Activity-Based Model with Dynamic
Traffic Assignment and Consideration
of Heterogeneous User Preferences
and Reliability Valuation
Application to Toll Revenue Forecasting in Chicago, Illinois
Ali Zockaie, Meead Saberi, Hani S. Mahmassani, Lan Jiang,
Andreas Frei, and Tian Hou
on reliable and credible forecasts of the projects’ effects on travel
behavior, the revenues the projects will generate, and their important
policy implications and overall performance expectations.
To forecast the impact of congestion pricing schemes, often in
conjunction with operational measures, it is essential to capture two
key elements: (a) the responses of users to these schemes and (b) the
resulting dynamics of traffic flow in the network. The responses of
users must include, at the first level, route choice and the effect of
tolls on that choice and, at the second level, other choice dimensions,
such as departure time and mode choices. At higher levels and over
the long run, the range of individual and household activity engagement and scheduling decisions may be affected. Traffic dynamics
must capture the interactions that take place along freeway links and
at urban junctions under varying traffic control and management
decisions, including real-time measures and traveler information.
Static assignment tools used in conjunction with conventional planning models fail to capture both of these elements adequately for the
purpose of forecasting toll revenues and pricing impacts. To capture
the first element, this study develops a framework for the integration
of an activity-based model (ABM) with a dynamic traffic assignment (DTA) and a simulation framework to support the analysis and
evaluation of various pricing schemes. Simulation-based DTA tools
capture the second of the above elements (traffic dynamics) and
provide a flexible framework for the first (user decisions), which
recent developments have further improved specifically to support
the realistic assessment of congestion pricing impacts. Therefore,
the objectives of this study are twofold: (a) to advance the state of the
practice in evaluating the potential impact of congestion pricing,
combined with other operational interventions, and forecasting toll
revenues and associated operational performance at the corridor,
urban, and regional levels and (b) to identify potential improvements to the state of the art in DTA models and procedures that are
required for these tools to meet the above needs. Also, the paper
integrates heterogeneous user preferences and reliability valuation
into dynamic network models to forecast toll revenues in a largescale network application and therefore builds on previous studies
by Jiang et al. (1), Zhang et al. (2), and Jiang and Mahmassani (3).
The remainder of the paper is organized as follows. The second
section presents the methodology, including the ABM-DTA integration framework and the capturing of user responses, heterogeneity,
To forecast the impact of congestion pricing schemes, it is essential to
capture user responses to these schemes and the resulting dynamics of
traffic flow on the network. The responses of users must include route,
departure time, and mode choices. To capture the effects of these decisions, this paper lays out a framework for the integration of the relevant
elements of an activity-based model (ABM) with a dynamic traffic assignment (DTA) model and a simulation framework to support the analysis
and evaluation of various pricing schemes. In this paper, a multicriterion
dynamic user equilibrium traffic assignment model is used; the model
explicitly considers heterogeneous users who seek to minimize travel
time, out-of-pocket cost, and travel time reliability in the underlying route
choice framework. In addition to the methodological developments, various demand and supply parameters are estimated and calibrated for the
selected application network (the Greater Chicago, Illinois, network).
This paper showcases the integration of ABM components and a DTA in
one coherent modeling framework for the implementation and evaluation
of congestion pricing in an actual large-scale network.
With continued growth in travel demand, traffic congestion is perceived as one of the most pressing problems in urban and metropolitan areas. Addressing this issue generally involves some type
of improvement in roadway infrastructure or capacity, along with
a growing array of demand-side interventions. State departments
of transportation, metropolitan planning organizations, and other
transportation agencies are considering tolling and pricing options
as a source of funding, a means to manage congestion, and a way to
provide additional traveler options. This increase in interest and use
requires a better understanding of the issues that distinguish pricing
projects from traditional highway improvements and a framework
for making better and fully informed decisions on how, when, and
what to charge. Decisions regarding pricing projects must be based
A. Zockaie, H. S. Mahmassani, A. Frei, and T. Hou, Northwestern University
Transportation Center, 600 Foster Street, Evanston, IL 60208. M. Saberi,
Department of Civil Engineering, Monash University, Melbourne, Victoria 3800,
Australia. L. Jiang, Citilabs, 1211 Miccosukee Road, Tallahassee, FL 32308.
Corresponding author: H. S. Mahmassani, [email protected].
Transportation Research Record: Journal of the Transportation Research Board,
No. 2493, Transportation Research Board, Washington, D.C., 2015, pp. 78–87.
DOI: 10.3141/2493-09
78
Zockaie, Saberi, Mahmassani, Jiang, Frei, and Hou
and travel time reliability. The third section presents the application of the proposed framework to the large-scale network of the
Chicago, Illinois, metropolitan area. The fourth section presents the
simulation results, with different performance measures, at the network and corridor levels. The last section concludes the paper with
a summary and directions for future research.
Methodology
In this section, two methodological contributions are presented.
First, a framework for ABM-DTA integration is presented. Second,
a multicriterion dynamic user equilibrium (MDUE) traffic assignment model that considers the heterogeneity of network users is
presented for application to a large-scale network for toll revenue
forecasting.
ABM-DTA Integration
In analysis of pricing strategies for their impacts on the flows in a
network, it is necessary to consider that the demand, which is used
as an input for the network assignment, is affected by the changes in
the generalized cost function values produced in the traffic assignment. Thus, the integration of transport supply and demand models
is critical, as each model is formulated to use forecast outputs from
the other. The proposed framework for the integration of demand
models and DTA to evaluate pricing strategies has several parts but
does not suggest a full ABM-DTA integration as has been done in
other studies (4–6). Instead of a full ABM-DTA integration, this
study limits the integration aspects to the direct effects on demand
from a pricing strategy. This limit allows the evaluation of strategies without going into the computationally demanding full loop
with an ABM. First, a baseline travel demand with calibrated travel
costs and skims is generated and used to update the travel times and
79
cost skims by solving the MDUE. Second, the pricing strategies are
introduced at the network level. The changed supply at the network
level is then used to update the travel time and cost skims by solving the MDUE again. Third, the generated disaggregated user travel
time and cost are then fed back into the ABM model, in which the
travel time and cost skims propagate through the sequence of interrelated choices and particularly affect all the short- and mediumterm traveler decisions, as shown in Figure 1. This process includes
the direct impacts of pricing on mode, occupancy, and departure time
choices, through generalized cost functions, being included in the
utility expressions for each choice alternative.
However, in the medium to long term, the pricing strategies can
also indirectly affect further user decisions. This effect is illustrated in Figure 1: accessibility measurement calculations are taken
into account; in return, these measurements affect the upper-level
choices of car ownership and daily activity patterns and maybe even
the longer-term choices of home, workplace, and school location
(not illustrated).
MDUE Traffic Assignment Model
Jiang et al. developed an MDUE traffic assignment model that explicitly
considered heterogeneous users (1). Jiang et al. applied the proposed
model to the New York metropolitan regional network. However,
their application was limited to the demonstration of convergence
behavior and solution quality and required the computational time
of the MDUE algorithm. In this study, the same MDUE algorithm
is applied to the Chicago metropolitan area network, as a large-scale
network, to demonstrate the applicability of the algorithm at the operational level to the forecasting of toll revenues and the associated
operational performance at the corridor, urban, and regional levels.
Details of the MDUE problem formulation and solution algorithm
can be found in Jiang et al. (1) and Jiang and Mahmassani (3) and will
not be repeated here.
FIGURE 1 ABM-DTA integration framework (O-D 5 origin–destination).
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Transportation Research Record 2493
To fully capture user responses in a toll revenue forecasting model,
in addition to the common travel time measures, the MDUE model
used in this study considers two attributes in a generalized cost function: (a) the out-of-pocket cost—namely, the toll—which may vary
by the time of day and the state of the system (e.g., prevailing or predicted congestion) and with the user class (car versus truck, highoccupancy versus low-occupancy vehicles, etc.) and (b) a measure
of travel time reliability, which reflects the variability of the travel
times experienced along certain facilities and paths. In the generalized cost function, the travel time and reliability measures are
multiplied by corresponding values of time (VOTs) and reliability,
respectively, to convert the measures into cost units (money). This
function is defined for each network link and further calculated for
each origin–destination (O-D) pair for a given path. Furthermore, an
additional bias constant associated with priced facilities is included
(7). This bias can be most effectively incorporated into a binary choice
model, frequently referred to as the “per route choice,” that is placed
between the mode choice and the route choice. The generalized cost
function can be written as follows:
τ ,m
τ ,m
 α × TTodp + β × TTSD odp

,m
τ ,m
τ ,m
GCτodp
+ α × TTodp
(α ) = γ + TCodp

τ ,m
 + β × TTSD odp
if nontolled path
(1)
otherwise
where
GC
=generalized cost;
o=subscript for an origin node;
d=subscript for a destination node;
τ=superscript for a departure time interval;
m=superscript for a vehicle class and equal to one for a
single-occupancy vehicle, two for a two-person shared
ride, and three for a three or more person shared ride;
p=subscript for a path p ∈ P m(o,d,τ);
P m(o,d,τ)=set of all feasible paths for a given vehicle class m
and a triplet (o,d,τ);
α=VOT;
β=value of reliability;
γ=toll constant bias;
TT τ,m
experienced path travel time for all trips of vehicle
odp=
class m departing from o to d in time interval τ that
are assigned to path p ∈ P m(o,d,τ);
τ,m
TC odp=experienced path travel cost for all trips of vehicle
class m departing from o to d in time interval τ that
are assigned to path p ∈ P m(o,d,τ); and
TTSDτ,m
=
r
eliability measure (standard deviation of travel time
odp
per unit of distance) for all trips of vehicle class
m departing from o to d in time interval τ that are
assigned to path p ∈ P m(o,d,τ).
In the above generalized cost function, the parameters α and β
represent the individual trip makers’ preferences in the valuation of
the corresponding attributes. The VOT varies across travelers, trip
purposes, trip times and locations, sociodemographics, and so forth
(8, 9). This heterogeneity has profound implications for the procedures used to predict users’ path, mode, and departure time choices
when congestion pricing exists in the network. Several studies in
the past have recognized that VOT is a continuous variable that
is distributed probabilistically across the user population (10–14).
Significant efforts have been put into addressing user heterogeneity,
both in the static regime and the dynamic context, and have resulted
in a wide variety of assignment models (15–20). A thorough review
of assignment models under road pricing can be found in Lu et al.
(21). A methodological breakthrough in this regard is presented in
Lu et al. in the form of a parametric path-finding procedure that
allows the network topology to determine the VOT ranges for which
a particular least generalized cost path tree is optimal (21, 22). This
approach has been integrated into a simulation-based equilibrium
DTA procedure and demonstrated in the recent publications of Jiang
et al. (1) and Jiang and Mahmassani (3).
Empirical evidence suggests that travelers value travel time reliability in addition to travel time (12, 13, 23). For instance, the socalled value of reliability index, which captures the willingness to
pay for a 1-min reduction in the standard deviation of travel time
(as an example measure of unreliability) has been found to be in the
range of 0.8 to 1.5 of the VOT that a traveler places on the reduction
of 1 min of average travel time (24). To incorporate this measure into
the integrated model, it is necessary to devise a method to generate
the measure for the respective paths and O-D pairs in connection
with the movement of vehicles through the network. The two most
basic statistics are the mean and the standard deviation, one depicting
the central tendency and the other describing the dispersion of the
distribution. Usually, the average travel time of a trip is relatively
easy to obtain and is either perceived, measured, or obtained from
theory or models; obtaining or predicting the standard deviation is
more challenging. It is assumed that there is a linear relationship
between the mean travel time per unit of distance and its standard
deviation, as follows:
σ ( t ′ ) = θ1 + θ2 E ( t ′ ) + ε
(2)
where
σ(t′)= standard deviation of travel time per unit of distance,
E(t′)=mean value of travel time per unit of distance,
θ1 and θ2=coefficients to be estimated, and
ε=random error.
For more details and comprehensive background, see Mahmassani
et al. (25).
This model leverages a simple yet robust relationship that can be
used to estimate the standard deviation of the travel time per unit
of distance when the average value is available. First established in
Mahmassani et al. on the basis of actual traffic observations (26), the
relationship has been recently investigated in greater depth through
the use of actual traffic data and simulation experiments (25, 27).
It has been shown that the average travel time per unit of distance
and its standard deviation are highly correlated and that the model
is valid on a multiscale and multilevel basis. It has also been shown
that this relationship is better applied at the path level than at the link
level. The preferences for reliability may also reflect heterogeneity.
The same approach used in this study for VOT may be extended to
incorporate both reliability and heterogeneity.
In addition to varying VOT and travel time reliability, this study
considers different vehicle classes (single-occupancy vehicles, a
shared ride of two persons, and a shared ride of three or more persons). Auto occupancy has a very strong impact on the generalized
cost function, as discussed before, and high-occupancy vehicles
tend to use the tolled facility and save on travel time, since the cost
(toll charges) can be shared between the driver and the passengers.
The treatment in this application is, then, the division of travel
cost (toll charges) by the number of occupants in the vehicle. For a
Zockaie, Saberi, Mahmassani, Jiang, Frei, and Hou
81
given tolled path, from origin o to destination d, departing at time τ,
vehicles from different auto occupancy groups view the travel cost
differently:
In the next section, the MDUE with the above-mentioned specifications will be applied to the large-scale network of Chicago, in line
with the ABM and DTA integration, to consider the effects of congestion pricing on network users’ route and mode choices and forecast
the toll revenues under different congestion pricing scenarios.
stant of $3.48, a value of reliability of $2.42/mi/min, a mean VOT of
$10/h, a minimum VOT of $0.67/h, and a maximum VOT of $50/h.
See Figure 3 for the estimated travel time distributions.
To capture the heterogeneity of reliability performance within
the network, the entire Chicago network is divided into 11 areas on
the basis of the population density and some geographic boundaries
(25, 27). Iterative DTA is performed to achieve user equilibrium and
time-varying O-D demand, calibrated with historical data. On the
basis of the simulated vehicle trajectories, the total travel time and total
travel distance of each vehicle are extracted, and thus the travel time
per unit of distance is calculated. Also, for each single path, the standard deviation of the travel times is computed. As the entire network
is divided into 11 areas, the paths are grouped into 121 (11 times 11)
groups, according to the O-D area that the paths belong to. For each
group, statistical linear regression analysis is conducted to calibrate
the relationship between the mean travel time per unit of distance and
its standard deviation.
Application to a Large-Scale Network
Pricing Schemes
Network and Time-Dependent Travel Demand
Three pricing schemes are considered for the Chicago network
application. The first pricing scheme is the do-nothing option. This
scenario is called “current pricing,” and the forecasted demand is
simulated in the current Chicago network with the existing toll
facilities. Additional lanes and new links are added to the current
network to create the future network on the basis of the design
study by CMAP (30). The future network includes 79 new links and
32 new nodes.
The second scheme is the fixed schedule pricing, in which the
forecasted demand is simulated in the future network. This pricing
scheme is suggested by CMAP and therefore named the “CMAP
pricing scheme” in this paper (30). Under this scenario, in addition
to the existing pricing scheme, two fixed toll rates (set by CMAP)
for peak (7:00 to 9:00 a.m.) and non–peak periods are considered
for new links and lanes. During the non–peak hours, a base toll is
implemented, and during peak hours an additional toll is added to
the nonpeak base toll to maintain a free-flow state on the tolled
lanes. The additional toll charge for a specific facility in the peak
period is assigned on the basis of the excessive delay caused by
congestion relative to the free-flow travel time.
τ
TCodp

 TCτodp

τ ,m
TCodp =  2
 τ
 TCodp
 3
if m = 1
if m = 2
(3)
if m = 3
The Chicago regional network is the study network (see Fig­
ure 2a). The network includes 40,443 links, 13,093 nodes, and
1,961 zones. The simulation horizon is 6:00 to 10:00 a.m. (240 min).
In total, 6,332,185 vehicles are generated with different VOTs. Figure 2b shows the demand profile for 240 min of simulation, obtained
from the CT-RAMP model, the ABM for highway pricing studies at the
Chicago Metropolitan Agency for Planning (CMAP) (28). (Minute 0
of the simulation corresponds to 6:00 a.m.) This demand is generated in 0.5-h time intervals by CT-RAMP, and the trips are distributed
uniformly over these time intervals by DYNASMART-P.
Estimation of Behavioral Parameters
The behavioral parameters are estimated on the basis of the CTRAMP model and estimates of route choice models based on
revealed preference data from the New York City area (28, 29). The
following behavioral parameters are used in this study: a toll con-
Number of Vehicles (per 30 min)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
0
50
100
150
Simulation Time (min)
(a)
FIGURE 2 Chicago (a) metropolitan area network and (b) demand profile for 6:00 to 10:00 a.m.
(b)
200
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Transportation Research Record 2493
Density
Income $0–$30,000
Income $30,000–$60,000
Income $60,000–$100,000
Income $100,000+
VOT ($/h)
FIGURE 3 VOT distributions based on Parsons Brinckerhoff study (28).
The third scheme is the state-dependent pricing. The forecasted
demand and the future network are used in the simulation. In addition to the existing pricing scheme, toll charges on the new lanes and
links are calculated on the basis of the simulated time-dependent link
travel times. In this scenario, the additional toll charges are implemented in peak and non–peak periods, and the amount is updated
every 10 min on the basis of the calculated delay in the previous
10-min interval. In the fixed schedule pricing, the additional toll is
implemented just in the peak hours and is a fixed amount, based on
a static traffic assignment. The state-dependent tolls on each facility are calculated as the product of delay on the facility in minutes
and the regional average VOT. The latter quantity was estimated
through the use of the ABM results. The toll charges are calculated
by the following expression:
toll = ( TT − TT
τ
i
τ
i
free
i
)×α
avg
(4)
where
i=tolled facility,
τ=time interval,
TTτi=current travel time on tolled facility i at time interval τ,
TTifree=free-flow travel time on tolled facility i, and
αavg=average VOT.
Network-Level Performance
Travel Time
The average travel times and total travel times are calculated for
all the vehicles that have reached their destinations at the end of
simulation. Figure 4 compares the estimated average and total travel
times under each pricing scheme. The results demonstrate that statedependent pricing results in slightly smaller average and total travel
times at the network level. The results also suggest that applying a
fixed toll rate may not necessarily improve the average and total
travel times at the network level.
Total Revenue
The forecasted revenue generated from the tolled links during the simulation period is summarized in Table 1. As shown, the CMAP and
state-dependent pricing schemes both generate more revenue than the
current pricing scheme. The revenue generated by the existing tolled
links is more or less the same for all three schemes. Also, it is estimated
that the revenue generated by the existing tolled links (144 links) is
greater than the revenue generated by the new tolled links (66 links)
because of the larger number of lanes in those links and, as a result,
the larger number of users. The state-dependent pricing increases the
revenue per day, even for the existing links.
Simulation Results
On the basis of the simulated vehicle trajectories obtained from
DYNASMART-P, a range of mobility-related performance measures,
such as travel time, travel speed, and waiting times, is extracted and
analyzed at various levels (e.g., the network, facility, O-D or path,
and link levels). In this section, selected results at the network and
facility levels are presented.
Facility-Level Performance
This section provides facility-level analysis for a selected tolled
facility in Chicago on the basis of the simulation results from the
three pricing schemes described earlier in the paper. Here, select
results from I-55 eastbound are presented and discussed. This facility
83
Total Travel Time (h)
Average Travel Time (min)
Zockaie, Saberi, Mahmassani, Jiang, Frei, and Hou
Scenario
Scenario
(a)
(b)
FIGURE 4 Travel times of completed vehicles at end of simulation for three pricing scenarios.
has four lanes in each direction. In the future network, one additional
toll lane is added in each direction.
Toll Revenue
Figure 5 presents the toll rate and revenue profiles of I-55 eastbound under the CMAP and state-dependent pricing schemes. The
toll rates are estimated to be higher during peak hours than during off-peak hours for both pricing schemes. The CMAP pricing
scheme has fixed rates during the peak period 7:00 to 9:00 a.m., and
the state-dependent scheme has a time-varying rate for the entire 4-h
morning peak. Therefore, the toll revenue–generated profiles have
different temporal trends.
Throughput
Figure 6 presents the average cumulative throughput profiles of the
same facility. Under the CMAP pricing scheme, the throughput of
the future tolled lane plus the nontolled lanes is roughly the same
as the throughput of the current nontolled lanes. Under the statedependent pricing scheme, the throughputs in the future tolled plus
nontolled lanes have considerably higher values. This finding demonstrates an inefficient utilization of the newly added lane when the
pricing scheme is not correctly designed.
TABLE 1 Toll Revenue Generated from Three Pricing Scenarios
over the Morning Peak Period, 6:00 to 10:00 a.m.
Pricing Scheme
Revenue
Generated by
Existing Links
($)
Revenue
Generated by
New Links
($)
Total Revenue
($)
Current
CMAP
State-dependent
141,924.00
139,651.00
142,481.00
na
58,511.00
63,176.40
141,924.00
198,162.00
205,657.40
Note: na = not applicable.
Breakdown Mitigation
Figures 7 and 8 show the flow and speed profiles for a portion of
I-55 eastbound. Figure 7 compares the flow and speed profiles for
a nontolled lane of the selected facility under different pricing
schemes. Figure 8 shows the flow and speed profiles under the
CMAP and state-dependent pricing schemes for a new toll lane,
which will be added to the network in future. In the nontolled lane,
the flow profile does not change significantly in any of the scenarios.
Also, flow breakdown occurs in every scenario, albeit with different start times and durations. For the CMAP and state-dependent
pricing schemes, but not the current pricing scheme, the flow breakdown recovers. The state-dependent pricing scheme has the shortest
breakdown duration. The results show that flows and speeds are
both higher in the priced lane for the state-dependent scheme than
for the CMAP fixed pricing. Although a relatively small and short
speed drop occurs in both scenarios for the tolled lane (Figure 8), an
abrupt breakdown is not observed.
Mode Choice
As mentioned earlier, the input demand used here by DTA to simulate traffic and compare different congestion pricing scenarios is
generated by an ABM equilibrated on the basis of static skims. A
mode choice model is developed on the basis of time-dependent
travel times, estimated by DTA, to compare the mode shares with
the ABM results. Here, the mode shares, based on the estimated
mode choice model, are shown for the selected O-Ds. To compare
the resulting mode shares from the DTA and the mode shares directly
obtained from the ABM, comparative stacked column charts are
plotted and shown in Figure 9 for four selected O-Ds. For Geneva,
Illinois, to the Chicago central business district, the transit share
increases from 47% to 49%, the park-and-ride share decreases from
48% to 46%, and the auto share remains the same. For Forest Park,
Illinois, to the Chicago central business district, a large shift from
transit to park and ride occurs. The transit share decreases from 53%
to 38%, and the park-and-ride share increases from 1% to 13%.
The change in the auto share is as small as 2%. For Joliet, Illinois,
to the Chicago central business district, a large drop from 18% to
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Transportation Research Record 2493
500
4
Joint 3
3.5
Revenue ($)
Toll Rate ($)
3
2.5
2
1.5
1
300
200
0
50
100
150
200
Time (min)
250
0
300
10
30
50
70
(a)
500
Joint 3
3.5
Joint 2
Single
400
Revenue ($)
3
Toll Rate ($)
90 110 130 150 170 190 210 230
Time (Min)
(b)
4
2.5
2
1.5
1
300
200
100
0.5
0
Single
100
0.5
0
Joint 2
400
0
50
100
150
200
Time (min)
250
0
300
10
(c)
30
50
70
90 110 130 150 170 190 210 230
Time (Min)
(d)
FIGURE 5 Financial profiles on I-55 eastbound (I-355 to I-90/94): (a) toll rate, CMAP; and (b) revenue, CMAP; (c) toll rate, state-dependent
pricing; and (d) revenue, state-dependent pricing (Joint 2 and Joint 3 represent a shared ride of two persons or three or more persons,
respectively).
Current nontolled lanes
Future nontolled lanes
Future tolled lanes
10,000
5,000
0
0
50
100
150
200
Simulation Time (min)
(a)
74% to 57%. The significant differences between the mode shares
before and after DTA simulation call for the equilibrium state to be
based on dynamic skims. The estimated changes in the networkwide
travel times and travel costs attributable to different pricing strategies are too small to produce considerably different mode shares
over the network for the three simulated pricing scenarios.
Cumulative Thoughput
Cumulative Thoughput
8% occurs for the auto share. The transit share increases from 56%
to 66%, and the park-and-ride share increases from 25% to 27%.
For Naperville, Illinois, to the Chicago central business district, a
considerable shift occurs from transit to auto and park and ride.
The auto share increases from 12% to 22%, the park-and-ride share
increases from 14% to 21%, and the transit share decreases from
Current nontolled lanes
Future nontolled lanes
Future tolled lanes
10,000
5,000
0
0
50
100
150
200
Simulation Time (min)
(b)
FIGURE 6 Average cumulative throughput on I-55 eastbound express lane (I-355 to I-90/94)
for (a) CMAP and (b) state-dependent pricing schemes.
1,500
1,000
500
0
0
50
100
150
200
Simulation Time (min)
85
Average Speed (mph)
Flow (vphpl)
Zockaie, Saberi, Mahmassani, Jiang, Frei, and Hou
100
50
0
0
1,500
1,000
500
0
0
50
100
150
200
Simulation Time (min)
(d)
Average Speed (mph)
Flow (vphpl)
(a)
100
50
0
0
1,000
500
0
0
50
100
150
200
Simulation Time (min)
(c)
50
100
150
200
Simulation Time (min)
(e)
Average Speed (mph)
Flow (vphpl)
(b)
1,500
50
100
150
200
Simulation Time (min)
100
50
0
0
50
100
150
200
Simulation Time (min)
(f)
0
0
50
100
150
200
Simulation Time (min)
(a)
1,000
0
0
50
100
150
200
Simulation Time (min)
(b)
Average Speed
(mph)
1,000
100
Average Speed
(mph)
Flow (vphpl)
Flow (vphpl)
FIGURE 7 Flow versus speed on a nontolled link on I-55 eastbound (I-355 to I-90/94) for
state-dependent (top), CMAP (middle), and current (bottom) pricing schemes (vphpl = vehicles
per hour per lane).
100
50
0
0
50
100
150
200
Simulation Time (min)
(c)
0
50
100
150
200
Simulation Time (min)
50
0
(d)
FIGURE 8 Flow versus speed on a tolled link on I-55 eastbound (I-355 to I-90/94) for
state-dependent (top) and CMAP (bottom) pricing schemes.
Transportation Research Record 2493
100
100
80
80
60
Auto
Transit
40
Park and ride
Mode Share (%)
Mode Share (%)
86
20
60
Auto
Transit
40
Park and ride
20
0
0
DTA
ABM
DTA
Method
ABM
Method
(b)
100
100
80
80
60
Auto
Transit
40
Park and ride
20
Mode Share (%)
Mode Share (%)
(a)
60
Auto
Transit
40
Park and ride
20
0
0
DTA
ABM
Method
DTA
ABM
Method
(c)
(d)
FIGURE 9 Comparative O-D specific mode share estimations by ABM and DTA between Chicago central business district and (a) Geneva,
(b) Forest Park, (c) Joliet, and (d) Naperville.
Conclusion
The main goal of this study was to forecast toll revenues and the operational impacts associated with congestion pricing strategies. To do
so, the paper proposed a framework for integrating an ABM with DTA.
The Chicago metropolitan area network, as a large-scale network with
an established tradition of road pricing, was selected. Also, a locally
calibrated ABM was used to forecast the demand and estimate the
behavioral parameters. To capture the heterogeneity of the reliability
characteristics within the network, the entire Chicago network was
divided into several areas on the basis of the population density and
geographic boundaries. Iterative DTA was performed to achieve user
equilibrium with time-varying O-D demand, calibrated on the basis
of historical data. On the basis of the simulated vehicle trajectories
for different groups of paths, statistical linear regression analysis was
conducted to calibrate the relationship between the mean travel time
per unit of distance and its standard deviation. Overall, the paper demonstrated an application of the MDUE, integrated with an ABM, to
a large-scale network for toll forecasting. To assess the impacts and
generated revenue of the selected congestion pricing schemes, various performance measures were measured and discussed at different
levels. The numerical results showed that congestion pricing could
potentially improve the performance measures (including revenue,
travel time, and throughput) in addition to the effects on mode shares.
In this study, the effects of congestion pricing on network users’
short- to medium-term decisions, including route and mode choice,
were explored. Users’ medium- to long-term decisions, such as vehicle ownership and residential location choice, may also be affected
by congestion pricing. This direction is an important one for future
research. Furthermore, the ABM and DTA integration, and the MDUE
used in this study, are trip based. To consider long-term decisions, it
is preferable to use a user-based approach, in which a chain of trips is
defined for each network user. In such a case, the equilibrium concept
should be revisited. Also, the minimization of the generalized cost
function along trip paths will no longer be sufficient to define and
attain an equilibrium state.
Zockaie, Saberi, Mahmassani, Jiang, Frei, and Hou
Acknowledgments
This research was supported by the U.S. Department of Transportation’s Office of Operations, under a task order titled Modeling
and Forecasting of Toll Revenues, performed under subcontract to
Science Applications International Corporation, Inc. The authors
acknowledge the helpful comments of Darren Timothy and John
Halkias of FHWA and Forrest Swisher of Science Applications International Corporation, Inc. The authors also appreciate the assistance
of CMAP staff, especially Kermit Wies, in making data available
for the study. The study team has also benefited from the advice of
Peter Vovsha of Parsons Brinckerhoff, who developed the ABM for
CMAP.
References
1. Jiang, L., H. S. Mahmassani, and K. Zhang. Congestion Pricing, Heterogeneous Users, and Travel Time Reliability: Multicriterion Dynamic
User Equilibrium Model and Efficient Implementation for Large-Scale
Networks. In Transportation Research Record: Journal of the Transportation Research Board, No. 2254, Transportation Research Board of the
National Academies, Washington, D.C., 2011, pp. 58–67.
2. Zhang, K., H. S. Mahmassani, and C. Lu. Dynamic Pricing, Heterogeneous
Users and Perception Error: Probit-Based Bi-Criterion Dynamic Stochastic User Equilibrium Assignment. Transportation Research Part C,
Vol. 27, 2013, pp. 189–204.
3. Jiang, L., and H. S. Mahmassani. Toll Pricing: Computational Tests
for Capturing Heterogeneity of User Preferences. In Transportation
Research Record: Journal of the Transportation Research Board,
No. 2343, Transportation Research Board of the National Academies,
Washington, D.C., 2013, pp. 105–115.
4. Willem, H., F. Viti, and C. M. J. Tampère. State of the Art on the Integration of Dynamic Traffic Assignment and Activity Based Models. Proc.,
Benelux Interuniversity Association of Transport Researchers Transport
Research Day, Namur, Belgium, 2011, pp. 24–30.
5. Chiu, Y. C., A. Khani, H. Noh, B. Bustillos, and M. Hickman. SHRP
2 Report: Technical Report on SHRP 2 C10B Version of DynusT and
FAST-TrIPs. Transportation Research Board of the National Academies,
Washington, D.C., 2013.
6. Javanmardi, M., J. Auld, and K. Mohammadian. Integration of TRANSIMS
with the ADAPTS Activity-Based Model. Presented at 4th Conference
on Innovations in Travel Modeling, Tampa, Fla., 2011.
7.Parsons Brinckerhoff. NCHRP Report 722: Assessing Highway Tolling
and Pricing Options and Impacts. Volume 2: Travel Demand Forecasting Tools. Transportation Research Board of the National Academies,
Washington, D.C., 2010.
8. Small, K. A., and C. Winston. The Demand for Transportation: Models
and Applications. In Essays in Transportation Economics and Policy:
A Handbook in Honor of John R. Meyer (J. Gomez-Ibanez, J. Tye, and
C. Winston, eds.), Brookings Institution Press, Washington, D.C., 1999,
pp. 11–55.
9. Wardman, M. A. Review of British Evidence on Time and Service Quality Valuations. Transportation Research Part E, Vol. 37, No. 2–3, 2001,
pp. 107–108.
10. Ben-Akiva, M., D. Bolduc, and M. Bradley. Estimation of Travel Choice
Models with Randomly Distributed Values of Time. In Transportation
Research Record 1413, TRB, National Research Council, Washington,
D.C., 1993, pp. 88–97.
11. Small, K. A., and J. Yan. The Value of “Value Pricing” of Roads: SecondBest Pricing and Production Differentiation. Journal of Urban Economics,
Vol. 49, No. 2, 2001, pp. 310–336.
12. Brownstone, D., and K. A. Small. Valuing Time and Reliability: Assessing the Evidence from Road Pricing Demonstrations. Transportation
Research Part A, Vol. 39, No. 4, 2005, pp. 279–293.
13. Small, K. A., C. Winston, and J. Yan. Uncovering the Distribution of
Motorists’ Preferences for Travel Time and Reliability. Econometrica,
Vol. 73, No. 4, 2005, pp. 1367–1382.
87
14.Cirillo, C., and K. W. Axhausen. Evidence on the Distribution of
Values of Travel Time Savings from a Six-Week Diary. Transportation
Research Part A, Vol. 40, No. 5, 2006, pp. 444–457.
15. Yang, H., W. H. Tang, W. M. Cheung, and Q. Meng. Profitability and
Welfare Gain of Private Toll Roads in a Network with Heterogeneous
Users. Transportation Research Part A, Vol. 36, 2002, pp. 537–554.
16. Yang, H., and H. Huang. The Multi-Class, Multi-Criteria Traffic Network
Equilibrium and Systems Optimum Problem. Transportation Research
Part B, Vol. 38, 2004, pp. 1–15.
17. Zhang, X., H. Yang, and H. Huang. Multiclass Multicriteria Mixed
Equilibrium on Networks and Uniform Link Tolls for System Optimum. European Journal of Operations Research, Vol. 189, No. 1, 2008,
pp. 146–158.
18. Cantarella, G. E., and M. Binetti. Stochastic Equilibrium Traffic Assignment with Value-of-Time Distributed Among Users. Transport Operational Research, Vol. 5, No. 6, 1998, pp. 541–553.
19. Nielsen, O. A. A. Stochastic Route Choice Model for Car Travelers in
the Copenhagen Region. Networks and Spatial Economics, Vol. 2, 2002,
pp. 327–346.
20. Mahmassani, H. S., X. Zhou, and C.-C. Lu. Toll Pricing and Heterogeneous Users: Approximation Algorithms for Finding Bicriterion
Time-Dependent Efficient Paths in Large-Scale Traffic Networks.
In Transportation Research Record: Journal of the Transportation
Research Board, No. 1923, Transportation Research Board of the
National Academies, Washington, D.C., 2005, pp. 28–36.
21. Lu, C. C., H. S. Mahmassani, and X. Zhou. A Bi-Criterion Dynamic
User Equilibrium Traffic Assignment Model and Solution Algorithm for
Evaluating Dynamic Road Pricing Strategies. Transportation Research
Part C, Vol. 16, No. 4, 2008, pp. 371–389.
22. Lu, C. C., H. S. Mahmassani, and X. Zhou. Equivalent Gap Function–
Based Reformulation and Solution Algorithm for the Dynamic User
Equilibrium Problem. Transportation Research Part B, Vol. 43, 2009,
pp. 345–364.
23. Lam, T., and K. Small. The Value of Time and Reliability: Measurement
from a Value Pricing Experiment. Transportation Research Part E, Vol. 37,
2001, pp. 231–251.
24. Parsons Brinckerhoff. SHRP 2 Report S2-C04-RW-1: Improving Our
Understanding of How Highway Congestion and Price Affect Travel
Demand. Transportation Research Board of the National Academies,
Washington, D.C., 2013.
25. Mahmassani, H. S., T. Hou, and J. Dong. Characterizing Travel Time
Variability in Vehicular Traffic Networks: Deriving a Robust Relation
for Reliability Analysis. In Transportation Research Record: Journal of the Transportation Research Board, No. 2315, Transportation
Research Board of the National Academies, Washington, D.C., 2012,
pp. 141–152.
26. Mahmassani, H. S., E. Jones, R. Herman, and C. M. Walton. Travel Time
Variability in a Commuting Corridor: Implications for Electronic Route
Guidance. Proc., 1st International Conference on Application of Advanced
Technologies in Transportation Engineering, San Diego, Calif., 1989.
27. Mahmassani, H. S., T. Hou, and M. Saberi. Connecting Networkwide
Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow. In Transportation Research Record: Journal of the Transportation Research Board, No. 2391, Transportation Research Board of the
National Academies, Washington, D.C., 2013, pp. 80–91.
28. Parsons Brinckerhoff. Activity-Based Model for Highway Pricing Studies at Chicago Metropolitan Agency for Planning (CMAP). Chicago
Metropolitan Agency for Planning, Ill., 2011.
29. Parsons Brinckerhoff. Transportation Models and Data Initiative: General Final Report: New York Best Practice Model. New York Metropolitan Transportation Council, 2005. http://www.nymtc.org/project/bpm
/model/bpm_finalrpt.pdf.
30. Congestion Pricing: An Analysis of the Go To 2040 Major Capital
Projects. Chicago Metropolitan Agency for Planning, Ill., 2012.
http://www.cmapweb02.thirdwavellc.com/documents/379669
/9b5465ad-5797-4c54-95e9-e170906d8e56.
The authors remain solely responsible for all contents of the paper.
The Standing Committee on Transportation Demand Forecasting peer-reviewed
this paper.