing the regime, depending on whether the first-best
case or the scenario represents the baseline that resembles the reality. In other words,
ignoring commute distance differences between user groups could cause
overestimation or underestimation in overall toll revenue. Overestimating revenue
may make it easy for planners and policy analysts to sell their proposed congestion
pricing regime, whereas underestimating revenue could endanger the same regime.
Thirdly, the scenario would notably underestimate the benefits that the
representative regime would bring to different user groups. Depending on whether the
first-best case or the scenario represents the baseline that resembles the reality, again,
biased estimated benefits by user group in the representative regime could be good or
bad. Again, overestimating user group benefits may make it easy for planners and
policy analysts to advocate their proposed congestion pricing regime, whereas
underestimating that the benefits could endanger the same regime.
5.6 Totally Ignoring User Group Differences Lead to Many Biases
In the “Ignore Multiple” policy scenario, it is assumed that planners and policy
analysts going for the representative regime simply treat all user groups identically in
terms of their value of time, toll-demand elasticity, commute distance, and road space
requirement when designing or evaluating the regime. Treating all user groups
identically produces biased estimations in all indicators that planners and policy
analysts would like to have about the representative regime.
First, compared to the baseline (the first-best case), the “Ignore Multiple”
policy scenario may underestimate the economic efficiency of the regime as much as
37%. Because in the first-best case the differences between user groups are

118
purposively set to the medians found in existing studies, the magnitude of
underestimation above is thus relatively conservative. In extreme cases where there
are huge differences between user groups in terms of value of time, toll-demand
elasticity, commute distance, and road space requirement the above magnitude could
be even bigger.
Second, the “Ignore Multiple” policy scenario underestimates the economic
benefits that the regime may bring to all users and different user groups as compared
to the first-best case. In one extreme, the SW per trucker in the scenario would be
underestimated by 50%. In the other extreme, the SW per user sees a 32% reduction.
Between these two extremes, the SW per motorist could be underestimated as much
as 31%. All of the above underestimations could be detrimental to planners and policy
analysts’ advocacy of the regime, as presenting such underestimated values would
reduce the regime’s popularity among different user groups.
Third, the “Ignore Multiple” policy scenario underestimates the overall toll
revenue, which may not be too bad assuming that planners and policy analysts’ goal is
only to forecast potential toll revenue of the representative regime for the tolling
authority. But the underestimation could also put any proposed regime at risk,
especially when the tolling authority has a plan to use a large portion of the expected
toll revenue to cover the costs of implementing the regime or to compensate user
groups that are priced off the toll road. If that is the case, planners and policy analysts
may have a hard time selling relevant policy proposal to the tolling authority.

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CHAPTER 6. CONCLUSIONS AND FUTURE DIRECTIONS

Pricing in general and congestion pricing in particular has become an increasingly
popular strategy to optimize the economic efficiency of congestible facilities such as
roads. Such efficiency has long been of great interest to planners and policy analysts. In
designing or evaluating congestion pricing, planners and policy analysts often— if not
always— encounter these recurrent subjects or topics: heterogeneous user groups,
unpriced alternatives, and policy constraints. A congestion pricing regime that has all
these subjects present is called “the representative regime.” In the context of this
dissertation, the representative regime has an unpriced time period and heterogeneous
user groups and faces certain policy constraints. The study of the representative regime
can provide many useful insights for planners and policy analysts interested in advocating
or implementing a congestion pricing regime. This dissertation reviews existing literature
related to the representative regime, develops a model of general form for the regime,
devises numerical cases about the regime, and examines the economic properties of the
regime based on the case findings.
This dissertation finds that the representative regime has not been well studied in
existing literature. This dissertation argues that insights into the regime have much
relevance to planners and policy analysts who are interested in congestion pricing. This
dissertation poses four research and policy questions about the regime, which cover the
optimal toll, social welfare, relative efficiency, and distributional effect characteristics of
the regime. Answers to these questions offer planners and policy analysts quite a few
insights, which may help them better design or evaluate a congestion pricing regime in a
real-world setting. Some of the most notable insights or findings from this dissertation are

120
summarized as follows:

 User Differentiation and Congestion Pricing
For policy analysts and planners interested in congestion pricing, it may be
tempting and truly convenient to treat all users as homogeneous when designing or
evaluating a congestion pricing proposal. The results of the cases and policy scenarios
developed for this dissertation, however, indicate that treating users as homogeneous
could cause notably biased estimations about the economic properties of the proposal.
For instance, when all truckers are treated to the same as motorists in terms of value of
time, demand elasticity, and road space requirement, the economic efficiency of the
representative regime could be underestimated as much as 37% when the first-best tolls
are charged. This indicates that not differentiating users could pose a political risk to a
congestion pricing proposal. But results of different cases developed for this dissertation
show that there is no panacea for differentiating users in a congestion pricing regime.
Nevertheless, given the differences between truckers and motorists identified in this
dissertation (see Subsection 2.4), it is probably worthwhile as least to classify users into
two user groups, truckers and motorists, and to focus on user group differences in value
of time, demand elasticity, commute distance, and road space requirement (PCE).
 Toll Structure and Congestion Pricing
Based on the results of the cases constructed for this dissertation, the economic
efficiencies of congestion pricing are relatively stable no matter whether the first-,
second-, or third-best tolls are charged, so long as users are categorized into appropriate
groups and reasonable group-specific data are used in relevant models. The results of

121
different cases constructed for the dissertation show that the second- and third-best tolls
could achieve 96% to 99% of the economic efficiency that their first-best counterparts
could. This finding means that planners and policy analysts advocating the representative
regime probably do not need to worry about the toll structure issue. But one caveat for
planners and policy analysts is that the above finding assumes that when deriving the
optimal tolls, planners and policy analysts reasonably classify users into different groups
and employ best available group-specific data such as value of time, demand elasticity,
and PCE in relevant models, as this dissertation does. Again, planners and policy analysts
interested in congestion pricing in general and the representative regime in particular
probably cannot avoid the issue of user differentiation.
 User Group Difference and Congestion Pricing
The results of the five policy scenarios constructed for this dissertation indicate
that ignoring user group differences in value of time, demand elasticity, road space
requirement, and commute distance all cause biases in the estimated indicator values of
the representative regime. Using the motorists’ demand elasticity value as a proxy for the
truckers’, for instance, may mean underestimating the economic efficiency of the regime
as much as 18% and overestimating the optimal toll for motorists in t
1
as much as 71%.
Assigning the value of time of motorists to truckers could mean underestimating the SW
per user as much as 15%.
 Unpriced Alternative, Policy Constraint, and Congestion Pricing
The results of the cases constructed for this dissertation indicate that offering
unpriced alternatives and/or meeting certain policy constraints does reduce the economic
efficiency of the representative regime; but the reduction does not necessarily remove

122
most of the optimal value of the regime. For instance, one could exempt all truckers from
paying tolls in t
1
and t
2
and still achieving 90-93% of the maximum social welfare gains
that the first-best tolls could obtain. One could also charge the second-best tolls and still
achieving 96-99% of the of the maximum social welfare gains that the first-best tolls
could obtain. But such gains have a common premise: Users are categorized into
appropriate groups and reasonable group-specific parameters are used when deriving
optimal tolls, whether they are first-, second-, or third-best. Of course, the above social
welfare gains also ignore the fact that different numbers of users by group could be
priced off or on the toll road in question when different toll structures are adopted. In the
third-best (3) case which exempt all truckers from paying tolls in t
1
and t
2
, for instance,
the numbers of truckers in t
1
and t
2
both would not change before and after tolling. In
other words, the social welfare gains obtained in the case could be completely attributed
to the fact that a large number of motorists is removed from t
1
and t
2
. In the second-best
case, more users tend to be priced off road than the first-best case. Results of different
cases in this dissertation allow planners and policy analysts to know better who would be
priced off and on and the quantity of the priced off and on where first-, second-, and
third-best tolls are charged, respectively. These results could be of special interest to
planners and policy analysts who care about the distributional effects of the
representative regime, as they present to planners and policy analysts a holistic and
segmented picture of who benefits and who suffers in the regime.
Despite the above insights and findings, this study can still be improved in several
directions. These improvements are related to the limitations of the numerical approach
developed and employed, assumptions made in the cases and policy scenarios

123
constructed, the data used to construct these cases and policy scenarios, and the network
set-up for these cases and policy scenarios.
 Limitations of the Numerical Approach
The numerical approach developed in this dissertation gives planners and policy
analysts to have an easy-to-use tool to explore the economic properties of the
representative regime. But unlike the mathematic derivation method, this tool only
discloses the possible direction and magnitude of the relationships among indicators
characterizing the representative regime such as economic efficiency, optimal toll,
demand elasticity, value of time, and road space requirements. It does not provide
irrefutable proof of these relationships. The mathematic derivation method can put all
indicators into equations, which enables one to make positive statements about
relationships among indicators. As mentioned above, applying the method to the cases
and policy constructed in this dissertation requires advanced economic knowledge and
mathematical skills.
 Assumptions Made
To simplify model calculations, this dissertation made assumptions in the cases and
policy scenarios constructed. Some of these assumptions may unrealistic. Thus one has to
a little be cautious with findings or conclusions from the cases and policy scenario. The
unrealistic assumptions made in this dissertation that could possibly be explored in future
research efforts include: travel time is the primary cost that users experience and care
most about, the costs of implementing the congestion pricing is free, and users switching
from time period A to time period B cannot exceed the maximum number of users
removed from A.

124
 Data Used
To parameterize the model of the general form, this dissertation used a lot of data
from various sources. Much of this data, with the exception of the traffic and commute
distance data, was derived from secondary sources, which means that more first-hand or
customized data could be used in the future. Such data should increase the usefulness and
applicability of the model developed. One possibility is to collect more first-hand data
about PierPASS and to develop an individualized model for the program. Using the data
and the model based on them, one may be able to conduct an in-depth case study of the
representative regime and be able to gain more insight into the regime in the real-world
setting.
 Network Set-up
For all cases and policy scenarios constructed in this dissertation, the network where
the cases and policy scenarios occur are at most a network with three links and three
nodes. Such a simple network could restrict the transferability of the conclusions made
about those cases and scenarios. That is, the conclusions may not work when the network
becomes more complex. In the future, the cases and scenarios may be expanded to a
general network, which would greatly increase the transferability of the conclusions
about the representative regimes based on the cases and policy scenarios.

125

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Abstract (if available)

Abstract Congestion pricing has received increased attention from planners and policy analysts as a cost-effective strategy to optimize the economic efficiency of congestible facilities like roads. In the real-world setting, the implementation of congestion pricing often involves heterogeneous user groups, unpriced alternatives for some users or user groups, and/or policy constraints such as the toll revenue collected must be at least equal to the costs of implementation. This dissertation focuses on a representative category of congestion pricing regimes (called “the representative regime” in the text) that has an unpriced time period, heterogeneous user groups, and/or has to meet certain policy constraints. Internet-based search and a literature review indicate that the representative regime has not been well studied

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Asset Metadata

Creator Zhou, Jiangping (author)

Core Title Congestion pricing with an unpriced time period and with heterogeneous user groups

School School of Policy, Planning, and Development

Degree Doctor of Philosophy

Degree Program Policy, Planning, and Development

Publication Date 08/06/2010

Defense Date 03/05/2010

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

Tag congestion pricing,efficiency,heterogeneity,OAI-PMH Harvest,unpriced alternative,user group

Place Name USA (countries)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Giuliano, Genevieve (committee chair), Moore, James Elliott, II (committee member), Schweitzer, Lisa (committee member)

Creator Email jiangpiz@usc.edu,zhoujp@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3333

Unique identifier UC1472973

Identifier etd-Zhou-3547 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-377723 (legacy record id),usctheses-m3333 (legacy record id)

Legacy Identifier etd-Zhou-3547.pdf

Dmrecord 377723

Document Type Dissertation

Rights Zhou, Jiangping

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu