ACKNOWLEDGEMENT:
First and foremost, I thank my advisor Dr. Fan for her constant support and
encouragement throughout my stay in Davis. The past two years of my Master’s study
under her guidance have been a wonderful learning experience. I sincerely appreciate her
providing a deadline- free working environment driven by interest rather than by pressure,
and her readiness to meet with and discuss issues not limited to my research alone at all
the times.
I would like to thank Dr. Mokhtarian for her advice and for her meticulous reviews of my
thesis. It was a gratifying experience for me to get such a detailed feedback and her
attention to detail will always inspire me to seek higher quality in my works. I would also
like to thank Dr. Zhang for his valuable time in reviewing this thesis.
I would also like to express my gratitude to my friends – Dina, JK, Shailendra, Siva and
Venkat for their thoroughly enjoyable company in a new country. I also thank my lab
mates – Changzheng, Hang, Steven and Yongxi for all their help academically as well as
personally.
Finally, I can never thank my parents and brother Sundeep enough for their unstinting
support. None of this work would have been possible without their understanding and
constant motivation.
i
ABSTRACT:
A methodology for evaluating and quantifying the benefits/ costs of converting a given
High Occupancy Vehicle ( HOV) lane into a High Occupancy/ Toll ( HOT) lane is
presented in this study. A mathematical programming model that seeks the optimal
pricing strategy, using a logit- like choice model embedded as constraints, forms the core
of the methodology. A salient feature of this study is the incorporation of equity into the
planning process by imposing constraints thus enabling planners to limit the inequities in
vertical as well as temporal dimensions. A HOV lane on a corridor on I- 80 in the San
Francisco Bay Area was studied for conversion under different objectives – revenue
maximization, total vehicular travel time minimization, total passenger time
minimization, total cost minimization and minimization of total vehicle miles traveled. It
was found that converting the HOV lane into a HOT lane would improve the objective
function in all programs except for total cost minimization. It was also found that the
capital and operating costs can be recovered in a reasonable amount of time ( three- five
yrs). The analysis revealed that there can be significant differences in the pricing
strategies across different objective functions. The variation in the system performance
measures across different programs was also studied and it was found that revenue was
the most sensitive performance measure. The results of all the programs revealed that
there is an inverse relationship between equity and efficiency, with the exact nature of
this relationship being a function of the objective. Furthermore, in situations where there
is no redistribution of revenues, the vertical equity situation cannot be improved even
though all the user groups can be made better off after the conversion.
ii
Additionally, Dynamic Programming models were constructed to solve for the optimal
sequence/ schedule of converting a given set of HOV lanes into HOT lanes. The optimal
sequences here minimized the total conversion time for a self- sustaining/ self- financing
sequence or minimized the total funding needed to complete all the conversions by a
certain deadline.
iii
TABLE OF CONTENTS
1. INTRODUCTION…………………………………………………………………….. 1
2. LITERATURE REVIEW……………………………………………………………... 5
2.1 High Occupancy Vehicle Lanes…………………………………………………. 7
2.2 Congestion Pricing……………………………………………………………….. 9
2.3 High Occupancy/ Toll Lanes……………………………………………………. 12
2.4 Chapter Summary……………………………………………………………….. 20
3. MODELING METHODOLOGY…………………………………………………….. 21
3.1 Objective functions……………………………………………………………… 22
3.2 Constraints on Lane Travel Times………………………………………………. 24
3.3 Constraints Describing the Behavior Model…………………………………….. 25
3.3.1 Estimation of Scaling Coefficient ( β) and Operating Costs ( OC) ……….. 31
3.3.2 Additional Notes on the Behavior Model…………………………………. 32
3.4 Equity related constraints……………………………………………………….. 33
3.5 Constraints on tolls……………………………………………………………… 37
3.7 Determining the Impact of Conversion on Emissions…………………………... 38
3.8 Chapter Summary……………………………………………………………….. 40
4. CASE STUDY………………………………………………………………………... 42
4.1 Estimation of Choice Model……………………………………………………. 44
4.2 Revenue Maximization…………………………………………………………. 46
iv
4.2.1 Impact on Performance Measures………………………………………… 47
4.2.2 Users of Managed Lanes………………………………………………….. 49
4.2.3 User Equity Analysis……………………………………………………… 51
4.2.3.1 Travel Cost Equity…………………………………………………... 52
4.2.3.2 Travel Time Equity…......................................................................... 60
4.3 Minimization of Total Vehicular Travel Time………………………………….. 61
4.3.1 Impact on Performance Measures…………………………………………. 62
4.3.2 Users of Managed Lanes…………………………………………………... 64
4.3.3 User Equity Analysis……………………………………………………… 65
4.3.3.1 Travel Cost Equity…………………………………………………... 66
4.3.3.2 Travel Time Equity………………………………………………….. 69
4.4 Minimization of Total Passenger Time………………………………………….. 70
4.4.1 Impact on Performance Measures…………………………………………. 70
4.4.2 Users of Managed Lanes…………………………………………………... 72
4.4.3 User Equity Analysis……………………………………………………… 73
4.4.3.1 Travel Cost Equity…………………………………………………... 73
4.4.3.2 Travel Time Equity………………………………………………….. 75
4.5 Minimization of Total User Cost………………………………………………... 76
4.6 Minimization of Total Number of Vehicles……………………………………... 77
4.7 Discussion……………………………………………………………………….. 77
4.7.1 Pricing Strategies……………………………………………………… 77
4.7.2 Impact on Performance Measures……………………………………... 78
4.7.3 Impact on Number of Vehicles………………………………………... 79
v
4.7.4 Impact on Travel Times and Volumes………………………………… 80
4.7.5 Impact on Emissions…………………………………………………... 81
4.7.6 Impact on Managed Lane Use Propensities…………………………… 82
4.7.7 Temporal Equity………………………………………………………. 83
4.7.8 Vertical Equity………………………………………………………… 84
4.7.9 Other Equity- related Comments………………………………………. 84
4.8 Chapter Summary……………………………………………………………….. 89
5. OPTIMAL SEQUENCING OF HOT LANE PROJECTS…………………………… 90
5.1 Total Conversion Time Minimization…………………………………………... 93
5.1.1 Additional Comments……………………………………………………. 100
5.2 Minimization of External Funding…………………………………………….. 101
5.3 Chapter Summary……………………………………………………………… 103
6. CONCLUSION…………………………………………………………………….... 104
REFERENCES………………………………………………………………………… 110
APPENDICES………………………………………………………………………..... 116
Appendix A: AMPL code……………………………………………………………… 116
Appendix B: MATLAB codes implementing DP models……………………………... 132
vi
LIST OF FIGURES:
Figure 2.1: Number of Vehicles Needed to Carry 45 People…………………………… 7
Figure 3.1 Income Distribution ( 2006) curve in Bay Area……………………………... 25
Figure 3.1( a) Plot of Speed Vs NOX Emission Factor………………………………….. 39
Figure 3.1( b) Plot of Speed Vs CO Emission Factor…………………………………… 39
Figure 3.1( c) Plot of Speed Vs VOC Emission Factor…………………………………. 39
Figure 4.1: Extent and location of study corridor………………………………………. 42
Figure 4.2: Relationship between Temporal Equity and Revenue………………...…… 53
Figure 4.3: Relationship between Vertical Equity and Revenue………………………... 55
Figure 4.4: Relationship between Temporal Equity and TVT………………………….. 67
Figure 4.5: Relationship between Vertical Equity and TVT……………………………. 68
Figure 5.1: Existing and Funded HOV Network in Bay Area…………………………... 91
Figure 5.2: Optimal schedules with differing initial projects…………………………… 96
Figure 5.3: Alternative Optimal schedule with project II undertaken first…………...… 97
vii
LIST OF TABLES:
Table 2.1: Details of currently operational HOT facilities in the US…………………… 13
Table 3.1: Distribution and Value of Time for different trip types……………………... 26
Table 3.2: Carpool formation costs’ distribution……………………………………….. 27
Table 3.3: Details of alternatives and costs after conversion…………………………… 30
Table 3.4: Details of alternatives and costs before conversion…………………………. 32
Table 4.1: Comparison of performance measures under revenue maximization……….. 47
Table 4.2: Comparison of modal shares before and after conversion…………………... 48
Table 4.3: Comparison of Emissions before and after the conversion………………….. 49
Table 4.4: Comparison of managed lane use propensity by income groups……………. 50
Table 4.5: Comparison of managed lane use propensity by trip types and by carpool
formation times………………………………………………………………………….. 51
Table 4.6: Average travel costs of users in each income group before and after
conversion……………………………………………………………………………….. 52
Table 4.7: Average travel costs of users in each income group before and after
conversion……………………………………………………………………………….. 55
Table 4.8: Money to be paid to users in each group in order to ensure perfect vertical
equity…………………………………………………………………………………….. 57
Table 4.9: Deficit in revenue that would be needed to ensure perfect vertical equity
( Perfect redistribution case).…………………………………………………………….. 58
Table 4.10: Deficit in revenue that would be needed to ensure perfect vertical equity
( Imperfect redistribution case – 40% efficiency of redistribution) ……………………... 59
Table 4.11: Average travel times of users in each income group before and after
conversion……………………………………………………………………………….. 60
Table 4.12: Comparison of performance measures under TVT minimization………….. 62
Table 4.13: Comparison of modal shares before and after conversion…………………. 63
Table 4.14: Comparison of Emissions before and after the conversion………………… 64
Table 4.15: Comparison of managed lane use propensity by income groups…………... 64
Table 4.16: Comparison of managed lane use propensity by trip types and by carpool
formation costs…………………………………………………………………………... 65
viii
Table 4.17: Average travel costs of users in each income group before and after
conversion……………………………………………………………………………….. 66
Table 4.18: Average travel costs of users in each income group after conversion…….. 68
Table 4.19: Average travel times of users in each income group before and after
conversion……………………………………………………………………………….. 69
Table 4.20: Comparison of performance measures under TPT minimization…………... 71
Table 4.21: Comparison of modal shares before and after conversion………………….. 71
Table 4.22: Comparison of Emissions before and after the conversion………………… 72
Table 4.23: Comparison of managed lane use propensity by income groups…………... 72
Table 4.24: Comparison of managed lane use propensity by trip types and by carpool
formation costs………………………………………………………………………….. 73
Table 4.25: Average travel costs of users in each income group before and after
conversion……………………………………………………………………………….. 74
Table 4.26: Average travel costs of users in each income group after conversion…….. 74
Table 4.27: Average travel times of users in each income group before and after
conversion……………………………………………………………………………….. 75
Table 4.28: Deviation in performance measures from their optimal values across
programs………………………………………………………………………………… 78
Table 4.29: Variation in mode shares across programs…………………………………. 79
Table 4.30: Variation in travel times and volumes on lanes across programs………….. 80
Table 4.31: Comparison of managed lane use propensity by income groups across
programs………………………………………………………………………………… 82
Table 4.32: Comparison of average travel costs of by income groups across programs... 83
Table 4.33: Loss in efficiency due to imposition of temporal equity across programs…. 83
Table 5.1: Details of the five corridors chosen for HOT implementation………………. 92
Table 5.2: Variation in the total conversion time with increasing spatial equity……….. 98
ix
1. INTRODUCTION
A number of demand management strategies are being considered to counter the rapid
growth in transportation related problems such as traffic congestion, air quality and
increasing operating costs. One of the most recent of these strategies directed towards
congestion alleviation is the implementation of High Occupancy/ Toll ( HOT) lanes. HOT
lanes combine the concepts of congestion pricing and High Occupancy Vehicle ( HOV)
lanes by offering Single Occupant Vehicles ( SOVs) priced access to the carpool ( HOV)
lanes. These lanes, thus, provide an opportunity to use both price and vehicle occupancy
as means for managing traffic as opposed to the HOV lane where only vehicle occupancy
is used as a control mechanism [ 1]. There are currently seven such HOT facilities
operating at different locations in the United States. In addition to generating much
needed revenues, these projects have been able to improve the performance of the system
with respect to a number of measures such as revenue, total cost, total vehicular time and
so on.
The success of the existing HOT lanes in realizing the objectives has engendered
considerable interest in the concept across the country. The HOV lanes in a number of
regions including California, Texas, Washington, Florida and Oregon are now being
examined for upgrading them to HOT lanes [ 1]. In addition to the benefits mentioned
above, the underutilization of the HOV lanes, evinced in the form of “ empty lane
syndrome” at a number of locations, has furthered the case of HOT lane implementation
[ 2].
This interest in turn has necessitated development of methodologies for evaluating the
conversion of a HOV lane into a HOT lane. As discussed in [ 3], there are numerous and
1
diverse factors influencing this decision on conversion. These factors may broadly be
categorized as facility, performance and institutional considerations. The focus of this
study is to investigate the potential improvements resulting from the conversion only in
terms of performance. As a part of this study, an optimization model is developed in
order to quantify the benefits in terms of various measures under different objectives that
might, at times, be competing. The basic output of the optimization model here describes
the pricing strategy to be followed, which can then be interpreted to determine the
optimal operation strategy, i. e. whether to operate the existing lane as a mixed flow lane,
HOV, or HOT lane.
The model developed as a part of this study is intended to act as decision support for
evaluating the conversion of an HOV lane on a given corridor. A behavior model
describing user behavior under pricing was estimated and embedded into the model as
constraints. The model was then used to determine the impacts of converting the HOV
lane into an HOT lane on a selected stretch of I- 80 in the San Francisco Bay Area.
A salient feature of the model is the explicit incorporation of equity into the planning
process. A set of equity constraints limiting the inequity in different dimensions were
imposed and an analysis of the loss in efficiency that results from improving the equity
was conducted. Another interesting analysis that was carried out involved examining the
differences in a number of variables as the planning agency’s objective changed. In
addition to the above, the propensities of different user groups to use the managed lane
were also examined. This model was then extended to construct two multistage models
that solve for the optimal conversion schedules when HOV lanes on more than one
corridor are to be converted.
2
The specific objectives of this study are:
i. To develop a methodology for quantifying the impacts of converting an HOV lane
into a HOT lane by incorporating equity considerations at the planning stage
itself.
ii. To analyze the impact of varying levels of equity on the efficiency of the HOT
lane.
iii. To analyze the differences in pricing strategies, managed lane use propensities
and other performance measures as the objective of the planning agency varies.
iv. To develop a multistage modeling approach that would solve for optimal
sequences/ schedules for conversion of multiple HOV lanes.
The rest of this report is organized in the following manner. The next chapter reviews the
current measures that are being adopted in order to alleviate the congestion problem. The
relevant literature on HOV lanes, congestion pricing and HOT lanes is reviewed and this
study is situated appropriately. Chapter three elaborates the methodology that is followed
for development of the decision support model. The various objective functions and
different types of constraints are described here. A case study applying the above model
to a selected corridor is presented in Chapter four. The pricing strategies and impacts of
conversion under different objectives are discussed. The trade off between equity and
efficiency is also dealt with in this chapter. The next chapter examines the issue of
optimal sequencing/ scheduling of multiple HOV to HOT conversions. Two Dynamic
Programming formulations which can be solved to obtain the self- financing sequence and
3
the sequence that minimizes external funding are described. The last chapter includes the
inferences from this study and a few directions for future research.
4
2. LITERATURE REVIEW
The costs associated with the transportation- related byproducts of economic growth have
been increasing at a rapid pace in the recent past. For instance, the cost of congestion1 in
85 metropolitan areas of the nation jumped from $ 12.5 billion in 1982 to $ 63.1 billion in
2003 [ 4]. This may be attributed to the burgeoning growth in the demand for
transportation infrastructure and as noted in [ 4], the supply has not been able to keep pace
with the demand.
The various efforts towards alleviating road congestion, as presented in [ 5], may broadly
be grouped into three categories:
a) Supply- side measures: These measures are primarily concerned with adding more
capacity to the system. The additional capacity may take the form of new roads,
additional lanes, new transit lines and so on. Supply side measures are the most
apparent and widely used measures geared towards congestion mitigation.
Conventional wisdom, however, suggests that it is not possible to build a way out
of congestion and thus the scope of supply side measures is limited. This is
especially so in urban areas owing to higher land costs and opposition from
various groups. In addition to these, the impact of adding capacity on urban roads
might not always be beneficial as it might lead to generation of more trips, i. e. an
increase in demand, or lead to an increase in the travel times as exemplified in the
Braess’ paradox phenomenon,.
1 These numbers are a quantification of only the delay and extra fuel consumed due to congestion and do
not include other effects such as worsening of air quality, lower reliability of travel, opportunity costs of
missed activities and so on.
5
b) Operational improvements: This class of efforts towards improving road
conditions may be described as “ getting more out of what we have” [ 5]. These
measures focus on improving the efficiency of the existing infrastructure by
improved management of short- term demand and by mitigating effects of road
incidents on traffic. Operational improvement measures include ramp metering,
signal timing optimization, incident management, restrictions on lane and
intersection usage, improvements in road geometries, and prominently, a number
of Intelligent Transportation Systems ( ITS) applications. These measures may be
thought of as improving the return on the investment and as reported in [ 4], can
have a significant impact on delay reduction. However, the benefits of these
approaches are limited by the maximum possible efficiency of the existing
infrastructure and as such, it will not suffice to deploy these measures on their
own.
c) Demand management strategies: These measures involve altering the demand for
the transportation facilities by inducing behavioral changes with respect to travel
decisions. A wide range of strategies are grouped under this category and are
directed towards improving transit usage and vehicle occupancy ( HOV lanes,
transit improvements, etc.), changing mode choices and time of travel ( flextime,
pricing, fuel taxes, bike/ transit integration, telecommuting, pedestrian
improvements, etc.) and proper land use management ( parking management,
smart growth reforms, transit oriented design, etc) [ 6], [ 5]. The main obstacle for
implementation of demand management strategies stems from the fact that the
6
effectiveness of these measures depends on changing the lifestyle patterns of
general populace and the trends of markets.
A comprehensive taxonomy of the congestion alleviation measures can be found in [ 5].
2.1 HIGH OCCUPANCY VEHICLE LANES:
The concept of rationing road space for High Occupancy Vehicles ( HOV) is one of the
primary demand management strategies that are currently being implemented with the
aim of alleviating congestion. A change in the American lifestyle towards greater
individualism has contributed significantly to the increase in the percentage of Single
Occupant Vehicles ( SOV) over the years [ 7]. This phenomenon in turn resulted in
consumption of more resources for transporting fewer people.
Figure 2.1: Number of Vehicles Needed to Carry 45 People2
HOV lanes are a type of managed lanes, wherein the access is limited to only the vehicles
that meet the person occupancy criteria. The implementations of HOV lanes were an
attempt at checking the drop in the HOV mode share [ 8] and increasing the number of
2Source: FHWA ( http:// ops. fhwa. dot. gov/ publications/ exemptvehicleshov/ chapter2. htm)
7
persons per vehicle. The primary objective here was to provide improved services to
HOVs and encourage carpool formation ( and transit usage) by reducing travel time and
by improving trip time reliability for such vehicles. Other objectives for HOV lanes
include improving overall system- wide travel times, improving the efficiency of public
transit services and reducing fuel consumption [ 9].
The first major HOV project in the U. S. was implemented on the Shirley Highway ( I-
395) in northern Virginia in 1969 [ 10]. There has been a steady rise in the number of
HOV facilities ever since and different versions of these projects have been implemented
all over the United States. As of now, there are 126 facilities spread across 27
metropolitan areas in the US and more are being planned [ 11]. A complete inventory of
HOV lane projects in the US can be found at http:// www. hovworld. com/. As noted in
[ 12] and [ 13], there are a number of instances wherein the HOV lanes proved to be a
valuable addition by encouraging carpooling and improving the vehicle occupancy levels.
However, the effectiveness of the HOV lanes has been limited in a number of other areas
such as New Jersey where a lane was closed in 1998 owing to lower carpool utilization
[ 12]. Analysis in [ 13] revealed that a HOV lane would be worth only in a narrow range of
conditions. The results of this analysis suggested that a HOV lane would be better than a
general purpose lane only when there is a high proportion of HOVs and when there is a
high volume of traffic. Consequently, the higher priority accorded to HOVs has led to
these lanes being underutilized giving rise to the “ empty lane syndrome” occurring when
a congested general lane is adjacent to a free flowing HOV lane. [ 14] analyzed the
California HOV system, which incidentally is one of the most extensive in the nation,
using empirical data from the Freeway Performance Measurement System ( PeMS)
8
database. It was found that the HOV lanes offer few benefits and are often underutilized
or suffer from degraded operations. The operation of HOV lanes has been questioned in a
number of regions including New Jersey, Twin Cities ( Minnesota), Long Island and
Virginia. Furthermore, as quoted in [ 3] and [ 4], the issues regarding the environmental
impacts and returns on other alternatives to HOV lanes are still not resolved.
On the whole, although there are a number of instances of successful HOV lane
operation, there does seem to be a need for efficient utilization of the capacity offered by
the HOV lanes in some of the regions.
2.2 CONGESTION PRICING:
Congestion pricing represents a widely advocated example of the Travel Demand
Management strategies. The concept of road pricing, first proposed by Pigou in 1920, has
long been propounded by economists in order to achieve higher efficiency in the usage of
transportation infrastructure [ 15]. Vickrey [ 16], for instance, stated that “ in no other
major area are pricing practices so irrational, so out of date, and so conducive to waste as
in urban transportation”. Congestion pricing is proposed as a means for cutting down on
these inefficiencies occurring in the transportation system.
It has been argued that users should be charged their external marginal costs which are
given by the difference between the actual social costs imposed by the user and the
individual trip cost experienced [ 17, 18]. The additional costs imposed by the additional
user on society include higher travel times, higher wear and tear, increased emissions and
so on [ 19]. The basic idea is to make the users cognizant of the true cost of their trips and
9
thus encourage only the trips whose benefits outweigh the total costs [ 18]. This marginal
cost congestion pricing has been frequently referred to as first- best congestion pricing.
There are, however, a number of problems associated with the implementation of this
first- best pricing. These include difficulties in computing optimal tolls in real world
scenarios, political opposition, equity issues and other technological issues [ 17]. In light
of these obstacles, research on implementing congestion pricing has focused on second-best
pricing strategies to a large extent [ 20].
Implementation of second- best pricing strategies can be broadly divided into two
categories [ 17], [ 21]:
a) Area- wide/ Cordon Tolling: This form of pricing involves charging users to use a
congested part of the city. The tolls here can be variable ( time/ distance based) or
fixed and are to be paid at different entry locations. This type of pricing has been
implemented in practice successfully at a number of locations. Notable examples
of this form of congestion pricing include Singapore’s area licensing scheme
( peak period pricing), London’s congestion pricing to enter the downtown area
and more recently Stockholm’s cordon pricing for the city center.
b) Facility Tolling: This form of tolling involves priced access to a single stretch of
a road/ bridge or even one or some of the lanes of a given segment. This has been
the predominant type of congestion pricing that has been operational in North
America. The most common form of facility pricing being implemented in the US
is HOT lanes. Examples of such projects are listed in the next section.
The main advantage of congestion pricing, as encapsulated in optimizing the objective
function, is the improvement in the welfare level of the society as measured by total
10
travel time, total cost, total emissions and so on. Individual drivers and businesses would
also be benefited by lower travel delays and improved reliability of the service [ 21].
Transit users and operators would similarly benefit due to improved speeds, reliability
and reduced costs [ 21]. In addition to the above, pricing also generates a stream of
revenue which could be used for improving the travel infrastructure of the region and/ or
for redistribution purposes.
A number of studies have focused on the mathematical modeling of congestion pricing
problems in transportation networks. Models solving for prices and tolling locations that
optimize some measure of social welfare have been formulated and solution methods
devised. These problems are usually formulated as a bilevel problem with the upper level
being optimization of the system- wide objective and the lower level being the user
equilibrium problem. The structure of the problems is similar to that of the well- studied
Network Design Problem. Some of the studies that present formulations and solution
algorithms to the pricing problem in transportation networks include [ 22], [ 23], [ 20], etc.
A number of other variations of the pricing problem incorporating multiple user groups
[ 24], variable demand [ 25, 26], road space rationing and pricing [ 27], stochastic and
dynamic equilibria [ 26] and so on have also been formulated.
Concerns about equity have also been incorporated into these formulations, albeit for
small networks, by Yang et al. in [ 24] and [ 28] and by Sumalee in [ 29]. The equity-related
constraints limited the cost incurred by each user group to be less than a certain
threshold, which is a certain percentage more than the pre- pricing cost. Yang et al. [ 28]
also analyzed and arrived at Pareto- improving pricing schemes for a small network under
equilibrium conditions.
11
The advances in methodological and technological aspects notwithstanding,
implementation of congestion pricing has not taken place in a manner commensurate with
the accepted magnitude of the traffic problems. The problem here has mainly been the
political and public acceptability of the concept [ 30]. “ The implications of status quo bias
and the invisibility of the prospective gains” [ 31] result in the existing conditions being
favored over proposed improvements, especially when the changes involve paying for
something which used to be free. The political acceptability of these projects is further
hindered by the associated equity issues with pricing being seen primarily as benefiting
the rich [ 30]. The idea that pricing is always regressive, however, has been refuted in
studies such as [ 18]. Appropriate usage of revenues plays a very important role in
shaping public opinion and the opinion can be turned around over time [ 32]. However,
[ 30] and [ 33] note that full- fledged pricing might be difficult to implement and tolled
access to HOV lanes for SOVs might be a way out.
2.3 HIGH OCCUPANCY/ TOLL LANES:
The low utilization of HOV lanes in some instances coupled with the necessity to
improve efficiency through pricing has led to the coining of the HOT concept by Fielding
and Klein [ 31]. The HOT lane concept represents an effort towards combining the
essence of pricing and HOV lanes ( i. e. higher priority to HOVs). HOT lanes allow HOVs
at a reduced or no price ( depending on the occupancy requirements) and provide priced
access to SOVs.
The prices and occupancy restrictions may be thought of as control mechanisms that
enable the HOT lane operator to manage the amount of traffic using the lane [ 1]. The
congestion ( or utilization) level of the managed lane can, thus, be controlled better in the
12
case of a HOT lane. In addition to effectively using the excess capacity on the HOV
lanes, HOT lane implementation can potentially lead to improvements in a number of
system performance measures such as total travel time, revenue, cost and so on.
However, as noted in [ 34], setting the tolls to balance these objectives would involve
certain compromises on the part of the planners. The other benefits accorded by HOT
lanes include improved reliability of travel, generation of additional revenue, more trip
options for users ( with a free option still in place), transit improvements, etc. [ 1]. Apart
from these, as noted in [ 31], HOT lanes can also act as an intermediate step for full-fledged
pricing of the highways. As noted in the previous section, HOT lanes are the
dominant form of congestion pricing that is being implemented in the US. As of February
2007, there are seven places in the US where HOT lanes are operational.
Table 2.1: Details of currently operational HOT facilities in the US
Location Name Length Lanes Occupancy Pricing
Houston, TX
Katy I- 10
QuickRide
13 mi 1
HOV2 toll/ free off- peak,
HOV3+ free, SOV prohibited
Flat $ 2 toll
Houston, TX
Northwest US
290 QuickRide
13.5 mi 1
HOV2 toll/ free off- peak,
HOV3+ free, SOV prohibited
Flat $ 2 toll
Minneapolis, MN I- 394 MNPASS 11 mi 2 SOV toll, HOV2+ free Dynamic Pricing3
San Diego, CA I- 15 FasTrak 8 mi 2 SOV toll, HOV2+ free Dynamic Pricing
Orange County,
CA
SR 91 Express
Lanes
10 mi 4
SOV toll, HOV3+ discount/ free
off- peak
Variable Pricing4
Denver, CO I- 25 HOT Lanes 6.5 mi 2 SOV toll, HOV2+ free Variable Pricing
Salt Lake City,
UT
I- 15 Express
Lanes
38 mi 2
SOV toll, HOV2+/ clean- fuel
free
$ 50 / vehicle/ month
3 Dynamic Pricing: Prices vary by the level of traffic in order to maintain speeds on the managed lane.
4 Variable Pricing: Tolls vary according to a predefined timetable that is known to the public in advance.
13
The locations, physical and operational details of the current HOT projects in the US are
shown in Table 2.1 [ 35]. In addition to these, two other projects are being constructed in
Houston and Maryland. A complete list of the HOT lanes projects that are under
development can be found in [ 35].
A number of studies have investigated and evaluated the impacts of these HOT lanes.
Sullivan and Burris [ 36, 37] conducted a benefit- cost analysis of SR- 91 and the
QuickRide projects for a period of ten years. The benefits and costs considered include
travel time savings, fuel costs, emissions, capital costs and operating costs. The overall
benefit- cost ratio was found to be 1.5 and 1.6 for the SR 91 and QuickRide projects
respectively, with significant savings in travel time observed in both the projects.
However, the benefits in terms of reduced emissions were found to be negative in both
the projects. The results for the fuel costs were mixed with an increase in consumption in
case of SR 91 and decrease for the QuickRide projects. On the whole, the net benefits, as
evinced by the benefit- cost ratio, were positive in both the cases.
Studies examining different impacts of the I- 15 project have also been conducted. The
traffic- related effects of the project have been found to be beneficial on a number of
counts by Supernak et al. [ 38]. These include better utilization of the managed lane,
sufficient revenues and redistribution of volumes to the peak shoulders. It was also found
that there was an improvement in the reliability of travel times and free flow conditions
were maintained for most of the periods [ 39]. An evaluation study of the MnPass [ 40]
also revealed beneficial effects of the HOT facility. The improvements that were
observed include increase in the vehicle throughput of the corridor, decrease in the travel
time on the general purpose lane and no negative impacts on CO emissions.
14
The public response to the HOT lanes has been positive in general and it was noted that
people would be willing to pay in order to bypass congestion at times [ 1, 41, 40]. The
various factors impacting the usage and acceptance of the HOT concepts have also been
empirically studied. Li [ 42] analyzed data from the SR 91 project and inferred that
income, commute trip, vehicle occupancy and age play a significant role in the user
decision regarding usage of the HOT lane. Sullivan also conducted a study into the
factors impacting SR 91 express lanes usage [ 41]. An analysis of the QuickRide
programs’ users behavior was conducted [ 43] and it was found that the carpool formation
disutility acted as a major deterrent to the facilities’ usage. Furthermore, it was found that
perception of higher travel time savings, longer trips, college education and sharing of the
tolls were found to increase the usage propensity. In addition to these, a FHWA report [ 1]
on development of HOT lanes lists the following variables as factors impacting HOT lane
use: toll, pricing structure, travel time on HOT lane, Value of Time ( VOT), perceived
HOT lane operating cost, costs associated with alternate means and routes, trip purpose
and frequency, vehicle occupancy, risk profile, income and other demographic
characteristics. Of all these variables, income, carpool formation cost, travel time savings,
toll, operating cost and trip type have been incorporated into the behavior model of the
current study, whose construction is described in the next chapter.
The benefits in efficiency notwithstanding, the equity issues of pricing have persisted in
the case of HOT lanes and they have been disparaged as “ Lexus lanes” [ 44]. HOT lanes
have been perceived as elitist and imposing an additional burden on the poor. Equity in
transportation projects is usually considered to be of two types: Horizontal equity, which
deals with equal treatment to similar groups, and vertical equity, which requires the
15
policies to be skewed towards the needy and disabled [ 45]. The main equity issue which
occurs in the context of HOT lanes is vertical equity [ 46]. User analysis studies of
different HOT projects [ 36], [ 37], [ 39] revealed that though all income groups use the
tolled facility, individuals from higher income groups are more likely to use them than
those from lower income groups [ 47],[ 41],[ 48]. Interestingly, the HOT concept received
approval from all of the income groups though. However, as noted in [ 46], redistribution
of revenues would play a very important role in determining the equitability of the
project. Thus, as noted in [ 46], a comprehensive approach that includes equity from
planning to implementation needs to be adopted.
Another issue with the HOT lanes has been that the conversion into HOT lanes might
increase the traffic on the managed lane thus leading to deterioration of conditions for
HOV users [ 49]. This issue can easily be mitigated by controlling the price to influence
the number of vehicles that will enter the managed lane in such a way that reasonable
speeds are maintained [ 39].
The numerous positives from the current HOT projects have spawned significant interest
in the concept and consequently, a number of agencies are considering conversion of
HOV lanes into HOT lanes at different locations. A number of corridors in California,
Texas, Florida, Oregon and Washington are being examined and feasibility studies
conducted for implementation of the HOT lanes [ 9]. An up- to- date listing of the projects
being developed can be found in [ 35].
This interest in HOT projects has in turn resulted in the creation of frameworks to aid in
the conversion process. A wide range of information about the development of the HOT
lanes can be found in [ 1]. Recognizing the nascent nature of the studies addressing the
16
conversion, a comprehensive sketch- planning tool has been developed by [ 3] in order to
support the assessment of the conversion of HOV lanes. The various factors that need to
be examined during the planning stage of the conversion were grouped into three
different categories:
a) Facility considerations: This category includes factors related to facility cross
section, lane separation, facility access, ease of enforcement, incident
management and so on.
b) Performance considerations: Factors in this category include managed lane
utilization, travel time savings/ reliability, societal benefits, environmental
impacts and so on.
c) Institutional considerations: This includes factors such as political and public
acceptance, revenue use, media relations and so on.
Each of the factors is then assigned weights and is scored based on the characteristics of
the corridor with respect to the corresponding factor. The interactions between the factors
were then quantified and a score assigned to each of the categories. These scores can then
be used to make the decision regarding the conversion.
[ 50] is another study catering to the conversion’s managerial aspect where a route map
for conversion of the HOV lanes into HOT lanes is presented.
Given this framework, the current study may be positioned in the performance
component of the conversion. As mentioned in the previous chapter, the focus of this
study would be to evaluate the conversion in terms of the benefits and costs resulting
from the conversion.
17
Other studies addressing the quantitative aspect of the planning process include [ 51],
[ 52], [ 53]. Kim [ 51] studied the conversion of an HOV lane in a single corridor by
assuming the tolls to be minimizing the system delay and concluded that HOT lanes are
more beneficial to the system when compared to HOV lanes or general purpose lanes.
Murray et al. [ 52] evaluated the impact of HOT lanes in a network by incorporating a
logit model predicting mode choice into the DYNASMART model. A study using this
methodology revealed that the system can be made more efficient by creation of HOT
lanes. The tolls charged were obtained by scaling up the link density with a multiplicative
factor. A sensitivity analysis of the improvement in travel time to various factors was also
conducted. McDonald and Noland [ 53] used a simulation model ( with a nested logit
model) of a hypothetical corridor to analyze the effects of HOT lanes. The analysis here
was conducted using a flat toll and the results suggested that HOT lanes provide the
greatest mobility benefits among general, HOV and HOT lanes. Safirova et al. [ 49]
studied the impacts of converting HOV lanes in Northern Virginia into HOT lanes by
incorporating a toll of 20 cents per mile into the demand model ( Washington- START
mode) and concluded that all income groups gain from the conversion with higher
income groups gaining more. These inferences are along the lines of the results obtained
in this study. A number of planning agencies also conducted feasibility studies for
converting the HOV lanes in their area into HOT lanes [ 50], [ 54].
In spite of useful insights from these studies, two important aspects that need to be
addressed at the planning stage include:
18
1) Equity: As mentioned above, this has been a major impediment for
implementation of the HOT concept. None of the above studies addresses this
issue in the planning stage of the HOT development.
2) Pricing objectives and strategies: The potential benefits accrued from the
conversion are very much a function of the price. However, this price has been
chosen in a non- optimal manner ( except in [ 51]) in most of the studies.
Furthermore, the optimal pricing strategy itself is a function of the performance
measure that needs to be optimized and thus, this issue warrants careful
consideration.
The gaps related to managed lanes’ planning literature have been discussed in [ 55] and
the above two aspects were alluded to in the planning and policy research discussion. The
methodology taken towards incorporating these issues in the current study is elucidated in
the following chapter. The first distinguishing feature of this study is the incorporation of
equity right at the planning stage. Equity, unlike in other studies, was considered
explicitly along two dimensions - vertical and temporal equity. The incorporation of
equity in the form of constraints here gives the planners an extra handle in limiting the
inequity along different dimensions and according to different measures. This treatment
also enables investigation of the relationship between equity and various measures of
efficiency.
As noted above, the pricing strategy depends on the performance measure that the
planning agency seeks to optimize. As a part of this study, the optimal pricing strategies
corresponding to different objectives were computed for a chosen corridor. This enabled
comparison of the trends in tolls and benefits across different objectives. Another
19
important contribution of this study is the development of a methodology that would
solve for an optimal approach to converting the given HOV infrastructure into HOT lanes
in a self- financing manner.
2.4 CHAPTER SUMMARY:
The relevant literature in the areas of HOV lanes and congestion pricing was discussed
along with the pros and cons of these two demand management strategies. The concept
and development of HOT lanes as a combination of HOV lanes and congestion pricing
were then presented. Next, existing studies examining the benefits/ costs and the user
characteristics of the HOT lanes currently operational in the US were reviewed. Studies
dealing with the HOV to HOT lane conversion were discussed and this study positioned
appropriately. The main contributions of this study to the literature in this area are the
incorporation of equity in the planning stage, the analysis of equity versus efficiency and
the analysis of multiple objectives for conversion.
20
3. MODELING METHODOLOGY
The decision about converting a HOV lane to HOT lane is rooted in wide ranging
considerations such as potential benefits, public acceptance for the pricing concept, social
equity, readiness of the operating agencies, lane geometry and other operational and
policy factors. The scope of our study, however, is limited to quantifying the potential
improvements in terms of system performance that could be brought about by such a
conversion. Thus, the models here are intended to assist decision makers by giving them
feedback on the pricing policies that correspond to optimal system performance
measures. The models here are constructed for the situation where conversion to HOT
lanes of the HOV lanes on a single corridor is being considered.
As mentioned earlier, the benefits and costs that accompany the conversion are a function
of the choices that different users make when faced with a certain toll for using the
carpool lane as a two- person carpool ( HOV2) or as a single occupant vehicle ( SOV).
Thus, the effects of conversion to a HOT lane must be quantified according to the pricing
strategy that would be adopted. As a part of this study, the prices to be set are treated as
decision variables and a program that optimizes the planning agency’s objective is
solved. The problem here has a convex objective function and nonlinear ( convex)
constraints. A simplistic version of the problem formulation is shown below:
Optimize Objective Function
Subject to, a) Constraints on lane travel times
b) Constraints describing the Behavior Model
c) Equity related constraints
d) Constraints on tolls
21
Each of the above elements of this program is described in detail under the following
sections. The above described optimization program was solved for the scenario where
there is one HOT lane on which three- person carpools ( HOV3) travel for free while
HOV2s pay a reduced toll. The benefits/ costs in terms of a number of performance
measures were then quantified and compared against the base case scenario where there
is only a HOV lane. Such a scenario- based analysis was performed for a chosen corridor
in the next chapter.
Note that the pricing strategy would also give the definition of the carpool that needs to
be adopted. For instance, an output of a very high toll for two- person carpools would
imply that the HOT lane needs to be operated as a HOV3 carpool lane excluding SOVs
and HOV2s. Similarly, a low toll for HOV2s and a very high toll for SOVs would imply
that SOVs are not to be allowed to buy into the managed lane while HOV2s may be
allowed at a price.
3.1 OBJECTIVE FUNCTIONS:
As far as the objective functions are concerned, different operating agencies might have
different measures of performance for operating managed lanes. It is also possible that
the same agency might have multiple objectives such as to minimize the total travel time,
maximize the revenue or to minimize the emissions and so on. The agency would, thus,
need to implement different pricing strategies. The pricing strategies corresponding to the
following objectives were considered for evaluating the benefits/ costs of the conversion:
a) Minimize Total vehicular travel time: This is a common objective function that is
used in a number of planning studies and can be obtained by summing up the
22
travel time experienced by all the vehicles on the road segment under
consideration.
b) Minimize Total passenger time: This can be computed by summing up the travel
time experienced by each individual user.
c) Maximize Total revenue: The total revenue is given by the total toll money that
can be collected using a certain pricing strategy.
d) Minimize Total number of vehicles: One potential objective for the agency might
be to reduce the total number of vehicles that are on the corridor. Minimizing the
total number of vehicles here is the same as minimizing the total VMT on a
corridor, another commonly used objective. However, this function was found to
behave very much like the total vehicular time for the case study that will be
described in chapter four.
e) Minimize Total user cost: The cost for a user here is the equivalent expected
dollar cost that can be obtained from the probabilities and the costs of different
alternatives in dollars. This cost here is an aggregate of a variety of costs such as
carpool formation costs, travel time costs, tolls and so on. Further details about
the costs are included in the behavior model discussion.
The implementation of the optimization model with each of the above objectives will be
referred to as a program from here on. For instance, the above model with revenue
maximization as the objective will be referred to as revenue maximization program.
Another transportation system performance measure that was considered for experiments
here was the total vehicular emissions. However, this measure could not be approximated
with a convex objective and had to be left out of the objective functions set. Instead, the
23
emissions were estimated under different programs in order to help decision makers
evaluate the impacts on air quality. A brief discussion on the quantification of emissions
under each scenario is presented at the end of this chapter.
3.2 CONSTRAINTS ON LANE TRAVEL TIMES:
These constraints describe the following elements of the model:
a) The relationship between the volume and the capacity on the general purpose as
well as the HOT lane. For the purpose of this study, the BPR function was
assumed to capture this relationship.
0 ( 1 ( ) ) b v t t a c
= + ,
where t = travel time on the lane,
t0 = free flow travel time on the lane ( travel time at speed limit),
v = volume on the given lane,
c = capacity of the lane ( assumed to be 1600 vph [ 51]), and
a, b = BPR parameters ( obtained from PEMS5 for the given segment).
b) The quality of service ( travel time) on the HOT lane. The idea behind the service
constraint is to maintain a certain level of service on the managed lanes. In other
words, it assures the users that their travel time on the HOT lane would be less
than a certain threshold. The threshold for this study was set at the corridor travel
time corresponding to 50mph. These constraints also ensure that the travel time
on the HOT lane is always no greater than that of the general purpose lanes.
5 PEMS web address: https:// pems. eecs. berkeley. edu/
24
3.3 CONSTRAINTS DESCRIBING THE BEHAVIOR MODEL:
A behavior model is embedded in the optimization model as constraints to predict the
choices of different classes of users over regular and managed lanes upon implementing a
certain pricing regime on the managed lane. Given the attributes of an individual and
those of the alternatives, the behavior model gives the probability of an individual
choosing the given alternative. In order to reflect the heterogeneity of the corridor’s
users, the users were categorized into different classes based on the following attributes:
a) Income: Individuals were categorized into four different quartiles according to their
hourly wage rate. The categorization was necessitated by the well documented
higher Value of Time ( VOT) for individuals with higher incomes, which might
translate into a preference for reducing travel time through paying tolls. The income
distribution of all the corridors here was assumed to be the same as the income
distribution of the study region – the San Francisco Bay Area. The values for the
10th, 25th, 50th, 75th and 90th percentiles of the incomes in this area were obtained
from the Bureau of Labor Statistics website [ 56] and an income distribution curve
was fitted with an R2 of 0.997.
WAGE RATE DISTRIBUTION
0
10
20
30
40
50
60
0 20 40 60 80 1
Percentage of Users
Hourly Wage Rate ($)
00
Figure 3.1 Income Distribution ( 2006) curve in Bay Area
25
The curve shown in Figure 3.1 was then used to divide the users into four quartiles
based on their hourly wage rates - $ 43.49 per hour, $ 26.11 per hour, $ 15.68 per
hour and $ 9.42 per hour.
b) Trip type: Corridor users were further classified into four classes based on the type
of their trip. The rationale behind this classification was the difference in the VOT
attached by the same user to different kinds of trips. For instance, an individual
making a work trip is much more likely to pay for the better service on HOT lanes
when compared to the same individual on a shopping trip. The distribution of trip
types for the Bay Area that was obtained from the BAYCAST- 90 summary [ 57]
and it was assumed the traffic on all the corridors of the study area was similar to
the following composition.
Table 3.1: Distribution and Value of Time for different trip types
Trip Type % of traffic VOT ( as % of hourly wage)
Work 40.37 46.40
Shopping and Social 29.33 23.00
School 12.40 2.00
Other 17.90 5.20
The average VOT resulting from the above trip type distribution was found to be
26.67% of the wage rate.
c) Carpool formation cost: Users were further classified into four different categories
based on the carpool formation cost, which corresponds to the extra amount of time
an individual needs to spend in order to form the carpool. Such time would include
26
time spent on pick up and drop- off of the rideshare partner( s). As mentioned earlier,
this cost plays an important role in the carpooling tendencies of the individual and
can vary significantly from individual to individual. The average carpool formation
time for a HOV2 is about 7.2 minutes and for a HOV3 is 11 minutes according to a
survey conducted in the Bay Area [ 58]. The exact distribution of this cost for Bay
Area users was not available. Hence, this distribution was estimated using the data
from a similar survey conducted in Texas. A distribution of this cost was reported
for Houston in [ 59], with an average value of about 6.18 minutes. The distribution
in [ 59] was then scaled up accordingly and the users were divided into four
quartiles. A similar procedure was followed for obtaining the distribution of three-person
carpool formation time.
Note that the above carpool formation times were reported by carpool users alone
and, thus, do not represent the inconvenience costs for current SOV users to form
carpool. In order to account for the costs to SOV users, the above values need to be
scaled up. The carpool formation time for Los Angeles ( LA) users was assumed to
be eight minutes on average in [ 60]. The average for LA users including SOV users
was assumed to be 15 minutes in [ 32]. The ratio of these two values was used to
scale the distribution shown proportionately. The final carpool formation costs
incurred by SOV users for each type of carpool are shown in table 3.2.
Table 3.2: Distribution of carpool formation costs
Quartile HOV2 cost HOV3 cost
I 0 0
II 0.047 hr 0.073 hr
III 0.212 hr 0.323 hr
IV 0.664 hr 1.014 hr
27
Thus, the total number of classes into which the corridor users have been classified is
4×4×4 = 64. Distinguishing users in different categories allows for determining the losers
and winners under each of the scenarios. For instance, this treatment would allow us to
quantify, on average, the travel times experienced by the rich and the poor under each of
the scenarios and thus aid in analyzing the important vertical equity issues. In addition to
the above, as opposed to most of the other studies where a single average VOT is
assumed, this study incorporates a distribution for VOT by allowing for heterogeneity in
users’ incomes and trip types.
In the absence of a full fledged stated preference data set for assessing the user response
to different pricing regimes, a logit- based behavior model was constructed by
enumerating the costs that an individual attaches to various alternatives. Accordingly, the
probability that an individual belonging to class i chooses alternative j is given by:
exp( )
( , )
exp( )
ij
ij
j
C
P i j
C
β
β
−
=
Σ − ,
where Cij is the equivalent dollar cost of alternative j for user class i, and
β is a scaling coefficient that needs to be estimated.
The above model may be thought of as a logit model in which the only variable is the
total dollar cost of an alternative for an individual. The total cost experienced by the user
for different choices is constituted by the following elements:
i) Travel time cost: This is simply the cost of travel time corresponding to the
particular alternative, converted into monetary units based on the income group and
the importance of the trip.
28
ii) Toll cost: This cost consists of the toll the individual pays in the tolled options and
is zero for the non- toll options. It is assumed here that the members of the carpool
share the toll costs, if any.
iii) Carpool cost: The carpool formation cost, as discussed above, is simply the extra
time needed to form a carpool and would thus depend on the number of persons
forming the carpool.
iv) Time shift cost: The cost incurred by users who shift their trip times from their
desired time to a different period is quantified using this. This cost is assumed to be
100% of the hourly wage rate for shifting an hour of travel time. This estimate was
obtained from [ 61]. However, preliminary model runs using this cost indicated it is
highly improbable for users to shift their time even by half an hour. This is because
of the fact that this cost dominates all the other costs and consequently, the
impedance attached to the corresponding alternatives is much larger in magnitude.
Thus, for the rest of the study, the users were assumed to be traveling at the same
departure times across all the scenarios. This, however, may only be partly true in a
number of situations. For instance, [ 41] suggests that while there was a change in
the magnitude and length of the PM peak period, there was very little shifting
during the AM peak. Another difficulty in quantifying this cost stems from the large
variation in the estimates of this cost, which ranged from 2- 3% to 300% of the
hourly wage rate [ 61], [ 62], [ 63].
29
v) Operating costs: These constitute the costs associated with operating a vehicle for
the trip distance including fuel cost and parking. This cost is assumed to be shared
by the members of the carpool. However, lack of data on trip distances, parking cost
distribution and other hidden costs necessitates treating this cost as a parameter to
be estimated. The procedure for estimating the scaling coefficient β and the
operating costs is presented below.
Given that only HOV3 vehicles can use the HOT lane for free, the various alternatives a
traveler faces have been enumerated and the applicable costs are shown in Table 3.3.
Table 3.3: Details of alternatives and costs after conversion
Alternative
Travel time
costs
Toll
costs
Operating
costs
Carpool costs
With toll as SOV on HOT
lane 1 t T1 OC 0
Without toll as SOV on
regular lane 2 t 0 OC 0
With toll as HOV2 on HOT
lane 1 t T2 / 2 OC/ 2 CC2
Without toll as HOV2 on
regular lane 2 t 0 OC/ 2 CC2
Without toll as HOV3 on
HOT lane 1 t 0 OC/ 3 CC3
where = travel time on HOT lane, 1 t
2 t = travel time on general lane,
T1 = toll imposed on SOVs,
T2 = toll imposed on HOV2s,
OC – operating cost,
30
CC2 – two- person carpool formation time, and
CC3 – three- person carpool formation time.
3.3.1 Estimation of Scaling Coefficient ( β) and Operating Costs ( OC):
The coefficient β along with the vehicle operating cost ( OC in Table 1) will be estimated
using the pre- conversion choice data ( i. e. data from the HOV lane scenario). The absence
of disaggregate data on the vehicle occupancy choice of different individuals necessitated
using aggregate data. The parameters here were estimated using the overall mode split
between carpools and SOVs during the peak period. The modal split was used as a proxy
for revealed choices of a “ representative” individual, i. e., the modal shares were assumed
to be the probability with which the representative individual would choose each of the
alternatives. The alternatives that exist for this individual before effecting the conversion
are SOV, HOV2 or HOV3.
At the first step, the costs associated with each of the modes will be computed for this
user. The carpool costs will be computed using average values for VOT and carpool
costs. In order to compute the travel costs, the total vehicular demand can first be
obtained from the PEMS database for a particular segment. The modal split on this
segment in conjunction with the BPR function can be used to compute the travel times on
the general purpose and carpool lanes. The toll costs before conversion are zero. Note
that computation of OC would need data on the trip distances and lack of this data
necessitates estimation from the revealed choice data. The following table shows the
alternatives and the corresponding costs in the pre- conversion scenario.
31
Table 3.4: Details of alternatives and costs before conversion
Alternative
Travel time
costs
Toll
costs
Operating
costs
Carpool costs
SOV on general lane 2 t 0 OC 0
HOV2 on general lane* 2 t 0 OC/ 2 CC2
HOV3 on carpool lane 1 t 0 OC/ 3 CC3
(* Assuming HOV2s are not allowed on the carpool lane)
The estimates for β and OC can then be obtained by solving two equations that set the
probability of choosing each alternative to be the existing market shares of these
alternatives:
( 1 2) 1
2
e C C x
x
− β − = and ( 1 3) 1
3
e C C x
x
− β − = ,
where β = scaling coefficient to be estimated,
Ci = cost ( in $) of choosing alternative i ( vehicle occupancy i), and
xi = modal share of vehicle with occupancy i ( 1 x + 2 x + 3 x = 1).
The operating cost OC is embedded in the cost corresponding to each alternative and is
obtained, along with the scaling coefficient β, as a solution to the above two equations.
An instance of the above described procedure has been constructed in chapter four ( case
study) and the estimate for β was found to be comparable to the β in one of the models in
the literature [ 64].
3.3.2 Additional Notes on the Behavior Model:
a) The travel costs on other parts of the trip beyond the studied corridor are assumed to be
the same for all the alternatives. In other words, there is no special treatment given to any
of the alternatives in the rest of the user’s trip which might lead to additional cost
32
components. This assumption would enable leaving out the costs corresponding to the
other parts of trips since these costs would cancel out. Hence, the individual’s choice
would depend only on the impedances of the alternatives on the corridor being examined.
One such situation where this assumption would not hold is the case where there are
carpool lanes elsewhere in the journey. The costs associated with carpool alternatives
would then be lower than the SOV alternative’s cost. The impact on the estimation of
ignoring the effect of these carpool lanes is that the estimate for parameter OC would be
lower than the case when there are no carpool lanes. The OC term now would be required
to incorporate the lower costs associated with the carpool alternatives as well, thus
pushing the estimate downwards.
b) An important assumption here is that users on the corridor continue to use the same
route even after the conversion. This assumption might hold reasonably well in situations
where the alternative routes involve a significant amount of impedance of any kind.
c) The above described model is an attempt at capturing the essential elements of a
choice model that should be obtained from a Stated Preference survey and only a model
based on survey data would provide a basis for drawing robust conclusions.
3.4 EQUITY RELATED CONSTRAINTS:
One of the significant criticisms levelled against the HOT lane concept is the idea that
they favor the rich. Equity constraints are introduced to place bounds on the potential
inequities of welfares between different income groups. The welfare of each income
group for the purpose of equity is quantified using two measures:
33
a) Average travel time: The weighted average of travel times experienced by all 16
groups in each of the four income groups is used as one of the measures to
quantify the welfare of the four income groups.
( ) ( ) ijk ijk
j k l
i
ijk
j k
n P l t l
T
n
=
ΣΣΣ
ΣΣ ,
where = average travel time for income group i, i T
( ) ijk P l = probability that a user of income group i, on trip type j and belonging
to carpool cost group k will choose alternative l,
t( l) = travel time experienced when alternative l is chosen, and
ijk n = number of users belonging to the group defined by income group i, trip
type j and carpool cost group k.
b) Average travel cost: This measure quantifies the expected impedance experienced
by an income group on average. The expected travel costs experienced by all 16
groups in each of the income groups are computed first. The dollar cost thus
obtained is then converted into its time equivalent for that particular individual by
scaling it down using the VOT of that group:
( () ())/ ijk ijk ijk ij
j k l
i
ijk
j k
n P l c l VOT
C
n
=
ΣΣΣ
ΣΣ ,
where = average travel cost ( in time units) for income group i after conversion, i C
ij VOT = value of time for individual belonging to income group i and on
trip type j,
34
( ) ijk c l = monetary cost associated with alternative l defined by income
group i, trip type j and carpool cost group k, and all of the other variables
are as
The conversio
costs according ps’ welfare can be judged. The dollar costs incurred
e
o measures. Equity constraints can further be classified into two types based on the
ncome group are at least as well
defined above.
n into time units is performed in order to provide a uniform measure of
to which all the grou
by higher income individuals will be higher than those for the lower income users
because of the higher VOTs. The dollar costs, if directly used, would wrongly indicate
that the rich are experiencing higher costs and thus, the policies directed at reducing the
costs would be skewed in favour of the rich. Costs in terms of time units, on the other
hand, would provide a more uniform measure to quantify the welfare of each income
group. Note that the travel time costs are only a part of the average cost and there are
other costs ( toll, carpool formation cost, operating costs) which influence this variable.
Equity constraints in the model attempt to limit the inequities with respect to the abov
tw
dimension they address – Temporal or Vertical equity.
The conversion project here is said to be temporally equitable if the conversion results in
the situation where the future users belonging to each i
off as they were before the conversion. In other words, perfect temporal equity refers to
the condition where the average costs of each income group are non- increasing with time.
Temporal equity thus involves comparing the welfare of individuals belonging to each
income group before and after the conversion. Constraints corresponding to temporal
equity specify that all of the income groups should be better off when compared to their
35
states of welfare before the conversion. Using the same notation as defined above, the
general form of temporal equity constraints is shown below:
Ci≤ Ci 0 ,∀ income groups i,
where C0 = average travel cost ( in time units) for income grou i p i before conversion.
Similar temporal equity constraints could with respect to travel time. A
rther
quity, on the other hand, is concerned with the welfare of the users only during
the post- conversion period. The principles of v re the policies to favour
also be imposed
relaxed version of the above constraint can be given in the following manner. Fu
analysis with this relaxed form will be carried out in Chapter four for a particular
corridor.
( 1 / 100) 0 , i i C≤ + x C∀ income groups i.
Vertical e
ertical equity requi
individuals who are at a disadvantage such as individuals with low incomes, minorities,
disabled and so on [ 45]. In the context of this study, vertical equity takes form as the
difference in the benefits/ costs incurred by each income group. Constraints
corresponding to vertical equity limit the average benefits/ costs across different income
groups and are intended to reduce the spread in these benefits/ costs. The general form of
vertical equity constraints is:
( 1 ) , i C≤ + θC∀ i and ( 1 ) , i C≥ − θC∀ i, i in income groups,
where θ = parameter to be specified by the planners beforehand, and
C = mean travel cost ac ll the income gr
be within a certain
ought of as constraining the
maximum difference across groups to be less than a certain fraction of the overall mean.
ross a oups.
The above constraints limit the average travel costs of each group to
percentage of the overall mean. This treatment may be th
36
The impact of changing θ on the efficiency loss has been studied for a specific corridor
in chapter four.
Note that the unit of analysis here is the income group and thus temporal equity does not
imply that all the users ( belonging to all 64 groups) gain from the conversion. It is
possible that the average measures corresponding to each income group improves but
function can be defined a
of each group in the weighted objective
non- negativity bounds on each
f the two tolls. Additionally, the toll for HOV2s is constrained to be less than or equal to
al constraint that can be imposed on the tolls, if
necessary, could set upper limits for each of these tolls.
there are both losers and winners within each income group.
A simpler way of incorporating equity concerns into the model is to use a weighted
objective that attaches appropriate weights to the terms associated with different groups
in the objective function. For instance, a modified revenue
lower weight can be assigned to the revenue from the lower income groups while a
higher weight is attached to the higher income groups. This ‘ weighted revenue’ function
can then be maximized instead of the regular revenue function to obtain a toll regime that
is more equitable to the lower income groups.
The advantage of addressing equity in the form of constraints rather than as weights in
the objective is the control achieved by directly imposing limits on the extent of benefits/
costs’ distribution. The actual benefits/ costs
approach may not exactly reflect the desired distribution.
3.5 CONSTRAINTS ON TOLLS:
The constraints imposed on the tolls to be set include the
o
the toll for SOVs. Another potenti
37
In addition to all the above constraints, a set of constraints that describe the current
conditions were placed. These constraints were imposed only for computation of the
initial conditions and do not affect price setting as such. The whole of this model was
coded in AMPL ( code shown in Appendix A) and the optimization solvers available on
ber of useful insights can be obtained from
is model.
OBILE6 software. MOBILE6 is an emission factor model and computes the
mount of pollutant per unit of travel ( grams per mile traveled). The impact of conversion
O) and
ecific characteristics such as altitude, humidity,
etc. The complete list of variables impacting these factors can be found in the MOBILE6
the NEOS website were used to solve for the optimal tolls. Note that the problem here is
a convex ( nonlinear) optimization program.
It is acknowledged that the model described in this chapter is a rather simplistic one and
does not account for network effects, elastic demand, route and time shifting. However,
as discussed in the following chapters, a num
th
3.7 DETERMINING THE IMPACT OF CONVERSION ON EMISSIONS:
The emissions corresponding to the before and after conversion scenarios were computed
using the M
a
on the emissions of Volatile Organic Compounds ( VOC), Carbon monoxide ( C
NOX was studied using a simple model.
The composite emission factor or the amount released per mile of travel for each type of
emission depends on a number of variables which include vehicle speed distribution by
hour and type, VMT distribution by vehicle type and roadway type, diesel sales fractions
by vehicle type and age and other site sp
38
manual [ 65]. As a part of this study, the values for all the input parameters except for
speed and facility type were set at the national default values provided in the model. The
facility type was set as freeway.
All three emission factors were then estimated at different speeds using the MOBILE6
model software. It was assumed here that the traffic is composed of only one stream with
all the vehicles moving at the same speed. The following graphs ( Figure 3.1) show the
relationship between speed and emission factors for NOX, VOC and CO.
SPEED Vs NOX EMISSION FACTOR
1.3
1.4
1.5
on ( g
1.35
1.45
1.55
1.6
0 10 20 30 40 50 60 70
Speed ( mph)
Emissi Factor / mile)
SPEED Vs CO EMISSION FACTOR
0 1
2
4 5
6
8 9
10
Speed ( mph)
CO Emi on Fact g/ mile)
3
7
0 10 20 30 40 50 60 70
ssi or (
Figure 3.1 ( a) Figure 3.1 ( b)
SPEED Vs VOC EMISSION FACTOR
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60 70
Speed ( mph)
VOC Emission Factor ( g/ mile)
3.1( a) Plot of Speed Vs NOX Emission Factor
3.1( b) Plot of Speed Vs CO Emission Factor
3.1( c) Plot of Speed Vs VOC Emission Factor
Figure 3.1 ( c)
While the VOC emissions per mile travel decrease first and then essentially level off with
an increase in speed, the NOX emissions first decrease and then increase with speed. The
lowest rate of NOX emissions seem to be occurring at 37.5 mph. The CO emissions per
mile first decrease and increase at a rate very small compared to that of the NOX
39
emissions. The lowest emissions seem to be occurring at 35 mph. These patterns in are in
accordance with those in [ 66]. The above relationship between speed and emissions was
then used to compute the quantities of emissions both before and after conversion in the
following manner.
Quantity of emission X ( in kg) = 1 1 2 2 ( ). ( ). X X η s VMT + η s VMT
where, ( s) X η - emission factor ( of X) at speed s,
s1 and s2 – speeds on managed and general lanes respectively, and
VMT1 and VMT2 – Vehicle Miles Traveled on managed and general lanes.
The speeds and VMTs ( number of vehicles) on the lanes change once the conversion has
been effected and the above expression can pute the emissions under the
nario
e estimates for
each sc hts into
on the managed
nes for a specific agency- defined objective. This approach would, thus, provide insights
uld be achieved by means of tolling. The heterogeneity in
be used to com
base sce and also for different programs.
The rather simplistic nature of the emissions model here implies that th
enario’s emissions may not be accurate, but they are likely to provide insig
the ordinal ranking of scenarios/ objectives based on vehicle emissions.
3.8 CHAPTER SUMMARY:
The core model that can be used to analyze the potential benefits and costs of converting
an HOV lane into an HOT lane was presented in this chapter. The model consists of an
optimization program that recommends the most effective pricing setting
la
into the optimal benefits that co
road users was accounted for by classifying them into different categories based on
hourly wage rate, trip type, and the carpool formation cost. A logit- like model was
40
constructed for describing the behavior of different types of users and was embedded into
the optimization model as constraints. The estimation of necessary parameters using
aggregate data was also discussed. Inclusion of equity constraints in the model allows for
direct handling of equity concerns at the early planning stage. Equity here was considered
along two dimensions ( Temporal and Vertical) and using two welfare measures ( travel
cost and travel time). Other types of constraints imposed include constraints describing
travel times, tolls and current conditions.
41
4. CASE STUDY
he impacts of converting an HOV lane to an HOT lane on a particular corridor are
xamined in this chapter. The corridor being considered belongs to the Interstate 80
eeway in Contra Costa county and is five miles long ( Buchanan to the I- 880 split on 1-
0W). This particular corridor has been identified as a high priority project for
implementation of the HOT lane growth rate of carpools on this
T
e
fr
8
because of the high
corridor [ 54]. It is expected that the HOV lane here will become crowded by the year
2020. Figure 4.1 shows a map indicating the extent of the corridor.
Figure 4.1: Extent and location of study corridor
There are five lanes on this stretch with one of the lanes serving as a carpool lane during
the AM ( 0500 – 1000 hours) and PM ( 1500 – 1900 hours) peak periods. The HOV lane
operates by allowing only carpools with three or more people to use it during the peak
periods. Data from the PEMS database indicates significant levels of congestion ( v/ c ratio
~ 88% during peak periods) on this stretch. Apart from utilizing the excess capacity on
42
HOV lanes, the HOT project on this stretch can also aid significantly in reducing travel
times and optimizing various performance measures.
The benefits/ costs associated with the conversion here were computed for a demand
level corresponding to the mean peak hour volume. It was further assumed that the HOT
lanes will be tolled only during the peak period. This is because the HOV lanes currently
are being operated only during the peak period and thus any extension to a 24 hour period
might encounter higher public resistance for this concept. A public opinion survey
following aspects were studied for the conversion policies
iii) Vertical and Temporal equity related issues.
conducted by the Metropolitan Transportation Commission ( MTC) revealed opposition to
SOVs buying into the HOV lanes with 64% of the respondents answering “ no” to the
concept. A majority ( 61%), however, did agree that carpool lanes are currently being
underutilized in the Bay Area [ 54]. Other studies have, however, found that the HOT
concept finds more acceptance when the usage of revenues is explicitly mentioned and
with progress of time [ 67].
A behavior model was first estimated for this stretch and the tolls that optimized various
performance measures were computed. The different objectives that were considered here
include maximizing revenue, minimizing total vehicular time, total cost, total passenger
time and total VMT. The behavior model was then embedded as constraints into the
optimization model and the
generated from various programs:
i) Changes in various performance measures before and after conversion.
ii) Usage of managed ( HOT) lanes by income, trip type and carpool formation
costs.
43
In addition to the above, some of the key questions answered in this chapter include:
impact of conversion on number of vehicles and carpools, pricing and operating
stra ies re of
inco gro
The estima the choice model parameters is presented in the next section. Impacts
of ers s are discussed in subsequent
k period flows on each Monday
ough Thursday during June 2007 were obtained and their average value was used as the
convert this vehicular demand into the
teg under different programs, impact of conversion on emissions, welfa
me ups before and after conversion, losses in efficiency due to equity and so on.
tion of
conv ion under different optimization program
sections. The last section in this chapter then deals with the variation in the performance
measures and other impacts across different programs.
4.1 ESTIMATION OF CHOICE MODEL:
The first step towards estimating a choice model was to obtain an estimate of the
passenger demand for the stretch during the peak hour. The PEMS database was used to
obtain the average flow ( per hour) during the peak hours on the detector closest to the
entry of the stretch in the West bound direction. Pea
th
vehicular demand for the stretch. In order to
passenger demand, the mode shares of SOV, HOV2 and HOV3 were needed. The modal
split for the Bay Area during the peak period was then computed using the modal splits
for each trip type during 2006 from [ 68] and the breakdown of peak period traffic
according to trip type as given in [ 57].
The average values for carpool formation cost and the value of time for a ‘ representative’
individual were then obtained by appropriately weighting the numbers using modal splits
and traffic composition ( based on trip types) from [ 57] and [ 68] respectively. The Bureau
of Public Roads ( BPR) function was used to compute the travel times on each of the lanes
44
and the necessary coefficients were obtained from the PEMS database: a = 0.506 and b =
5 ( rounded off to the nearest integer due to solver limitations). The capacity per lane, as
the coefficients estimated in a similar mode choice
rating costs. However, as explained in Chapter
given in [ 54], was assumed to be 1600 vehicles per lane per hour. The travel times thus
computed were then used to obtain the travel costs for the representative user using an
average VOT. Thus, the total cost ( excluding OC) corresponding to each alternative for
the representative user was computed in the HOV scenario. Note that there are no toll
costs in the pre- conversion scenario.
Next, assuming the share of each mode to represent the probability of the mode being
chosen, the parameters β ( scaling coefficient) and OC ( operating costs) were estimated
using the procedure described in the previous chapter to be 0.5782 and 74.65 cents
respectively. This value for coefficient β translates into 0.0864 when the impedances
( costs) for each of the alternatives are expressed in terms of time units instead of dollars.
This value falls within the range of
model, which is from 0.05 to 0.085 [ 64].
Assuming the gasoline operating cost in the Bay Area to be 9.89 cents/ mile ( in 2006
dollars) [ 69], the estimate of 74.65 cents for OC translates into 7.55 miles of trip distance
on average. After subtracting out the actual average trip distance in the Bay Area in 2006
( 6.7 miles [ 57]) from the OC estimate, the rest of the operating cost (~ 7.8 cents) is
somewhat low to be considered as other costs such as the parking costs. Thus, the model
here seems to underestimate the exact ope
3, this might partly be because of the preferential treatment given to carpools elsewhere
in the trip or due to the exclusion of other types of costs that are incurred by users.
45
This behavior model was then used in solving for the tolls under different optimization
programs, whose results are presented in the following sections.
4.2 REVENUE MAXIMIZATION:
The tolls that maximize total expected revenue were computed and the toll for both SOVs
le, for instance, contains
lls that are at times even higher). Such reasonable toll for both types of vehicles
would be to operate the lanes as HOT lanes with
at
the service quality constraint on the managed lane was binding. This suggests that there is
and HOV2s was found to be $ 5.46 per trip. This toll, though somewhat on the higher
side, is still within the reasonable range ( The SR 91 toll schedu
to
suggests that the optimal policy here
free access only to HOV3s. This result also implies that a revenue of $ 2824.78 per hour
could be obtained by operating HOT lanes under revenue maximization, which translates
into an annual revenue of about $ 6.36 million, assuming operation only on weekdays.
These toll revenues from the HOT lane, if used entirely for repayment, will be sufficient
to recover the capital and operating costs in just over three years. The capital cost
estimate from MTC was put at $ 3.7 million per mile for upgrading the HOV lane on this
corridor [ 54]. Thus, the total capital cost here amounts to $ 18.5 million. The operating
and maintenance costs, on the other hand, were estimated to be $ 0.35 million per year.
This toll policy, however, has led to a worsening of travel time on the managed lane. The
average travel time on the HOT lane was found to be six minutes as opposed to 4.75
minutes in the pre- conversion case. The travel time on the other lanes, however,
improved from 8.11 minutes to 6.54 minutes. The conversion, thus, seems to reduce the
difference between the travel times on the lanes. An interesting observation here is th
46
still scope for increase in the revenue if the service ( i. e. travel speed) on the HOT lane
were to be lowered from 50mph. This has been confirmed with a numerical experiment
which reduced the quality on the HOT lane and found an increase in the revenue
generated. As expected, the utilization level of the HOV lane improved by almost 28
percentage points while the utilization level of the general lanes fell by eight percentage
points.
4.2.1 Impact on Performance Measures:
Table 4.1 shows the changes in the various performance measures caused by the
conversion, under the revenue maximization program. The measures shown here are for
one hour of operation.
Table 4.1: Comparison of performance measures under revenue maximization
Performance Measure
( for one hour of operation)
Before Conversion After Conversion Difference % Change
Revenue $ 0 $ 2824.74 + $ 2824.74 -
Total Vehicular Time 952.58 hrs 815.46 hrs - 137.12 hrs - 14.39%
Total Passenger Time 1333.38 hrs 1236.45 hrs - 96.93 hrs - 7.27%
Total Cost $ 17924.2 $ 19692.6 + $ 1768.4 + 9.87%
VMT 37536.95 miles 38021.85 miles + 484.9 miles + 1.29%
It c e table that there is a significant amount of benefit in terms of
revenue, total vehicular and passenger times by converting the HOV lane into the HOT
lane and operating under the revenue maximization program. The largest improvement,
in terms of e change, w otal ve el t de by
14.39%. On the flip side, there was also an increase in the total cost ( impedance) that is
an be seen from the abov
percentag as in the t hicular trav ime which creased
47
incurred by the users, on the o .4 y be considered a loss in
cial welfare if there is no redistribution of the revenues. However, if it were possible to
of SOVs and HOV2s increased by 0.17 and 4.57
percentage po sed by 4.75
percentage points. These observations suggest es here is
brought about by the dominance of the latter effect - three- person carpools breaking- up
into SOVs and HOV2s – over t er ef . e., in w pools. This
greater dissolution of the thr rson seem indi t the savings in
carpool formation time brought about by switching to the two- person carpool outweigh
rder of $ 1768 . This cost ma
so
return the toll revenues perfectly to the users, it would still be possible to make a “ profit”
worth $ 1056.38 and ensure that the total cost does not deteriorate after the conversion.
There is also an increase in the total VMT which is a direct consequence of the increase
in the number of vehicles using this stretch. The volume here increased from 7507
vehicles per hr to 7604 vehicles per hr.
Table 4.2: Comparison of modal shares before and after conversion
Before Conversion After Conversion
Mode
# Users Proportion # Users Proportion
SOV 4882 43.43% 4900.58 43.60%
HOV2 3028 26.94% 3542.24 31.51%
As shown above, while the modal share
HOV3 3332 29.64% 2798 24.89%
ints respectively, the share of three- person carpools decrea
that the negative effect on volum
he form fect i crease in t o- person car
ee- pe carpools s to cate tha
extra costs associated with the HOV2 alternatives under the HOT lane scenario.
Note that despite the increase in the number of vehicles, there is a drop in the total
vehicular travel time which is brought about by the decrease in the travel time
experienced by a number of vehicles on the general lane.
48
The impact of this conversion on emissions was estimated for three different types of
emissions – VOC, CO, NOX using the model described in Chapter 3. Table 4.3 shows the
amounts of each of these ( per hour of operation) released under both before and after
conversion scenarios.
Table 4.3: Comparison of Emissions before and after the conversion
Emission Type ↓ Before ( kg/ hr) After( kg/ hr)
VOC 15.47 15.59
CO 220.38 224.39
NOX 50.46 51.05
m to suggest that the conversion here has a slightly detrimental
impact on air conversion.
The values for all the e c itial values and given
the simplistic nature of the l, the stre f this inf is not exactly known at
this stage. The increase in all the three e s here e due to increase in the
number of vehicles ( increase in VMT).
The above results see
quality, with all of the emissions predicted to be higher after
emissions, how ver, are quite lose to the in
mode ngth o erence
mission might b
4.2.2 Users of Managed Lanes:
The probability of an individual choosing to use the HOT lane ( as a HOV or SOV) is
examined through segmentation of users by income, trip type and carpool formation
costs. The following table shows the variation in the probability of individuals belonging
to different income groups choosing to use the HOT lane.
49
Table 4.4: Comparison of managed lane use propensity by income groups
Income Groups↓ Before After
Quartile 1 ( Low) 0.322 0.361
Quartile 2 0.303 0.336
Quartile 3 0.286 0.309
Quartile 4 ( High) 0.274 0.284
The results here suggest that lower income people have a higher probability of choosing
the HOT ght seem
counterintuitive at f wev should ted that lower income
individuals, even pr ersion, ore likely to carpool and thus have a
higher probability of using the managed as carp HOT lanes. Empirical
evidence for lower income people carpooling more than higher income people may be
found in [ 68]. This might be because of the fact that lower income individuals might be
g to different trip types choosing the
lane when compared to higher income individuals. This mi
irst glance. Ho er, it be no
ior to the conv are m
lane ool on
willing to carpool more in order to save more on the ( fixed) operating costs that are
uniform for all of the income groups in this model.
Although there is an increase in the propensity to choose the managed lane, the reason for
such a choice differs across the groups. While higher income individuals use the lane
more by paying a toll either as a SOV or HOV2, lower income individuals gain access by
carpooling more either as a HOV2 or HOV3. This is because higher income individuals,
who are more willing to pay money for savings in time, are more likely to choose the toll
option once the conversion has been made.
The results for the probabilities of travelers belongin
HOT lane ( Table 4.5( a)) are similar to the results for income based segmentation. Users
on trips with lower values of time are more likely to choose the managed lane. This is
50
predominantly due to the higher carpooling tendencies that are associated with lower
value trips in a manner similar to the behavior of the lower income groups. Empirical
evidence for higher carpooling rates in school, other and shopping trips can be found in
[ 68].
Table 4.5: Comparison of managed lane use propensity by trip types and by carpool formation
costs
Trip Type ↓ Probability Group # Probability
Work 0.272 Group 1 0.429
Shop 0.316 Group 2 0.393
Other 0.389 Group 3 0.291
School 0.409
Group 4 0.178
( a) ( b)
T
lines. Individuals who have a higher carpooling cost are less likely to use the HOT lane
when compared to individuals with lower carpooling costs.
Note that all of the above results tained withou ng the equity constraints.
4.2.3 User Equity Analysis:
As mentioned in the previous chapter, the two variables that are used to measure the
welfare of the income groups here are average travel time and average travel costs ( in
units of time). Equity here is analyzed along two dimensions – Temporal and Vertical.
Discussion about the results of the experiments and the relationships between equity and
he results for the segmentation along the carpool costs ( Table 4.5( b)) are along expected
are ob t imposi
efficiency under this revenue maximization program follows.
51
4.2.3.1 Travel Cost Equity:
a) Temporal Equity: The average costs ( in units of time) for different users, segmented
by income, before ( HOV) and after the conversion ( HOT) are shown in Table 4.6.
Table 4.6: Average travel costs of users in each income group before and after conversion
( unconstrained case)
Income Quartile 1 ( Lo) Quartile 2 Quartile 3 Quartile 4 ( Hi)
HOV case 0.819 hrs 0.574 hrs 0.418 hrs 0.318 hrs
HOT case 1.112 hrs 0.746 hrs 0.515 hrs 0.371 hrs
As shown in the table, the conversion, when evaluated in terms of the average cost, seems
to have a negative effect on all the groups with an increase in cost observed across all the
income groups. It can also be seen that this increase is largest in the case of lower income
groups. This project, when operated under the pure revenue maximization program, thus
seems to h iment on tem uit ing f s worse off
when com e curr
was then attempted to arrive at a pricing strategy which would ensure that each income
decrease in the optimal revenue from the original
ave a detr al effect poral eq y by mak uture user
pared to th ent users.
It
group of the current users on an HOV lane are not made worse off in the future if the
HOV lane is converted to an HOT lane. This was done by imposing constraints which
ensured that the average cost for each income group was non- increasing. These additional
constraints on the optimization problem narrow down the solution search space thus
leading to a loss in efficiency. The “ cost” corresponding to achieving temporal equity in
this case may be thought of as the
( unconstrained) problem to this new constrained problem. The optimal revenue, on
solving the constrained optimization problem, was found to be $ 84.42 per hour, which is
52
$ 2740.35 less than that of the original problem. This difference represents in the loss in
efficiency due to temporal equity and the policy makers would, thus, need to strike a
balance between equity and efficiency.
Further analysis was carried out in order to ensure that policy makers get a higher amount
of flexibility in this seemingly binary decision on efficiency vs. equity. This was done in
the following manner: Instead of constraining the average costs of each income group to
be strictly less than 100% of original costs, constraints specifying that the new average
costs can be less than ( 100+ x)% times the original costs were imposed.
Average Cost ( i) ≤ ( 1+ x/ 100) × Initial Average Cost ( i),
where i is the index denoting income group.
The variable of x in the above inequality was then increased and the objective value
observed. Figure 4.2 shows the increase in efficiency as the extent of temporal equity is
decreased i. e. as x is increased.
Temporal Equity Vs Efficiency ( Revenue)
100.00%
120.00%
l
0.00%
40.00%
% of
R
20.00%
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00%
x
← Temporal Equity
O ma
even
60.00%
80.00%
pti
ue
Figure 4.2: Relationship between Temporal Equity and Revenue
53
The y- axis of the plot shown above gives the ratio ( percentage) of the optimal revenue in
the constrained case to the optimal revenue in unconstrained case and thus, is a measure
of efficiency in this case. Thus, as seen from the plot, the efficiency here increases
linearly with a decrease in temporal equity i. e. as x is increased from 0%. However, once
a certain threshold value for x is reached, there would be no further increase in the
efficiency. This threshold value here corresponds to x being 35.7%. In other words, once
x hits a value of 35.7%, the constrained problem becomes equivalent to the o iginal
unconstrained v s of x.
is only
r
ersion and no loss in efficiency is observed for higher value
Note that whole of the above analysis corresponds to the case when there is no possibility
of compensating any of the losing groups. However, in cases where it is possible to
perfectly redistribute the revenues obtained, equity can be achieved at a lower loss of
efficiency, i. e. at a lower cost by simply reimbursing the users who have lost because of
this conversion. The cost of achieving total temporal equity in this case, as noted in 4.2.1,
would be $ 1768.4 ( the difference in total cost between the HOV and HOT scenarios).
Note that this value is much lower than the loss in efficiency resulting from the
constrained optimization problem where the value of x is set to 0. However, this
for theoretical purposes since perfect redistribution would not be possible in reality.
Therefore, depending on the effectiveness of the available redistribution mechanisms,
policy makers would then need to decide upon a combination of the appropriate
constrained problem ( i. e. x) and redistribution package.
b) Vertical Equity: Table 4.7 shows the average travel costs ( in units of time) of different
income groups before and after the conversion.
54
Table 4.7: Average travel costs of users in each income group before and after conversion
Income Before Conversion After Conversion
Quartile 1 ( Low) 0.819 hrs 1.112 hrs
Quartile 2 0.574 hrs 0.746 hrs
Quartile 3 0.418 hrs 0.515 hrs
Quartile 4 ( High) 0.318 hrs 0.371 hrs
Focusing on the post- conversion scenario alone, it can be seen that the travel costs of
lower income individuals are a lot higher than those of higher income individuals.
xperiments that involved constraining the maximum difference between the average
constraining the cost of each of the groups to lie within a certain percentage ( θ) of the
overall average travel cost. The variation in e
then examined by va value of th tage θ.
E
costs of each groups under the HOT lane scenario were conducted. This was done by
efficiency ( m asured by revenue here) was
rying the is percen
Vertical Equity Vs Efficiency ( Revenue)
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
54% 56% 58% 60% 62% 64% 66%
θ
← Vertical Equity
% o ma imu
reven e
120.0%
f x m
u
Figure 4.3: Relationship between Vertical Equity and Revenue
As shown in Figure 4.3, the relationship between equity and efficiency here is
characterized by two thresholds. The lower of the two thresholds corresponds to the value
55
below which it is not possible to reduce θ without making the problem infeasible. An
implication of the existence of this lower threshold is that it is impossible to ensure that
all of the groups experience exactly the same cost. Decreasing θ value below this
threshold would simply make the problem infeasible. The value of this lower threshold
was found to be 55.6%.
The graph shown above also indicates that there would not be any loss in the
performance measure ( revenue) when the allowable percentage deviation ( θ) from the
mean is more crossing this
e planning stage itself, with all the political considerations in
g vertical equity- related constraints on the model.
than a certain upper threshold ( 62.1%). The problem, on
thresholds, once again becomes equivalent to the original unconstrained problem.
However, once θ goes below this threshold, the efficiency gradually decreases until the
predetermined deviation value ( θ) hits the lower threshold ( 55.6%) below which the
problem simply becomes infeasible.
On the whole, there seems to be a ( linearly) decreasing relationship between vertical
equity and efficiency. Thus, vertical equity ( θ) would be one of the parameters that policy
makers need to fix at th
mind.
Now, turning to the vertical equity situation before the conversion, note that the travel
costs of lower income individuals are much higher than those of the higher income
groups even before the conversion ( Table 4.7). This is again because of the higher
prevalence of carpooling among lower income individuals. The maximum deviation ( θ)
from the mean in the pre- conversion scenario is 53.8%, which is lesser than the minimum
θ that could be achieved by imposin
Thus, unlike temporal equity, there will be some loss of equity ( in vertical equity sense)
56
that takes place upon implementing the conversion under the revenue maximizing price
regime.
otal vertical equity can be calculated by taking the difference ( in average costs)
It should be noted that the above vertical equity is only for the case where there is no
redistribution. Now suppose that the operating agency is in a position to distribute the toll
revenue to any of the user groups perfectly, i. e., there is no wastage associated with
redistribution. The only way to reduce the extent of vertical inequity once the trips have
been made is to compensate the losing groups in such a manner that their average
benefits move as close as possible to those of the winning groups. Transfer of money
from winning groups to losing groups is not possible once the trips have taken place. The
winning group here is the high income quartile. Thus, the amount of revenue needed to
achieve t
between the corresponding groups of the lower income and high income quartile and then
converting them into monetary units. This exercise has been performed for the
unconstrained revenue maximization problem and the following amounts ( table 4.8) were
to be paid to each of the income groups in order to ensure that all four groups had the
same average cost ( that of the high income group).
Table 4.8: Money to be paid to users in each group in order to ensure perfect vertical equity
( Unconstrained problem)
Income Group Money to be paid
Quartile 1 ( Low) $ 2160.94
Quartile 2 $ 1863.05
Quartile 3 $ 1199.22
Quartile 4 ( High) $ 0
Total $ 5223.21
57
As expected, the money to be paid decreases as we move from lower income quartiles to
higher income ones. The total amount to be paid out as compensation here is $ 2398.43
mo or
different values of θ in the feasib are summarized in Table 4.8.
Table 4.9: Deficit in revenue that would be perfect vertical equity
tribut
θ Reve Money to ) Deficit ($)
re than the amount generated in revenues. A similar exercise was carried out f
le region and the results
needed to ensure
( Perfect redis ion case)
nue ($) be paid ($
63.00% 2824.78 5223.21 2398.43
62.10% 2806.73 5213.67 2406.94
62.00% 2744.81 5181.52 2436.71
61.00% 2164.56 4905.39 2740.83
60.00% 1659.54 4679.55 3020.01
59.00% 1223.97 4484.76 3260.79
58.00% 847.70 4312.64 3464.94
57.00% 520.18 4158.17 3637.99
56.00% 231.59 4017.83 3786.24
55.60% 124.96 3965.02 3840.06
Thus, in case full redistribution is a possibility, implementing the pricing regime from the
unconstrained problem ost effi vertical equity.
However, in cases where full redistribution is not possible, operating under the
unconstrained revenue maxi may not most t way to equity.
Suppose that on f th es could b or redist
total amount to be paid out as compensation changes for different values of θ. It can be
would be the m cient way of ensuring
mization lead to the efficien
ly 40% o e revenu e used f ribution. In this case, the
58
seen from Table at set 55.6% w ld the lea ay to achieving
full vertical equi
Table 4.10: Deficit in revenue that would be needed to ensure perfect vertical equity
4.10 th ting θ = ould yie st cost w
ty.
( Imperfect redistribution case – 40% efficiency of redistribution)
θ Deficit ($)
63.00% 4093.30
62.10% 4090.98
62.00% 4083.60
61.00% 4039.57
60.00% 4015.73
59.00% 3995.17
58.00% 3973.56
57.00% 3950.10
56.00% 3925.20
55.60% 3915.04
The choice of the equity level planning stage would, thus, depend on the
effectiveness of redistribution that chie g different mechanisms.
On the whole, there seems to be a decreasing relationship between temporal as well as
vertical equity and efficiency, when equity in travel costs is considered. Furthermore, the
relationship is linear, i. e. as equity in es, r reases at a linear rate within the
interval described by the two th . H the decrease in revenue per unit
change in the equity measures ( x a a lo in the case of vertical equity.
at the
can be a ved usin
creas evenue dec
resholds owever,
nd θ) is t higher
59
4.2.3.2 Travel Time Equity:
a) Temporal Equity: Table 4.11 shows the average travel times before and after
conversion across different income groups.
Table 4.11: Average travel times of users in each income group before and after conversion
Income Quartile 1 ( Lo) Quartile 2 Quartile 3 Quartile 4 ( Hi)
HOV case 0.1171 0.1182 0.1192 0.1198
HOT case 0.1051 0.1059 0.1062 0.1064
Conversion of the HOV lane into a HOT lane seems to benefit all the groups in terms of
( i. e. reduction in the objective - revenue) that
not translate into worsening of travel time
b) Vertica he trav s of the inco ividuals average, are
lower than the hig ome ind s bo re and after the conversion.
his, as explained above, is due to the higher prevalence of carpooling among lower
urve were very close
the 100% mark. This means that the loss in efficiency due to imposing the vertical
travel time. There is no loss of efficiency
occurs in order to ensure that the conversion is temporally equitable. In other words, the
increase in the revenue generation here does
for future users when compared to the travel times of current users.
l Equity: T el time lower me ind , on an
those of her inc ividual th befo
T
income individuals. Higher income groups, however, seem to be benefiting at a higher
rate in terms of the percentage decrease in the travel times. In light of the closeness of the
travel times experienced by all the income groups, it can be conjectured that the loss in
efficiency is very little with the increase in equity. The analysis described above ( section
4.2.3.1) reveals that the two thresholds on the efficiency vs. equity c
to
60
equity constraints does not begin to take place till a point that is quite close to the perfect
vertical equity.
Furthermore, the maximum ( θ) deviation before the conversion was 1.2% and this value
reduced to 0.3% after the conversion suggesting that the conversion here improves
vertical equity in terms of travel times. This is because of the fact that the conversion
drives the travel times on both the lanes to be closer than they were before. Note that
there is no real issue with vertical equity here since the weaker groups have lower costs
compared to the stronger ones. Thus, there is no strong necessity to study the equity in
the travel time sense in this program.
The above results highlight the fact that there is no single definition for quantifying the
EHICULAR TRAVEL TIME:
he minimization of total vehicular time ( TVT) resulted in a very high toll for SOVs,
benefits and costs of different groups. For instance, in this case study it was not sufficient
to use travel time as the measure in all of the instances in order to examine the
equitability of a project and formulate fair strategies. Thus, a comprehensive equity
analysis needs to include quantification of benefits/ costs with respect to different
measures that are deemed appropriate.
4.3 MINIMIZATION OF TOTAL V
T
suggesting that they should not be allowed onto the HOT lane. HOV2s, on the other
hand, should be allowed on the HOT lane at a toll of $ 3.26. The least possible TVT here
was 786.54 hours of travel time per hour, which is 17.43% less than the HOV lane
scenario.
61
The revenue that can be obtained from the above tolling regime is $ 1824.2 per hour,
which translates into an annual revenue of $ 4.1 million. These revenues, if used entirely
wards recovering the costs, would break even with the capital and operating costs in a
e required in the
travel time on the general lane was 6.37 minutes ( 21.46% less than the pre-to
period of about five years. This is about two years more than the tim
revenue maximization program.
As observed in the previous section, while the travel time on the managed lane
deteriorated there was an improvement of conditions on the general lanes. The travel time
on the managed lane was six minutes ( 26.2% more than the pre- conversion scenario)
while the
conversion scenario). Once again, the quality constraint was found to be binding, the
travel time on the managed lane is thus same as the one observed under revenue
maximization. So, a relaxation of the service constraint led to an improvement in the
TVT.
4.3.1 Impact on Performance Measures:
Table 4.12 shows the changes in the various performance measures before and after the
conversion, under the TVT minimization program.
Table 4.12: Comparison of performance measures under TVT minimization
Performance Measure
( for one hr of operation)
Before Conversion After Conversion Difference % Change
Revenue $ 0 $ 1824.19 + $ 1824.19 -
TVT 952.58 hrs 786.53 hrs - 166.05 hrs - 17.43%
Total Passenger Time 1333.38 hrs 1170.26 hrs - 163.12 hrs - 12.23%
Total Cost $ 17924.2 $ 18688.3 + $ 764.1 + 4.26%
VMT 37536.95 miles 37465.65 miles - 71.3 miles - 0.19%
62
The results here indicate an improvement in all the performance measures except with
respect to the total user cost. However, in the case of perfect redistribution, it would still
be possibl ut due to
the tin s e o ri e
maximization. There is also a significant improvement in the total passenger time from
the pre- conversion scenario on the order of 12.23%.
In contrast to the revenue ma program marg em e
total VM a decrease al number of vehicles from 7507 to 7493. Table
4.13 show ariation in er o the es b nd
e to raise $ 1060.09 in revenue, even after ensuring that nobody loses o
conversion. Interes gly, this value is imilar to the on btained du ng revenu
ximization , there is a inal improv ent in th
T due to in the tot
s the v the total numb f users across three mod efore a
after the conversion.
Table 4.13: Comparison of modal shares before and after conversion
Before Conversion After Conversion
Mode
# Users Proportion # Users Proportion
SOV 4882 43.43% 4635 41.22%
HOV2 3028 26.94% 3938 35.02%
HOV3 3332 29.64% 2669 23.73%
As observed under the revenue maximization regime, there is a drop in the modal shares
of SOVs and HOV3s. There is, however, an increase in the share of two- person carpools
on the order of 8.08 percentage points. Thus, the decrease in the number of vehicles here
seems to be a result of increase in the num
formation rate of two- person carpools dom
three- person carpools. Thus, th ults h to suggest tha
ber of people choosing HOV2. Note that the
inates the contrary effect – dissolution of
e res ere seem t the two- person carpool
63
becomes the preferred alternative now an due h the g up of some of
e three- person carpools and SOV users forming carpools.
d this is to bot breakin
th
The impact of this conversion on the three types of emission is shown Table 4.14.
Table 4.14: Comparison of Emissions before and after the conversion
Emission Type ↓ Before ( Kg/ hr) After ( Kg/ hr)
VOC 15.47 15.34
CO 220.38 221.69
NOX 50.46 50.46
The results here seem to be more encouraging than the previous case with a negative
impact on emissions of CO alone. The values for all the emissions, however, are again
very close to their initial values.
4.3.2 Users of Managed Lanes:
The likelihood of individual onging to nt incom ps choosing the managed
lane before and after the co on is show able 4.1
Table 4.15: Comparison of managed lane use propensity by income groups
s bel differe e grou
nversi n in T 5.
Income Groups↓ Before After
Quartile 1 ( Low) 0.322 0.384
Quartile 2 0.303 0.354
Quartile 3 0.286 0.322
Quartile 4 ( High) 0.274 0.289
There is a clear increase in the propensity to use the managed lane after the conversion.
Furthermore, the propensity to use the HOT lane increases from higher income to lower
64
income in nversion
probabilities in this her ose un e revenue maximization
program. The following tables s anaged lane for users
segmented according to their trip types ( Table 4.16( a)) and carpool formation cost groups
( Table 4.16( b)).
omparison of managed lane use propensity by trip type and carpool formation cost
dividuals for reasons discussed previously. Note that all the post- co
program are hig than th der th
how the probabilities of using the m
Table 4.16: C
Trip Type ↓ Probability Group # Probability
Work 0.277 Group 1 0.453
Shop 0.331 Group 2 0.417
Other 0.415 Group 3 0.306
School 0.435
Group 4 0.172
( a) ( b)
The results above are in line with the reasoning that there is a higher likelihood of
carpooling in the contexts of lower value trips and lower carpooling costs. Once again,
the propensity to use the managed lane here is higher than the corresponding propensity
observed for the revenue maximization regime, across all of the income groups. The
higher probabilities ( of choosing managed lane) observed in this program are a reflection
of the increase in the extent of carpooling that is happening here.
4.3.3 User Equity Analysis:
As discussed above, Temporal and Vertical equity issues here are analyzed for travel time
and travel cost.
65
4.3.3.1 Travel Cost Equity:
a) Temporal Equity: The average costs ( in units of time) corresponding to different
come quartiles before ( HOV) and after the conversion ( HOT) are shown in Table 4.17.
of users in each income group before and after conversion
in
Table 4.17: Average travel costs
Income Quartile 1 ( Lo) Quartile 2 Quartile 3 Quartile 4 ( Hi)
HOV case ( hrs) 0.819 hrs 0.574 hrs 0.418 hrs 0.318 hrs
HOT case ( hrs) 1.041 0.700 0.486 0.351
The conversion here seems to increase the travel costs experienced by individuals
ome groups, as observed under the revenue maximization
time
compare s for strain sug hat th efficiency
here, in order to render the conversion tem e groups, is
0.69 hours of vehicular travel time.
belonging to all of the inc
program. In order to ensure that all of the income groups on average experience lower
travel costs after the conversion, a constrained version of the optimization model was
implemented. The objective then was found to be 857.22 hours of vehicular travel
d 786.53 hour the uncon ed case gesting t e loss in
porally equitable for all incom
7
Further analysis was then carried out by gradually relaxing the temporal equity
constraints in a manner similar to the procedure described in Section 4.2.3.1. The limit on
the average cost of each group was set to be a certain percentage ( x) more than the
average cost experienced in the pre- conversion state. The following graph ( Figure 4.4)
shows how the efficiency ( in terms of vehicular travel time) changes with the change in
the extent of temporal equity.
66
Temporal Equity Vs TVT
780
790
800
810
820
840
850
860
870
0.0% 5.0%
TVT ( rs)
830
10.0% 15.0% 20.0% 25.0% 30.0% 35.0%
x
← Temporal Equity
h
Figure 4.4: Relationship between Temporal Equity and TVT
Once again, the efficiency decreases with the increase in temporal equity till a certain
threshold is reached. The threshold here is at x equals 27% and beyond this, there is no
loss in efficiency with an increase in temporal equity. The relationship between x and
efficiency in the region below the threshold appears to be quadratic in nature, unlike in
the revenue maximization case where it was linear. Note that the quadratic relationship
here results in higher losses in efficiency for unit increase in equity near the threshold
when compared to losses when x equals 0. In other words, the loss in efficiency occurs at
a higher rate near the threshold when compared to the loss rate under conditions closer to
perfect temporal equity.
As noted in 4.3.1, in situations where perfect redistribution would be possible, the
revenue from the unconstrained model would suffice to achieve total temporal equity.
The problem of designing the right redistribution package, however, becomes more
complex now and would require a triangular tradeoff involving revenue, vehicular travel
time and equity.
67
b) Vertical Equity: The following table ( table 4.18) shows the average travel costs ( in
units of time) of different income groups in the post- conversion scenario.
Table 4.18: Average travel costs of users in each income group after conversion
Income Avg Cost ( hrs)
Quartile 1 ( Low) 1.041
Quartile 2 0.700
Quartile 3 0.486
Quartile 4 ( High) 0.351
As exp income
individuals is much higher than that of higher incom
scenario. The differences in average costs experienced were then constrained by limiting
the cost of each group to be w θ) of the overall mean. Figure
4.5 shows how the efficiency decreases ( i. e. TVT increases) as this θ is decreased. Note
at relationship is characterized by two thresholds once again.
ected, the time equivalent of travel cost experienced by the lower
e individuals under the HOT
ithin a certain percentage (
th
VERTICAL EQUITY Vs TVT
780
800
820
840
860
54% 56% 58% 60% 62% 64%
T ( h )
880
66% 68%
Vertical Equity
TV rs
Figure 4.5: Relationship between Vertical Equity and TVT
The two thresholds under TVT minimization, as shown in the above graph, occur at θ
equals 55.2% and 61%. In other words, there would not be any loss in efficiency when
68
the θ value is over 61% and the problem becomes infeasible when θ is reduced to a value
less than 55.2%. Thus, the most vertically equitable situation in the post conversion
scenario corresponds to θ equals 55.2%. Note that the relationship between the two
thresholds is quadratic as in the case of temporal equity.
This θ value in the pre- conversion scenario happens to be 53.8%. Thus, there will again
necessarily be a reduction in vertical equity due to the conversion. This, however, is true
only if there is no redistribution of revenues. The revenue deficit under perfect
redistribution of revenues was found to be the least for the unconstrained problem. The
decision about the θ would, however, need to be based on the weights attached to TVT,
revenue and vertical equity. Inferences similar to those in section 4.2.3.1 could be drawn
for different levels of redistribution packages.
4.3.3.2 Travel Time Equity:
a) Temporal Equity: Table 4.19 shows the average travel times before and after
conversion across different income groups.
Table 4.19: Average travel times of users in each income group before and after conversion
Income Quartile 1 ( Lo) Quartile 2 Quartile 3 Quartile 4 ( Hi)
HOV case ( hrs) 0.1171 0.1182 0.1192 0.1198
HOT case ( hrs) 0.1032 0.1036 0.104 0.1044
As expected, there is an improvement in the average travel times of all the income
groups. Thus, there is no loss in efficiency, i. e. increase in TVT, with the imposition of
temporal equity in terms of travel time. Also, the improvement in the travel times of all
69
the groups is higher under TVT minimization than was the improvement under revenue
maximization.
b) Vertical Equity: The average travel tim lower income individuals are lower
than those of the higher income individuals both before and after the conversion because
f, as explained previously, higher carpooling among lower income individuals. Since the
l for SOVs under TPT minimization seems to suggest that the SOVs are
ot to be allowed on the HOT lane. The toll for HOV2s, on the other hand, was $ 4.10.
20.54% and - 19.98% from the previous travel times
n managed and general lanes respectively. Unlike the cases for revenue maximization
, implying that there
4.4.1 Impact on Performance Measures:
Table 4.20 shows the changes in the various performance measures before and after the
conversion, under the TPT minimization program.
es of the
o
disadvantaged individuals are already better off, the need to impose vertical equity
constraints is obviated ( see 4.2.3.2).
4.4 MINIMIZATION OF TOTAL PASSENGER TIME ( TPT):
The optimal tol
n
Thus, except for the minor difference in the HOV2 toll, this program is very similar to the
TVT minimization ( HOV2 toll = $ 3.26) program. The toll revenue under the TPT regime
was $ 1870 per hour and the corresponding annual revenue was $ 4.2 million.
The travel times on the managed and general lanes were 5.73 minutes and 6.49 minutes
respectively. These values differ by +
o
and TVT minimization, the quality constraint here is not binding
would not be any loss by maintaining the LOS on the HOT lane.
70
Table 4.20: Comparison of performance measures under TPT minimization
Performance Measure
Before Conversion After Conversion Difference
( for one hr of operation)
% Change
Revenue $ 0 $ 1870.41 + $ 1870.4