Estimating Traffic Conditions of the Radial-ring Expressway Network by
Fusing Probe and Detector Data into Traffic Simulations
Azusa Goto 1*, Kazunori Ooshima 1, Kosuke Yamada 2, Ryota Horiguchi 3, Shin Sakaki 1,
Hidenori Yoshida 1
1Intelligent Transport Systems Division, National Institute for Land and Infrastructure Management, Asahi 1,
Tsukuba, Japan
2
Urban Planning and Management Division, Pasific Consultants Co, Ltd., 3-22 Kandanishiki-cho, Chiyoda-ku,
Tokyo, Japan3
i-Transport Lab. Co., Ltd., 9th floor, 3-10 Kandaogawa-cho, Chiyoda-ku, Tokyo, Japan*goto-a92uj@mlit.go.jp

Abstract: This paper introduces a framework to estimate road network traffic conditions by fusing probe and detector data
into traffic simulations. In this traffic simulation, the trajectories of some vehicles are controlled by the observed probevehicles, then the speed reductions of these vehicles propagate according to the kinematic wave theory. In addition, theorigin-destination matrix is calibrated using a mathematical model so that the errors in the estimated link traffic volumes
from the detector data can be minimized. By applying this framework, the traffic conditions on the Tokyo Metropolitan
Expressway Network were estimated. By comparing the estimation results with the observation, it was confirmed that theestimation showed a good accuracy in terms of link traffic volumes, and traffic congestion at the typical bottlenecks could
be reasonably represented to some extent.
1. Introduction
The Tokyo Metropolitan Expressway Network inJapan has developed for a long time since the 1960s. First,
radial roads were constructed to make the surrounding areas
accessible to the metropolitan centres, currently the ringroads that connect these radial roads have been mostly
completed [1]. Since various routes will become available
for road users after the completion of this radial-ring
expressway network, it will be more important to utilize ITS
technologies, such as dynamic route guidance or congestion
charges, to realize a more efficient road network operation.
In order to implement such operational measures, it isessential to understand traffic conditions in a network,
which means not only traffic flows and speeds of individual
sections but also traffic flow distributions from each origin
to destination. It will allow road network operators torecognise where congestion happens, where vehicles within
the congestion come and go, and where and how they canalleviate congestion by encouraging vehicles to detour.
However, existing detectors (or sensors) give us
limited information about traffic flows and speeds at
specific sites. Since these detectors are not so densely
located on some sections, e.g., 1 or less in 5 km, thisinformation is not enough to understand traffic flow
distribution conditions over a whole network. On the other
hand, we are recently able to obtain some probe data by
vehicle-infrastructure cooperative system so-called “ETC
2.0 system” in Japan. Although the number of probevehicles is still limited, this data contains a series of timeand position (longitude and latitude) information of probevehicles for every 200 m, which tells us where and when
they reduced their speeds. It is expected that we will able toestimate traffic conditions in more detail by fully utilizingthese different kinds of data.
Therefore, the objective of this research is to develop

a framework to estimate road network traffic conditions byfusing probe and detector data into mesoscopic traffic
simulations. In the simulation, vehicles are generated andattracted according to the time-varying origin anddestination matrix (hereafter referred to as “OD matrix”),
which cannot be directly observed and therefore is estimatedby calibrating the initial OD matrix using the observed linktraffic counts from detector data. Then positions of thevehicles are estimated by incorporating the time-space
trajectories of probe vehicles into the fundamental diagramof traffic flow based on the variational theory developed by
Daganzo [2]. This can give us information about traffic
conditions where detectors are not installed, as well as
traffic flow distributions, which are not limited for probevehicles.
So far, the framework has been developed for
performing post evaluations of an operational measure bycomparing estimated traffic conditions before and after
implementation, thus all data was collected and inputtedoffline. However, it is also applicable to real-time trafficmonitoring if all the data is connected online in the future.
This will contribute to realizing effective road network
management by implementing some operational measures
based on dynamic traffic conditions.
The following parts of this paper consist of aliterature review and the position of this research (section 2),
an explanation of the methodology (section 3), a case study
to verify how much accurately traffic conditions are
estimated by the proposed methodology (section 4) andfinally the conclusion and future work (section 5).
2. Literature Review
Previous studies ([3] ~ [8]) have already developed
the frameworks for estimating and/or monitoring road
network traffic conditions by inputting observed data into
traffic simulations. In the traffic simulations, the most1

important tasks are estimation of demand (i.e., OD matrix)
and calibration of supply parameters (i.e., fundamental
diagram).
In most of the existing frameworks, the OD matrix isestimated or calibrated according to the observed traffic
volumes by some detectors and/or sensors based on typicaltraffic conditions. For example, Dynasmart-X [3], DynaMIT[4], and Aimsun Live [5] select the OD matrix based on the
database that contains the relationship between OD matrices
and observed traffic volumes by detectors and/or sensors in
the past on the highway and motorway network. HEROINE[6] and RISE [7], which were developed by the urban
expressway companies in Japan, utilize the onramp traffic
volumes directly for calibrating OD matrix between theonramps and off-ramps. The calibration is based on thehistorical pattern of OD matrix considering the day of theweek and other factors with the temporary changes of theobserved onramp traffic volumes.
In order to apply these frameworks ([3] ~ [7]), it isnecessary to obtain a historical pattern of OD matrices.
However, it needs a large amount of data and thus is very
difficult, since we cannot observe ODs of all vehicles ingeneral. Besides, the Tokyo Metropolitan Expressway
Network, which is our subject to study, has not been
completed yet; some of the sections are still underconstruction. Thus, the historical patterns of OD matrices
may not be applicable due to the openings of new sections in
the future.
Without using the historical patterns of OD matrices,
for another example, since road administrators have recently
been able to obtain the OD matrix of vehicles that use theelectric toll collection (ETC) system in Japan, Hirai, et al.
[8] utilized this data for estimating the OD matrix of all
vehicles (including the ones which pay tolls in cash, notthrough the ETC system) on the entire inter-urban
expressway network. This OD matrix of ETC users wascalled “ETC-OD matrix”. Because users of the ETC system
accounted for about 90% of all expressway users, the ETCOD matrix could be a good initial input for estimating the
OD matrix of all users. Since this approach does not needhistorical pattern of OD matrices but can fully utilize thedata available for road administrators, it was also adopted inour study.
On the other hand, the calibration of supply
parameters had been conventionally achieved though theanalysis on the bottleneck capacities on expressways byusing historical detector data, as also incorporated in theabove study [8]. However, it also requires plenty of data,
since supply parameters vary by road geometry (e.g.,number of lanes, lane width, gradient) as well as day of theweek, weather condition, ambient lighting condition, type ofroad users (e.g., long-distance traffic or commuter traffic),
etc. Instead of calibrating the parameters to these
influencing factors, many of the above-mentioned
frameworks ([3] ~ [7]) use observed speed data by detectors
and/or sensors. The use of actually observed data isadvantageous also in grasping the congestion caused by not
only fixed bottlenecks but also some temporary incidents(i.e., traffic crashes or falling objects on roads) that cannot
be calibrated in advance.
In our study, we focused on the use of probe data,
because the detectors and/or sensors are sometimes locatedwith large spacing (for example, 5~10 km) especially on

NEXCO
East

MEX
NEXCO
CentralFig. 1. Expressway network in the Tokyo Metropolitan
area with route numbers (dotted lines means underconstruction as for 2017)
intercity expressways in Japan, only detector data is notprecise enough for detecting congestions. From thisviewpoint, probe data had a great advantage because it
contains continuous speed information with denser spacing
as far as probe vehicles are driving on the roads.
The utilization of probe data is one of the mostsubstantial challenges in traffic estimation. For example,
Work et al. [9], Herring et al. [10] showed the applicabilityof probe data for estimating travel time (or travel speed).
Choi and Chung [11] developed a data fusion technique tocombine probe and detector data for more reliable andaccurate estimation. While most of the existing studies
including above used only travel time (or travel speed)
information of probe vehicles, Mehran et al. [12] proposed amethodology to utilize individual vehicle trajectories (timespace) based on Daganzo’s variational theory [2] for
estimating trajectories of other vehicles at the corridor level.
This approach has the great extensibility to utilize whatprobe data contains, not only time-space but also vehicle
type for example in the future research. Therefore, our study
was aimed to incorporate this approach for calibrating the
supply parameters into network simulations.
3. Methodology
3.1. Subject network
The subject road network was a whole expressway
network in the Tokyo metropolitan area as illustrated in Fig.
1. It has 1599.7 km for both directions covering the area of
about 1.1×104 km2, consisting of 2214 links in Digital Road
Map (DRM) [13]. As shown in the figure, the network isoutlined by three ring roads (C2, C3, and C4) and several
radial roads with 29 junctions. This allows road users tochoose several routes, especially when passing through themetropolitan area from and to outside the outer ring road(C4).
The three different colours in Fig. 1 stand for thecompanies that are in charge of construction, operation, andmanagement for these expressway sections: Metropolitan
Expressway Co., Ltd., (MEX) for the central part, Central
Nippon Expressway Co. Ltd., (NEXCO Central) for thewest part, and East Nippon Expressway Co., Ltd., (NEXCOEast) for east and north part.
2

3.2. Overview of traffic estimation process
In this research, traffic conditions were estimatedusing a traffic simulator with different kinds of observed
data. Fig. 2 shows the flowchart of the whole estimation
process.
The estimation process consisted of two steps. At thefirst step, we calibrated the OD matrix, which was one of themost important inputs for traffic simulations. The OD matrix
in this study must specify the traffic demands between theonramps and off-ramps on the subject expressway network
during each time interval. In order to obtain the OD matrix,
we prepared an initial OD matrix based on the ETC-OD
matrix, and calibrated it through the iterative process of
traffic simulation and minimization of the errors in linktraffic volumes from the detector data.
By inputting the calibrated OD matrix at the first step,
we carried out the traffic simulation with ETC 2.0 probe
data at the second step. Actually, the iteration at the firststep also included traffic simulations as shown in Fig. 2, butthese were done without the probe data.
3.3. Data
As stated, three kinds of data were utilized in thisframework: detector data, ETC- OD matrix and probe data.
The following subsections introduce them in detail.
3.3.1 Detector data: In total, 408 detectors were installedin the subject network; that is, on average for every 300600 m on the expressways under MEX and at least one
between every on/off-ramps (about 5~10 km) on theexpressways under NEXCO Central and East. With thesedetectors, we obtained traffic volume and average spot
speeds aggregated once every 5 minutes for two categories
of vehicle types (i.e., passenger cars and heavy vehicles).
Several types of detectors were used at different sites,
for example, inductive loop detectors, ultrasonic detectors,
and video image processor detectors. From them, we
excluded detectors with errors and missing records, and thedetectors that seemed inaccurate when comparing traffic
counts with upstream and downstream detectors in the data
cleansing process.
3.3.2 ETC-OD matrix: As briefly mentioned in section 2,
the ETC-OD matrix was the OD matrix of ETC users which
specified the traffic volumes between the onramps and offramps during each time intervals. This matrix was calculated
in each of the three expressway companies (MEX, NEXCO
East, and NEXCO Central) by aggregating the records oftimes when vehicles passed through the tollgates located atonramps, off-ramps, or boundary junctions between
different expressways with the ETC on-board units(including ETC 2.0 on-board units that are explained in
3.3.3).
In this research, we first combined these matrices
into one matrix in order to make the ETC-OD matrix in thewhole subject network with the aggregation intervals of 15
minutes for each type of vehicles (passenger cars or heavy
vehicles). Here, several assumptions were made about
diverging and merging volumes at boundary junctions where
expressways under different companies intersect.
Then, we approximately converted it into the
OD matrix of all vehicles by multiplying the elements by theStart
Initial OD matrix

ETC-OD
matrix(real num)

Discretization of OD matrix
OD matrix(integer)

Traffic simulation

Data assimilation

Estimation of OD matrix
Detectordata

Calibration of
OD matrix(minimization of errors
in link traffic volumes)

Updated OD matrix(real num)

Data assimilation

Converged

No

Yes

ETC2.0probe data

Traffic simulation
End

Fig. 2. Flowchart of the whole estimation process
on-board unit
200m

direction
200m

45 degrees or moreroadsideunit

Fig. 3 schematic image of travel record in probe data
by ETC2.0 system
inverse of the average percentage of ETC users in theexpressway companies according to their destination offramps. The ETC system in Japan has been in operation
nationwide since 2001, and the percentage of ETC users iscurrently almost 90% among all expressway users.
The OD matrix obtained in the above procedure wasused for the initial OD matrix in Fig. 2. Since this procedure
was done with several simplifications, the initial OD matrix
would not be accurate enough for estimating dynamic traffic
conditions. That was why the optimization was further
carried out as shown in Fig. 2.
3.3.3 Probe data: Probe data was obtained from the ETC
2.0 system. The ETC 2.0 system is a vehicle-infrastructure
cooperative system using the DSRC (Dedicated Short Range
Communications) between ETC 2.0 on-board units androadside units. The system has been deployed nationwide by
the Ministry of Land, Infrastructure, Transport and Tourism
since 2011. While the ETC system was only for electric tollcollection, the ETC 2.0 system had additional functions ofdynamic route guidance, safe driving assistance, and probe
data collection.
In the probe data collection of the ETC 2.0 system,
time and position (longitude and latitude) information ofeach probe vehicle is recorded and accumulated in its onboard unit every 200 m or when its direction changed
45 degrees or more as illustrated in Fig. 3. Then, theaccumulated data is uploaded when probe vehicles passedby roadside units, which are generally set every 10~15 km
on intercity expressways and 4 km on urban expressways on
3

Startflow
link capacityqc

Time to update
route choice?
(every 15 min)

Yes

No

Update oflink cost

Traffic
generation

OD matrix(integer)back wave
speed wdensity
jam density kj

Route choicemodel

Data assimilation
ETC2.0probe data

critical speedvc

free-flow speedvfFig. 5. Fundamental diagram

Traffic flow
model

cumulative flow
Terminate simulation?

D’No

arrival demand
flow A*

Update of time(every 1 sec)arrival flow A
discharge flow
D

Yes

qc

End

Fig. 4. Flowchart of traffic simulation

kj L
time

average. The roadside units send the data to the central
server, and finally the central server connects the data ofeach probe vehicle downloaded by different roadside units
for every day in order to make continuous trajectories ofprobe vehicles. For more information, please refer to thereport [15].
Although the use of the ETC 2.0 system is gradually
increasing year by year, it is still limited in total traffic
volume. On average, we can collect probe data from about
2~3% of all vehicles traversing the subject expressways. For
example, probe data was collected from 40 vehicles, which
accounted for 3.3% of the total 1,221 vehicles on one
section of the E1 expressway (bound for Tokyo, upstream of
Yokohama-Machida IC) during the evening peak from16:00 to 16:15 on Sunday, 5th June, 2016.
3.4. Traffic simulation
In the main part of the estimation process, we
simulated traffic with the existing simulator, namely
SOUND (Simulation On Urban road Network with Dynamic
route choice; [16], [17]), which had been developed by iTransport Lab. Co., Ltd., by adding a special function forincorporating probe data. Fig. 4 shows the general flowchart.
SOUND is a mesoscopic traffic simulator dealing withdiscrete vehicles with 1-second update intervals. In thissimulation, vehicles are generated according to the
OD matrix, and their movements are simulated by the traffic
flow model and route choice model in the following way.
3.4.1 Traffic generation: Traffic was randomly generated
at every time step (i.e. 1 second) from onramps according to
a 15-minute OD matrix. Here, the OD matrix was updated
during the calibration step as explained in subsection 3.5 indetail.
3.4.2 Traffic flow model: SOUND estimates the number ofvehicles and the positions of individual vehicles on each linkat every time step according to the fundamental diagram.
Here, a simple fundamental diagram is assumed as shown in
Fig. 5. It is defined by link capacity 𝑞𝑐 and jam density 𝑑𝑗 .
In a free-flow regime (blue line in Fig. 5), forward wave
speed, which is the angle from the horizontal axis, decreases

L/w

Fig. 6. Estimation of cumulative arrival flow
distanceΔxcumulative
traffic volume
Q
Q+1

Q
w

wΔt

Q+1

t

Q+kjwΔt

t+Δt

time

Fig. 7. Impact of a probe vehicle trajectoryfrom free-flow speed 𝑣𝑓 to critical speed 𝑣𝑐 as density
increases. In a congested flow regime (red line in Fig. 5),
backward wave speed 𝑤 is calculated as follows.
𝑤=𝑞𝑐𝑞𝑘𝑗 − 𝑐⁄𝑣𝑐(1)

In SOUND, expressways are segmented into links onwhich vehicles are conserved (no entry and exit exist). Thenthe number of vehicles on each link is first calculated asfollows:
In principle, each vehicle is put into the list of freeflow states when entering into a link, and transferred into thelist of ready-to-discharge states after spending the link travel
time by free-flow speed, which is expressed by 𝐿/𝑣𝑓 where
𝐿 denotes link length, while keeping the first-in-first-out.
Then, vehicles in the list of ready-to-discharge states canmove to the downstream link according to the cumulative
arrival flow curve, which is obtained by applying Newell’s
simplified kinematic wave theory [18].
Fig. 6 illustrates an example of the cumulative flow
diagram of a link. The cumulative arrival-demand flow
curve A* is determined by the cumulative number ofvehicles in the list of ready-to-discharge states of an
upstream link (blue solid line). On the other hand, for its
downstream link, the cumulative discharge flow curve D at
its downstream end is drawn with the slope of its link
4

Table 1 parameters of the links(a)MEX
Parameters
6-lane2200
𝑞𝑐 [pcu/h/lane]
𝑘𝑗 [pcu/km/lane]𝑣𝑓 [km/h]
100
60
𝑣𝑐 [km/h](b)NEXCO East and Central
Parameters
4-/ 6-lane
2400
𝑞𝑐 [pcu/h/lane]
𝑘𝑗 [pcu/km/lane]𝑣𝑓 [km/h]
100
70
𝑣𝑐 [km/h]

4-lane
2200
80
80
54

IC and JCT
2000

2-lane
2000
80
80
54

IC and JCT
2000

60
36

60
36

capacity 𝑞𝑐 (red solid line). Because of backward wave
propagation, the acceptable cumulative flow curve D’ at the
upstream end of this link can be obtained by shifting the
curve of D with 𝐿/𝑤 to the right and 𝑘𝑗 𝐿 to the top (reddotted line). Finally, the cumulative arrival flow curve A is
the minimum of A* and D (black solid line).
After that, with the given boundary of the cumulative
number of vehicles at the downstream end of each link, thepositions of individual vehicles inside the link are calculated
one by one from the downstream to upstream by applying
Daganzo’s variational theory [2]. Since not only thedownstream end of links but also the observed vehicle
trajectories of probe vehicles can be regarded as boundaries,
we could incorporate probe data in this simulation. Fig. 7
illustrates how to estimate the position of the following
vehicle based on the leading vehicle trajectory. As shown in
Fig. 7, when the cumulative traffic volume of the leading
vehicle is 𝑄 at time 𝑡, that of the vehicle at 𝑤∆𝑡 downstreamof the leading vehicle at time 𝑡 + ∆𝑡 is calculated as
𝑄 + 𝑘𝑗 𝑤∆𝑡. Assuming the vehicles are linearly distributed
between them, SOUND estimates the position of thefollowing vehicle of which the cumulative traffic volume is
𝑄 + 1 at time 𝑡 + ∆𝑡.
The parameters for determining a fundamental
diagram are traffic capacity 𝑞𝑐 , jam density 𝑘𝑗 , free-flow
speed 𝑣𝑓 and critical speed 𝑣𝑐 . Usually they need to becalibrated especially at bottlenecks based on empiricalanalysis, so that congestion phenomena can be reasonably
represented. However, since this approach requires a large
amount of empirical data, these parameters were uniformly
set according to Table 1 in this research. Instead ofcalibrating these parameters, probe data was incorporated
for representing congestion.
3.4.3 Incorporation of probe data: Specifically, in thissimulation, we controlled the speeds of some vehicles sothat they could precisely track the observed trajectories ofprobe vehicles. Then, the speed reduction of a probe vehicle
influenced the following vehicles as explained in 3.4.2. As aresult, this triggered congestion in the simulation.
If the number of probe vehicles was not so small,most of the traffic congestion was captured by this approach.
Furthermore, although it is outside the focus of this paper,by using this approach, it becomes possible to grasp thecongestion caused by not only fixed bottlenecks but also
some temporary incidents (i.e., traffic crashes or falling

Table 2 Coefficients of the route choice model
Vehicle type
Passenger cars
Heavy vehicles
Weekday/end Weekday Weekend Weekday Weekend
0.240
0.242
0.341
0.257
𝛼
0.311
0.181
0.330
0.219
𝛽
𝛾
0.064
0.055
0.064
0.055
𝜃
Note: “-“ means not available
objects on roads) that cannot be calibrated in advance. Thisis the great advantage of incorporating probe data, especiallyfor further development of a real-time traffic monitoring
system.
3.4.4 Route choice model: SOUND assumes that road
users have perfect information and choose their routes
dynamically based on updated travel time and tolls of theiralternative routes every fifteen minutes. Thus, user route
choice probability is formulated by the logit model asfollows.
𝑝𝑗 =exp(−𝜃𝑐𝑗 )∑𝐽𝑘=1 exp(−𝜃𝑐𝑘 )𝑐𝑗 = 𝛼 × 𝑡𝑖𝑚𝑒𝑗 + 𝛽 ×

𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑗
𝑣𝑓𝑗(2)+ 𝛾 × 𝑡𝑜𝑙𝑙𝑗 (3)Where, 𝑝𝑗 : probability to choose route 𝑗, 𝐽: total number ofavailable routes, 𝑐𝑗 : cost of route 𝑗, 𝑡𝑖𝑚𝑒𝑗 : expected travel
time of route 𝑗 based on link travel time of the current time
step (every fifteen minutes) , 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑗 : distance of route 𝑗,𝑣𝑓𝑗 : free-flow speed of route 𝑗, 𝑡𝑜𝑙𝑙𝑗 : toll of route 𝑗, 𝜃: route
choice sensitivity parameter and 𝛼, 𝛽 and 𝛾: coefficients.
Coefficients 𝛼, 𝛽 and 𝛾 were set as listed in Table 2.
These coefficients were estimated based on the observed
trajectories of the ETC 2.0 probe vehicles (for dependent
variables) and route travel times from the detector data (forindependent variables) by the maximum likelihood method.
The data used for this estimation was observed during Juneof 2016 and 2017, which contains the trajectories of
1,034,542 vehicles in total (i.e., 380,370 vehicles in 2016
and 654,172 vehicles in 2017).
In the above estimation, the impact of tolls
represented by the coefficient 𝛾 could not be estimated. Thiswas because tolls are determined by only origins anddestinations regardless of routes for almost of OD-pairs inthe subject network after April 2016 until today; in otherwords there was no difference in tolls when drivers chose
their routes. Here, it should be noted that there was an
exception in the toll policy that tolls on the routes using
MEX’s sections costed higher than other routes for several
OD-pairs, in order to reduce number of vehicles penetrating
the centre of the metropolitan area. However, the impact of
this exception could not be reflected in the model due to thelack of the detailed toll data. In addition, please note that theabove-mentioned toll policy has been applied only for ETC
users (about 90% of all vehicles) in reality, but the model
was applied for all users in the simulation for simplicity.
3.5. Calibration of OD matrix using detector data
The OD matrix was calibrated using detector data as
5

shown in Fig. 2. That means the OD matrix was iteratively
revised in order to minimize the sum of errors in estimatedlink traffic volumes from the observed volumes in detectordata.
For this calibration, we used the mathematical model,
which had been proposed by Kobayashi et al. [19] andapplied by Hanabusa et al. [14]. The advantage of thisapproach was that the number of iterations could bedrastically reduced. The previous application to the entire
Japan expressway network [14] needed only three to fivesimulation runs to converge the results. This was importantsince it took time to run traffic simulation.
This model minimizes the sum of errors in estimating
link traffic volume 𝐸, which is expressed by the following
equation.
2

𝐸 = ∑𝑖 ∑𝑡(𝑞𝑖,𝑡 − 𝑞̂
𝑖,𝑡 )

(4)

Where, 𝑞𝑖,𝑡 : the estimated traffic volume of link 𝑖 in time
step 𝑡 in the simulation, 𝑞̂
𝑖,𝑡 : the observed traffic volume oflink 𝑖 in time step 𝑡 from detectors.
In the above equation, although 𝑞𝑖,𝑡 cannot be
generally obtained without running the simulation, it ismathematically expressed with the relation to OD traffic
volumes as follows.
𝜔,𝜏 𝜔,𝜏
𝑞𝑖,𝑡 = ∑𝜔 ∑𝜏 𝑝𝑖,𝑡
𝑄
(5)
𝜔,𝜏
𝑝𝑖,𝑡
=

𝜔,𝜏

𝑞𝑖,𝑡

𝑄 𝜔,𝜏

(6)

Where, 𝑄𝜔,𝜏 : traffic volume of OD pair 𝜔 that departed in𝜔,𝜏
time step 𝜏, 𝑝𝑖,𝑡
: probability that a vehicle of OD pair 𝜔𝜔,𝜏that departs in time step 𝜏 passes link 𝑖 in time step 𝑡 , 𝑞𝑖,𝑡:the estimated traffic volume of OD pair 𝜔 that departed intime step 𝜏 passed link 𝑖 in time step 𝑡 in the simulation.
Assuming a binary choice for the logit model (c.f.,𝜔,𝜏equation (2)), 𝑝𝑖,𝑡
is also expressed by the following
equation.
𝜔,𝜏
𝑝𝑖,𝑡
=

1
𝜔,𝜏
1+𝑒𝑥𝑝(−𝜃∆𝑐𝑖,𝑡
)

(7)

𝜔,𝜏
Where, ∆𝑐𝑖,𝑡: difference in costs for a vehicle of OD pair 𝜔that departed in time step 𝜏 passing link 𝑖 in time step 𝑡 frompassing aother link under the alternative routes.
By substituting equation (7) into (5), 𝑞𝑖,𝑡 is expressed
as a function of 𝑄𝜔,𝜏 (subject for this calibration), 𝜃 (given
𝜔,𝜏
parameter from Table 2) and ∆𝑐𝑖,𝑡
as follows.

𝑞𝑖,𝑡 = ∑𝜔 ∑𝜏

𝑄𝜔,𝜏
𝜔,𝜏
1+𝑒𝑥𝑝(−𝜃∆𝑐𝑖,𝑡
)

(8)

𝜔,𝜏
Generally, it is difficult to obtain ∆𝑐𝑖,𝑡. In this model,
𝜔,𝜏∆𝑐𝑖,𝑡 is estimated by solving the simultaneous equations (6)𝜔,𝜏and (7), assuming that ∆𝑐𝑖,𝑡is calculated by the simulation
𝜔,𝜏

result and constant while optimizing𝑄.

Table 3 percentage of ETC users (passenger cars)
Month
MEX
NEXCO East
NEXCO Central
Jun. 2016
94.7
89.6
91.8
Jun. 2017
95.5
88.9
92.2

1

𝑄𝜔,𝜏

𝜃

𝑞𝑖,𝑡

𝜔,𝜏
∆𝑐𝑖,𝑡
= − ln ( 𝜔,𝜏 − 1) (9)As a result, equation (4) becomes differentiable at𝑄𝜔,𝜏 with the following constraints.
𝑄𝜔,𝜏 ≥ 0 (10)∑𝜏 𝑄𝜔,𝜏 = 𝑄𝜔 (11)Where, 𝑄𝜔 : total traffic volume of OD pair𝜔.
3.6. Output
In order to evaluate operational measures, it isnecessary to see the impacts with several indices at different
scale, because some measures may have a positive impact
on a certain section but a negative impact on a wholenetwork, and vice versa. For example, link speeds and linktraffic volumes are necessary to see congested conditions ofindividual road sections; on the other hand, we also need to
calculate the total delay in a whole network. Because theproposed framework in this study could simulate
movements of all vehicles on a network, these indices could
be calculated at various scales.
Furthermore, as mentioned in chapter 1, the purposeof traffic estimations in this research was to understandtraffic flow distributions that make it possible to think about
how to operate road networks more efficiently by diverging
some traffic into alternative routes. For this purpose, theproposed framework could calculate route-sharing rates forany route of an arbitrary OD pair by dividing the number ofsubject OD traffic volumes that used the subject route by the
total OD traffic volume. This is one of the most important
outputs of the proposed framework, since it cannot bedirectly obtained by the observed data in most of the routes
and OD pairs.
4. Validation
This section introduces a validation to see whether
the simulated results can reasonably represent actual traffic
conditions or not.
4.1. Outline of the estimated scenarios
We estimated traffic conditions on Monday, 6th Junein 2016 and Monday, 5th June in 2017 using the observed
probe and detector data on these days.
The average percentages of ETC users were as listed
in Table 3 during the study periods. We used this values toconvert the ETC-OD matrix into the initial OD matrix as
explained in 3.3.2.
As mentioned already, tolls were determined by only
origins and destinations regardless of routes. That resulted in
the route choice model used in this study insensitive to tolls
as shown in 3.4.4. Therefore, we did not input tolls for all
links in the simulation.
6

20

40

60

80

100 missing
record
E1 (bound for Tokyo)

distance[km]Mainline tollgate

40
20 JCT (for C4)
0 OiMatsuda-IC
0:00
4:00

8:00

12:00

16:00

20:00

24:00

16:00

20:00

24:00

a
E1 (bound for Tokyo)

60 JCT (for C2)

distance[km]Mainline tollgate

40
20 JCT (for C4)
0 OiMatsuda-IC
0:00
4:00

8:00

12:00
time

b
Fig. 8. Comparison of speed contours: the E1
expressway on 5th June, 2017 (a) observed by detectors
and (b) estimated by simulator
E4(bound for Tokyo) S1

JCT (for C2)

40
30 JCT (for C3)

Mainline tollgate

20
10

JCT (for C4)

0 Kazo-IC
0:00

4:00

8:00

12:00
time

16:00

20:00

24:00

16:00

20:00

24:00

a
JCT (for C2)

E4(bound for Tokyo) S1

4.2.1 Link speed: Fig. 8 and Fig. 9 are examples of the
speed contours which show 5-minute link speeds on sectionsof the E1 expressway and the E4 and S1 expressways wherecongestion often occurred. The speeds in the upper figures(a) were observed by detectors and the ones in the lower
figures (b) were estimated by the simulator.
We found that congestion, where the link speeds
were lower (indicated by reddish colour in the speed
contours), could be represented in the simulation mostly at
the same location and time with the observed data. For
example, in Fig. 8, the congestion that happened from themainline tollgate and the JCT for the C2 expressway in themorning and evening hours were indicated in bothobservation and estimation. However, the link speeds were
estimated much lower than the observation especially after
the beginning of the congestion from the JCT for theC2 expressway in the morning. This happened because
sometimes there was a difference in travel speeds by lane,
especially at merging and diverging sections; in other words,
sometimes one lane was congested while the other was notcongested depending on which direction these lanes wereconnected. Because the differences in traffic conditions bylane could not be considered in the traffic flow model
applied in the simulation, if one probe vehicle was drivingon a congested lane, the speed reduction was reflected on
the cross-section even though the other lane were notcongested. Such kinds of overestimations of speed
reductions were also found on other sections, typicallyaround merging and diverging sections.
On the other hand, the beginning of the congestion in
the evening in Fig. 8 delayed about 10 minutes in thesimulation from the observation. For another example, inFig. 9, the link speeds in the morning from the JCT for theC2 expressway were overestimated. One of the reasons ofthese examples was because speed reductions in thissimulation were triggered by those of probe vehicles only.
Therefore congestion did not occur in the simulation until aprobe vehicle reached the actual congested section, andspeed reductions were less reflected if there were few probevehicles.

10

60 JCT (for C2)

distance[km]4.2. Estimation of link speeds and traffic volumes
Link speeds and link traffic volumes were the mostfundamental outputs of the traffic estimations, which could
be used for other indices such as the total delay. Therefore,
in order to verify the simulated results, these estimatedvalues were compared with the ones observed by detectors.

Speed[km/h]
040
distance[km]We used a personal computer with Intel Core i75820K 3.30 Ghz CPU, SSD 128 GB. In order to get theresults converged, we needed to repeat the process ofcalibration of OD matrix two times. That means, in total, we
run the traffic simulation three times (two times during thecalibration of the OD matrix and one time with probe data
incorporation). It took approximately 10 hours in total:
2.5 hours for running the traffic simulation and 1.1 hours for
estimating the OD matrix by the iteration with themathematical model respectively. Although the calculation
time could be shortened by applying the mathematicalmodel for the estimation of the OD matrix as mentioned insubsection 3.5, it was still long. That must be improved in
the future work.

30 JCT (for C3)

Mainline tollgate

20
10

JCT (for C4)

0 Kazo-IC
0:00

4:00

8:00

12:00
time

b
Fig. 9. Comparison of speed contours: the E4 and S1
expressways on 6th June, 2016 (a) observed by detectors
and (b) estimated by simulator
In addition, in Fig. 9, we found that the estimatedlink speeds during uncongested periods did not agree withthe observed speeds on the S1 expressway (the upper part of
the figure). This was because the free-flow speeds were
simply inputted as listed in Table 1, and not calibrated
considering the geometry and other influencing factors ofeach link.
As a whole network, Fig. 10 shows the distributionsof the estimated link speeds according to the observed linkspeeds for every 10 km/h in all links. As shown in Fig. 10,
link speeds were overestimated in many links, especiallywhen the observed speeds were low. This implied that7

75 percentile value
Median25percentile value

100
80

5 percentile value
60

40
20
0

0

20

40

60

80

100

Observed link speed vobs [km/h]

Fig. 10. distributions of estimated link speeds by rangeof observed ones on 5th June, 2017
congestion and speed reductions were not sufficiently
represented in the simulation because of the reasonsmentioned above.
4.2.2 Link traffic volume: Fig. 11 shows the scatter
diagram of the observed and estimated link volumes. We
found that traffic volumes were well estimated in general
although there were still some links with over- andunderestimations.
Fig. 12 shows the correlation coefficients between
the estimated and observed link traffic volumes by time of
day of the two scenarios in 2016 and 2017. The result
showed that the estimated link traffic volumes were highly
correlated with the observed volumes in all the time units,
but actually there were some fluctuations. Because linkspeeds were over- and underestimated on some sections asshown in 4.2.1, it must affect the estimation of link traffic
volumes, too though both the traffic flow model and theroute choice model. Analysis in more detail (e.g., differencein accuracy by traffic flow level, impact of the number ofprobe vehicles) needs to be conducted to identify the reasons
in order to improve the accuracy of the estimated results.
5. Conclusion
In this research, we developed the framework to
estimate traffic conditions by fusing probe and detector data
into traffic simulations, and applied it on the Tokyo
Metropolitan Expressway Network. By comparing theestimation results with the detector data, it was confirmedthat the estimation showed a good accuracy in terms of linktraffic volumes. Traffic congestion at the typical bottlenecks
could be reasonably represented to some extent.
However, the link speeds were likely to beunderestimated especially at merging and diverging
bottlenecks, but also overestimated in many cases. Against
this issue, more analysis in detail in each bottleneck needs tobe conducted in order to identify the causes of low accuracy
considering the impact of the number of prove vehicles andmake necessary improvement for each section. Besides, theimpact of such errors in link speeds on the accuracy of theestimated traffic volumes needs to be investigated.
Furthermore, in the current framework, the impact of
tolls cannot be taken into account because it was notincluded in the route choice model. We would like to

Estimated link traffic volume qsim [veh/15min]Estimated link speed vsim [km/h]

95 percentile value

qsim=qobs
1600

qsim=0.99qobs
R2=0.93

1200

800

400

0
0
400
800
1200
1600
Observed link traffic volume qobs [veh/15min]Fig. 11. comparison of estimated and observed linktraffic volumes on 5th June, 2017
1.0
Correlation coefficient

120

2016

2017

0.9
0.8
0.7
0.6
0.5
7

8

9

10 11 12 13 14 15 16 17 18 19
time unit

Fig. 12. Correlation coefficient between observed andestimated link traffic volumes by time of day
improve this by obtaining the detailed toll data andanalysing the impact of tolls in detail for each OD pairs, sothat the framework will be applicable to evaluate the impact
of changing tolls.
After these validation and improvements, we would
like to conduct case studies to evaluate the operational
measures.
Acknowledgments
The authors would like to express their appreciation
to Metropolitan Expressway Co., Ltd., East Nippon
Expressway Co., Ltd., and Central Nippon Expressway Co.
Ltd. for providing their detector data and ETC-OD matrices.
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