International Symposium of Transport Simulation 2014

Development of a Network Traffic Simulator for
the Entire Inter-urban Expressway Network in Japan*

Shoichi Hirai a , Jian Xinga, Ryota Horiguchib,Tomoyoshi Shiraishib, Masato KobayashibaNippon Expressway Research Institute Co., Ltd.,1-4-1 Tadao Machida-shi Tokyo, Japanb
i-Transport Lab. Co., Ltd., 3-10 Kanda-Ogawamachi, Chiyoda-ku, Tokyo, Japan

Abstract
This paper describes the development of a network traffic simulator for the entire inter-urban expressway network inJapan. With recent developments, the network topology is getting more complex, and traffic prediction based on
statistical analysis is becoming harder since it does not take into account the drivers’ behavioural changes on the
network. Looking at the issue from the seeds and needs perspective, there would be needs to develop a network
traffic simulator dealing with traffic flow dynamics and driver behaviors. From the seeds side, road operators are now
motivated to utilize the electronic toll collection (ETC) trip data collected every time a vehicle passes an ETC tollgate
located at interchanges. Fully using ETC data is expected to improve the accuracy of time-dependent O-D matrix androute choice behavior model which is important in simulation studies. In this paper, the concept of traffic modelingand route choice behavior modeling in the expressway network simulation will be described, followed by calibrationof time-dependent O-D matrix.

© 2014 Published by Elsevier Ltd. Selection and peer-review under responsibility of ISTS 2014
Keywords: traffic simulation, expressway network, O-D matrix calibration, route choice behavior*

Corresponding author. Tel.: +81-42-7911679.
E-mail address: s.hirai.aa@ri-nexco.co.jp (S. Hirai)

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1. Introduction
This paper describes the development of a network traffic simulator for the entire inter-urban
expressway network in Japan (Fig. 1). Inter-urban expressways stretch for more than 8,000 km over Japanand serve approximately 5 million trips per day. There are more than 20,000 detectors installed on theexpressways, collecting vehicle counts and speeds every 5 minutes.

Fig. 1: Inter-urban expressway network in JapanThe road-operator companies use this traffic sensor data to predict traffic congestion caused by
weekend leisure traffic, road works, incidents, etc. So far, they simply apply statistical analysis of thetravel purposes and their expertized heuristic knowledge to make the prediction. With recent
developments, however, the network topology is getting more complex, and traffic prediction is
becoming harder since statistical analysis does not take into account the drivers’ behavioral changes on
the network. Therefore, there is a need to develop a network traffic simulator based on traffic flow
dynamics to deal with traffic congestion, considering driver behaviors.
Looking at the issue from the seeds side, road operators are now motivated to utilize the electronic tollcollection (ETC) trip data, collected every time a vehicle passes an ETC toll gate located at interchanges.
Nowadays, ETC is used in close to 90% of the total number of trips on expressways. Fully using ETC
data, therefore, is expected to improve the accuracy of time-dependent O-D matrix and route choice
behavior model which is important in simulation studies.
In the following chapters, the concept of traffic modeling and route choice behavior modeling in theexpressway network simulator (ENS) will be described, followed by calibration of time-dependent O-D
matrix.

Hirai et al./ ISTS2014 Corsica

2. Modeling concept of the Expressway Network Simulator
The ENS is developed based on a mesoscopic traffic simulation model, SOUND [SOUND, 2014],
which was developed at the University of Tokyo [Yoshii and Kuwahara, 1995] and has been revised
through its use in many practical studies. This chapter outlines major modeling components in SOUND
and their modifications for the ENS.
2.1. Discrete vehicle trip generation with time-dependent O-D matrix
SOUND deals with the discretized trip of each vehicle attributing its origin, destination, departure time,
vehicle type, etc. The trip generation number of each vehicle type is aggregated to time-dependent O-D
matrix with designated time interval. At the beginning of each interval, all generated vehicles areaccumulated into the departure queue of their origins. The accumulated vehicles are randomly shuffledand provided their departure times in the interval according to the Poisson arrival model.
In the case of the ENS, the time interval is set to 15 minutes. As a ramp link at an interchange isconnected to an origin and destination point (centroid), as shown in Fig. 2, there are more than 1300
interchanges in the entire network of the ENS, resulting in approximately 1.7M O-D pairs for each timeinterval and vehicle type.

Centroid

Fig. 2: A centroid connecting to interchange ramp links

2.2. Modelling of traffic flow dynamics
2.2.1. Flow-density evolution with the kinematic wave theory
Fig. 3 shows the inner-link structure adopted by SOUND, i.e. a link length L consists of a vehicle
queue for the thru-lanes and queues for the auxiliary lanes, if they exist, at both left and right sides of theroad. A vehicle arriving at the link is pushed at the end of the thru lane queue, and will be ready todischarge after the lapse time L/vf. The vehicle ready to discharge will be removed from the thru queue
keeping the first-in-first-out law, unless the discharging flow rate per unit time exceeds qd. A vehicle
changing the lane is exceptionally extracted from the middle of the thru lane queue when the vehicle
reaches the upstream end of the auxiliary lane, and is added to the end of the auxiliary lane queue.

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Hirai et al. / ISTS2014 Corsica

Auxiliary lane queue
Direction

Thru lane queue

L

Fig. 3: Inner-link spatial components of SOUND

Similar to other mesoscopic traffic simulation models (e.g. [Dynasmart, 2011], [INTEGRATION,
2014], etc.), SOUND maintains traffic density and vehicle positions on a link, second by second,according to the fundamental diagram of traffic flow. As shown in Fig. 4, SOUND uses the triangularapproximation of flow-density relationship which is parameterized with vf – free flow speed, kj – jamdensity, qc – link capacity. Another parameter, qd, is given to regulate the discharging flow rate from thethru lane queue.
Flow
qc
qd

vf
0

w
kc

kj

DensityFig. 4: Triangular approximation of the flow-density relationship of fundamental diagram

As for the queue length and the vehicle position update, SOUND features the simplified kinematicwave theory (K-wave) [Newell, 1993]. Fig. 5 illustrates the update procedure. The upper graph is the
cumulative flow diagram of a link where A* denotes the cumulative demand curve to the link (i.e. readyto-discharging flow from the upstream link) and D denotes the cumulative discharging flow curve theslope of which is regulated by qd. The backward wave occurring at the downstream end reaches to the
upstream end and forms the cumulative curve D’ which is given by shifting D to the right with w-1L and to
the top with kjL. As D’ means the acceptable cumulative flow to this link, the cumulative arrival flow
curve A can be drawn by taking the lower curves either A* or D’.
The cumulative flow curve Q(x) at a certain middle section x distance from the upstream end of the link
can be drawn with the same procedure, namely by taking the lower curves of either the forward wave or
the backward wave. The forward wave from the upstream end will reach x to form the cumulative curveA(x) which is given by shifting A to the right with vf-1x. The backward wave forms D(x) at the section x thecurve of which is given by shifting D to the right with w-1(L-x) and to the top with kj(L-x).
SOUND calculates the cumulative flows for every inner-link sections discretized with x interval
iteratively applying the procedure above. The location of the i-th vehicle the cumulative volume of whichis Q at the upstream end can be found between the section where Q(x)  Q and Q < Q(x+x).

Hirai et al./ ISTS2014 Corsica

5

Cum. #A A* A(x) D’

kjL

w-1L
vf-1x

w-1(L-x)
kj(L-x)

D(x)
D
time

distanceLsaturated flowk = kcJamk = kjx

free flowk < kcpresent

time

Fig. 5: Shockwave propagation and inner-link traffic status updated by the K-wave theory

2.2.2. Consideration of bottleneck capacity change for a stationary bottleneck
It is known that the capacity of an expressway bottleneck changes depending on various factors, e.g.
day of week, lighting conditions, weather conditions, etc. [Ishida and Xing, 2000], as shown in Fig. 6.
Also known is that the flow rate peaks just before congestion starts, and gradually drops as the queue
grows.
The ENS emulates those phenomena by adjusting the discharging capacity of SOUND link dependingon time of day and the lapse duration from the start of congestion. Fig. 7 is an example of the capacity
and the flow rate changes at a bottleneck section. In this case, the discharging capacity qd is initially set tothe level of BDF (break-down flow rate). Once the demand rate exceeds qd and a queue forms, the ENS
watches the average travel speed of the bottleneck section. When the travel speed becomes lower than thethreshold speed, (a) the ENS gradually reduces qd to the level of QDF (queue discharging flow rate). The
level of QDF varies during twilight (b) and nighttime (c).
For the practical use of the ENS, the parameters BDF and QDF for 465 known bottleneck sections on
the expressways were calibrated through analysis of detector data collected over 5 years, if incidence ofcongestion is enough. Otherwise, let us follow the capacity model proposed by [Ishida and Xing, 2000] asshown in Table 1.

6Hirai et al. / ISTS2014 Corsica

Daytime vs twilight

Daytime vs nighttime
6000

6000

N =43

（

薄
明 4500

N = 2

5000

夜 4500▲7.5%

台 4000／時
3500

台 4000／時 3500
）

）

BDF

▲1.2%

Nighttime [veh/hr]

5500

5000

（

Twilight [veh/hr]

5500

3000

3000

2500

2500

2000
2000 2500 3000 3500 4000 4500 5000 5500 6000

2000
2000 2500 3000 3500 4000 4500 5000 5500 6000

昼（台／時）
Daytime[veh/hr]※分析サンプル数が3サンプル以上の地点を対象

6000

6000

N =46

（

薄
明 4500▲1.7%

Nighttime [veh/hr]

5500

5000

N =27

5000

（

Twilight [veh/hr]

5500

夜 4500▲6.6%

台 4000／時
3500）

台 4000／時 3500）QDF

昼（台／時）
Daytime[veh/hr]※分析サンプル数が3サンプル以上の地点を対象

3000

3000
2500

2500
2000
2000 2500 3000 3500 4000 4500 5000 5500 6000

2000
2000 2500 3000 3500 4000 4500 5000 5500 6000

昼（台／時）

昼（台／時）
Daytime[veh/hr]

Daytime [veh/hr]

Fig. 6: The capacity drop rate for twilight and night to daytime [Ishida and Xing, 2000]

6000

DemandBDF

Flow [veh./hr]

5000

QDF
4000

Throughput
3000

(a)

2000
1000

(b)

Daytime

0
16:00

17:00

Twilight
18:00(c)Nighttime

19:00

20:00

21:00

22:00

20:00

21:00

22:00

Time of day

Av. Speed [km/hr]

120

Av. travel speed

100
80
60
40

Threshold speed

20
0
16:00

17:00

18:00

19:00
Time of day

Fig. 7: The capacity and flow rate changes at a bottleneck section on the ENS

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7

Table 1: Bottleneck capacity estimation model for the sag sections [Ishida and Xing, 2000]
2 lanes

3 lanes

BDF

t

QDF

t

BDF

t

QDF

t

Horizontal curvature [1/km]-106.65

1.23-145.98

1.58

-

-

-

-

Gradient of upstream section [%]-34.900.64-62.84

1.08

-

-

-

-

Length of upstream section [m]

-

-

-

-

-87.492.54-83.84

1.69

Gradient of downstream section [%]-128.32

2.86-185.98

3.87

-9.88

0.19

-153.03

1.97

Length of downstream section [m]-158.88

2.63-129.04

1.95-167.89

3.59-190.22

2.50

Difference of gradient [%]

90.27

1.98

130.33

2.65

20.16

0.68

140.06

2.68

Vertical curve radius [km]

0.24

1.22

0.38

0.69

5.06

2.72

3.03

1.25

Dummy for holidays-22.430.37-42.120.65-79.83

1.34-86.480.98

Intercept

3548.9729.64

3238.35

25.49

5171.2328.77

4628.42

15.70

R

0.64

0.70

0.82

0.80

R2

0.41

0.49

0.67

0.64

2.3. Modeling of drivers’ route choice behavior
SOUND incorporates drivers’ route choice model with dynamic stochastic user optimal (DSUO)
principle, namely the logit choice model according to the generic cost function weighting the distance, theexpected travel time under the present traffic condition, the toll fare, and the total queue length along eachroute from the present position to the destination. Table 2 shows the coefficients used in the generic costfunction of the route choice model derived from the analysis on the observable route choice data [Ishida,2013].
Table 2: Parameters for the route choice model in the ENS [Ishida, 2013]
Small cars
Value

Large vehicles

t-valueValue

t-value

Toll fare [yen]-0.011-57.290-0.005-58.871

Estimated travel time [min]-0.038-40.276-0.079-57.809

Queue length [km]-0.015-6.717-0.040-9.827

Dummy for incident occurrence-0.137-1.462-0.564-6.556

Likelihood ratio

0.448

0.550

Hitting ratio

0.835

0894

Num. of samples

20000

20000

The original route choice model of SOUND assumes the perfect rationality of driver. However, theavailable traffic information on the real expressway is limited. For instance, drivers at an expressway
junction are informed of traffic conditions through the variable message signboard (VMS) installed atroadside, but the content of the information is different with the type of VMS, as shown in Fig. 8.
The most informative VMS is installed at type A junctions that can display pictures of queue length

8Hirai et al. / ISTS2014 Corsica

and travel time for both alternative routes. The type B simply provides travel times. No available dynamic
information at type C junctions. The ENS takes into consideration these differences of the information
available to the driver at each junction.

Fig. 8: Various VMSs installed on the expressways

3. Calibration of time-dependent O-D matrix using ETC data
Providing accurate O-D matrix is one of the most important issues to ensure reliability of thesimulation results, but, on the other hand, is one of the most difficult tasks in the data acquisition phase.
Many researchers have worked on this topic, and most of them take the numerical searching approach tominimize errors in link flows evaluated through the iterative framework with simulation which establishes
the relation between link flows and O-D path flows. Oneyama [1996] developed the estimation
methodology of time-dependent O-D matrix by enhancing the road network to 3-D (X-Y and time axis)
and by applying the entropy maximization method to minimize error in vehicle counts. Kitaoka [2002]
applied the genetic algorithm to search the optimal O-D matrix to minimize the errors in vehicle counts.
Balakrishna [2007] applied the simultaneous perturbation with stochastic approach (SPSA) [Spall, 1998]
to reduce the computational cost for the numerical search.
Those iterative approaches, however, repeat simulations many times, and will consequently be lesspractical when the simulation run time is costly. As the ENS takes couple of hours for one run, it isexpected to calibrate the O-D matrix within a few runs, hopefully 3 to 5 runs.
3.1. Calibration framework combining traffic simulation and mathematical model
To reduce the number of simulation runs, we have proposed the combined framework with simulationand mathematical model [Kobayashi, 2012]. Fig. 9 illustrates the procedure for the O-D matrix estimation

Hirai et al./ ISTS2014 Corsica

9

in which the framework consists of two iteration loops. The outer loop (1) runs the ENS to evaluate thelink flows and their O-D compositions, and the inner loop (2) iteratively applies the numerical searchalgorithm which is less costly than the ENS to the mathematical model derived from the simulation
results.
Start
Aggregate&
enlarge

ETC tripdata

InitialOD matrix

Discretization(real num)

Input
OD matrix

End(integer)outer loop
(1)

Optimized
OD matrix

Terminate?

Detector
data(real num)
inner loop
(2)

Simulation(ENS)

Optimization(math model)

ObservedvolumeFig. 9: Estimation process for O-D matrix

The mathematical model which establishes the relation between link flows and O-D path flows can bederived from the simulation result as follows:(eq. 1)

where

k
w
u



h

(eq. 2)
suffix of a link,suffix of an O-D pair,suffix of a vehicle type,suffix of a time slot for link throughput volume,
suffix of a time slot for departure (demand),link throughput volume of the vehicle type u for the link k at ,
choice probability for the O-D flow w for type u departing at h to the link k at ,
O-D flow w for type u departing at h,link throughput volume of the O-D flow w for type u at h for the link k at .

As the choice probability can be also calculated from the cost difference of two alternatives byassuming the logit choice model as follows:10

Hirai et al. / ISTS2014 Corsica

1
∆

1_

(eq. 3)logit sensitivity parameter for cost difference,
cost difference for the O-D flow w for type u departing at h to the link k at .

where
∆

From (eq. 2) and (eq. 3), the cost difference can be estimated from the simulation result as follows:∆11(eq. 4)The evaluation function to minimize the errors in link volumes now can be determined as follows:(eq. 5)whereobserved link throughput volume.

As the optimization formula with (eq. 1) ~ (eq. 5) is differentiable with the O-D flow
and theroute choice sensitivity parameter, we may now apply any numerical search algorithm using
differential coefficient, the calculation costs of which are much less than traffic simulation, and find the
optimal O-D matrix and the logit sensitivity parameter. In this paper, we use simple steepest descentmethod, which it is not essential.
3.2. Accumulation of ETC trip data for initial O-D matrix
In Japan, the electronic toll collection (ETC) system started operations in 1996 and its rate of use,
nowadays, is close to 90% of the entire number of trips on expressways. As the ETC system collects the
on-board unit ID when a vehicle passes a toll gate, it is easy to accumulate the IDs into the O-D matrix(ETC-OD) at any desired time interval. If the vehicle count data at each entrance toll gate is available, theETC-ID will be expanded in proportion to the ETC trip number to the vehicle count at the entrance. The(expanded) ETC-OD can be used as the initial O-D matrix for the calibration.
3.3. Calibration results
For validation, the O-D matrix on a specific day, Sunday, 12 October 2012, has been calibrated
following the procedure above. Fig. 10 compares the link traffic volumes reproduced by the ENS with thevehicle counts from detector data. The coefficient of determination (R2) in the simulation result with theinitial O-D matrix was 0.809 and, after 2 simulation runs in the outer loop, was improved to 0.963, which
is fairly accepted. The RMS error was also reduced to almost half of the initial value.
Fig. 11 shows the speed contour maps of major expressways (Kan’etsu, Joban and Tohoku
Expressways) bound for Tokyo. On this day, many leisure travelers returning to Tokyo in the afternoon
peak hours caused considerable traffic jam. Although the speed changes in the simulation results seem tobe drastic as they follow the triangular approximated fundamental diagrams, we may see a similarity inthe queue growth and shrink in the evening peak.

Hirai et al./ ISTS2014 Corsica

Initial
RMSE
5658.23 [veh/day]

Optimized (2 times)
R2
0.809

8.E+4

Simulation [veh/day]

Simulation [veh/day]

8.E+4

11

6.E+4
4.E+4
2.E+4
0.E+0
0.E+0 2.E+4 4.E+4 6.E+4 8.E+4

Observation [veh/day]

RMSE
2366.30 [veh/day]

R2
0.963

6.E+4
4.E+4
2.E+4
0.E+0
0.E+0 2.E+4 4.E+4 6.E+4 8.E+4

Observation [veh/day]Fig. 10: Comparison with the link traffic volumes before and after the O-D matrix calibration

Fig. 11: Speed contour map reproduced by the ENS with the calibrated O-D matrix

4. Conclusions and future directions
In this paper, the concept of the expressway network simulator (ENS) was described followed by thecalibration of time-dependent O-D matrix using ETC trip data. By using well calibrated O-D matrix, we
may conclude that the ENS can reproduce traffic volumes and queues on expressways with acceptableaccuracy. Following items are our future scope: Efficient calibration of the fundamental diagram for evident and hidden bottlenecks
 Improving the triangular shaped fundamental diagram in SOUND so that it is more realistic such as shaped

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Hirai et al. / ISTS2014 Corsica

Improving drivers’ route choice modeling
Incorporating the urban expressway network in metropolitan areas
Incorporating arterial road network, and departure time choice relating to time-varying toll fare
Incorporating the resting behaviors of long trip drivers at service areas

Acknowledgements
The authors gratefully acknowledge the valuable suggestions and guidance provided by the membersof Expressway Network Simulation Development Committee chaired by Prof. Kuwahara of Tohoku
University.

References
Balakrishna, Antoniou, Ben-Akiva, Koutsopoulos and Wen (2007), Calibration of microscopic traffic simulation models: methods
and application, Transportation Research Record 1999, pp. 198-207.
Dynasmart (2014), description available at http://www.its.uci.edu/ctss/sim_models/dynasmart.html (website visited on May 8, 2014)
INTEGRATION (2014), description available at http://filebox.vt.edu/users/hrakha/Software.htm (website visited on May 8, 2014)
Ishida, Fukase, Ishibashi, and Kiyomiya (2013), Analysis of route choice behavior on intercity expressways, Proceedings of 33rd
Conference of Japan Society of Traffic Engineers (in Japanese).
Kitaoka, Teramoto, Oneyama and Kuwahara (2002), Reproduction of traffic condition based on estimation of origin-destination
flow, Proceedings of Infrastructure Planning (in Japanese).
Kobayashi, Horiguchi, Hanabusa and Koide (2012), Estimation of time-dependent O-D matrix and route choice model parameter
for a large scale network simulation, Proceedings of 32nd Conference of Japan Society of Traffic Engineers (in Japanese).
Newell (1993), A simplified theory of kinematic waves in highway traffic, part I: General theory, Transportation Research B, Vol.
27B No. 4, pp. 281-287.
Oneyama, Kuwahara and Yoshii (1996), Estimation of time dependent OD matrices from traffic counts, Proceedings of the 3rdWorld Congress on Intelligent Transport Systems, Orlando.
SOUND (2014), description available at http://www.i-transportlab.jp/products/sound/index.html (website visited on May 8, 2014, inJapanese)
Spall (1998), An overview of the simultaneous perturbation method for efficient optimization, Johns Hopkins APL Technical Digest,
19(4), pp. 482-492.
Ishida and Xing (2000), Status and subjects on capacity of intercity expressways, Proceedings of Infrastructure Planning, 660, pp.
79-87 (in Japanese).
Yoshii and Kuwahara (1995), SOUND: A traffic simulation model for oversaturated traffic flow on urban expressways, Preprint at
7th World Conference on Transportation Research, Sydney.