Standard Verification Process for
Traffic Flow Simulation Model- Draft Version -Version 1

99/11/25

Released by
WG5/WS, Japan Society of Civil Engineering

Version 2 2002/6/11
byTraffic Simulation Committee, Japan Society of Traffic Engineers
simulation@jste.or.jp
Chairperson: Prof. Masao Kuwahara, Institute of Industrial Science, University of Tokyo
Co-Authors: Dr. Ryota Horiguchi, i-Transport Lab. Co., Ltd.
and Prof. Toshio Yoshii, Kochi Technology University

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Contents
１． INTRODUCTION............................................................................................................. 1
２． SIMULATION MODEL DEVELOPMENT PROCESS............................................................ 3

1)

Specifications…（Determination of model specifications） ........................................................ 3

2)

Modeling…（Contrivance of the model operation principle） ..................................................... 33)

Implementation…（Programming and debugging）................................................................... 44)

Verification…（Verification using virtual data） ....................................................................... 4

5)

Validation…（Verification using actual data） .......................................................................... 4

３． TRAFFIC PHENOMENA TO BE MODELED THROUGH SIMULATION................................ 5

1)

Generation of vehicles ............................................................................................................ 5

2)

Bottleneck capacity／saturation flow rate at link’s downstream end .............................................. 5

3)

Drawing and elimination of breakdown and shock wave propagation speed.................................... 7

4)

Capacity of merge/diverge area and merge/diverge ratio .............................................................. 95)

Decrease in the right-turn capacity due to opposing traffic in a signalized intersection ....................11

6)

Route selection behavior ....................................................................................................... 12

４． SIMULATION MODEL STANDARD VERIFICATION PROCESS - VERIFICATION .............. 16

(1)
1)
2)
3)
4)
5)
6)
(2)
1)
2)
3)
4)
5)
6)
7)

A．Q-K TYPE MODEL VERIFICATION PROCEDURE ...................................................................... 16
Generation of vehicles .......................................................................................................... 16
Bottleneck capacity／Saturation flow rate at link downstream end.............................................. 18
Spreading out cars, eliminating jams and shock wave propagation rate ........................................ 20
Capacity and merge ratios in the merge section ........................................................................ 25
Decrease in right-turn capacity due to straight through traffic in the signalized intersection ............ 27
Route selection behavior ....................................................................................................... 29
B．CAR-FOLLOWING TYPE MODEL VERIFICATION PROCEDURE ................................................... 31
Generation of vehicles .......................................................................................................... 31
Relationship between model parameters, flow characteristics and bottleneck capacity.................... 33
Relationship between model parameter and saturation flow rate.................................................. 39
Spreading out vehicles, and eliminating traffic jams, and shock wave propagation rates ................. 42
Capacity and merge ratio of the merge area.............................................................................. 47
Decrease in the right-turn capacity due to opposing traffic in signalized intersection...................... 48
Route selection behavior ....................................................................................................... 50

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Released Papers
R. Horiguchi, M. Kuwahara and T. Yoshii: A Manual of Verification Process for Road Network Simulation
Models - an Examination in Japan, Proceedings of 7th World Congress on Intelligent Transportation
Systems, Turin, 2001.
R Horiguchi and M. Kuwahara: The Art of Utilization of Traffic Simulation Models - How Do We Make
Them Be Reliable Tools?, Proceedings of the Internatinal Symposium on Transport Simulation, August
19-20, 2002, Yokohama, Japan.

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Standard Verification Process for Traffic Flow Simulation Model〜Verification Manual(Draft)〜１．Introduction
This manual describes the standard verification process used to verify the model’s reproducibility of
traffic conditions in the development of a traffic flow simulation model.
simulation models have conventionally been developed.

Many traffic flow

Due to independent verification ofindividual models or lack of wide recognition of the verification process, comparison of models interms of performance was impossible and users other than a developer could not select the model
appropriate for their purpose. If models can be compared on a common basis or if a standard
verification process can be applies, users will have a tool for judgment.

This in turn will promoteutilization of simulation in practical transportation impact assessments.
The model verification process is roughly divided into two stages.

In one stage, the reproducibilityof assumed traffic phenomena is evaluated by comparing with theoretical values the result of model
application to virtual data set for frequent appearance of phenomena. In the other stage, evaluation ismade to see if the model can comprehensively reproduce actual traffic conditions, including various
traffic phenomena.
“validation.”In this paper, the former is referred to as “verification” and the latter

Validation requires data on traffic demand and operation, which are inputs tosimulation, and highly reliable measurement data indicating traffic conditions to be compared with thesimulation result. However, data gathering has imposed a substantial burden on model developers,
hindering validation. Against this background, construction of benchmark data for reproduction
verification is under way, so that model developers can share it during modeling. This manual
specifically deals with the standard verification process while providing only an outline of how toproceed with validation.

For specific details of validation, refer to the separate “Standard

Benchmark Data Set Manual (Provisional Title).”The main purports of verification in this manual are summarized as follows:・This verification deals mainly with a so-called network simulation model. It generally consists ofmodeling by simplifying various phenomena to handle traffic conditions comprehensively.
Contrary to this, local simulation models dealing with sag or weaving areas are generally developedon the basis of an approach that more precise logic is to be constructed through more detailed
analysis of the traffic phenomena concerned.
・One problem here is that the simulation model logic has become a black box. Its characteristics are
unknown to those other than the developer. It is difficult to understand everything only from theliteratures.
・Before discussion of the adequacy of comprehensive reproducibility of a model while using actual
data, it is necessary to clarify how phenomena critical in terms of traffic engineering are modeled
and to check if specific phenomena are reproduced truly as modeled.
・Accordingly, it is not important here whether or not modeled phenomena agree correctly with actual1

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traffic phenomena. Similarly, verification is not to compare merits and demerits among models.
・We will discuss whether or not model behavior has sufficient (or practically applicable)
reproducibility within the scope of application of the simulation model in the next validation stage.
Subsequently, the term, “simulation model,” unless otherwise indicated, refers to the network
simulation model.
In this manual, we first describe how the verification process is positioned in the standard development
process of a simulation model.

After discussing critical traffic-engineering phenomena that thesimulation model must take into account, the standard verification process is described with specificvirtual data setting presented in each step.

Finally, specific examples of applying the standard

verification process to several existing simulation models are introduced in the Appendix.

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２．Simulation Model Development Process
The simulation model development process generally follows the flow, including the processes shownin Fig. 1. Description below is concerned with how each process is positioned.

1) S p e c i f i c a t i o n…(Determination ofmodel specifications)2) M o d e l i n g…(Contrivance of model
operation principle)

Debugging3) Implementation…(Programming anddebugging)4) V e r i f i c a t i o n…(Verification with
virtual data)

5) V a l i d a t i o n…(Verification withmeasurement data)

Assurance that theoperation principle
complies with thespecification
Assurance that themodel specification
is appropriate toapplication purpose

Fig.1 General simulation-model development process
1)

Specifications…（Determination of model specifications）
From the users’ point of view, the simulation model may be thought of as a black box defined by
input and output.

If this model is to be used widely, there must be a common recognition of its

specifications or system input and output items, and its behavior must be guaranteed by the system.
For this purpose, requirements must be organized on the basis of consideration of needs andapplication purposes when determining the model specifications.

It is also necessary to

determine what kind of traffic phenomena must be handled.
2)

Modeling…（Contrivance of the model operation principle）
Contrivance of the model operation principle consists of the process of constructing an algorithm
complying with the model specifications of 2.1 and of deciding how such an algorithm is to beincorporated into the model. Here the originality of the developer plays an important role, which
may often result in operation according to a different algorithm depending on the model even when
the same specifications are complied with.

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3)

Implementation…（Programming and debugging）
This process consists of programming to run the operation principle contrived in 2.2 on a computerand debugging to check if the computer operates according to the algorithm.

Generally,

debugging must be distinguished as an operation different in nature from verification.
4)

Verification…（Verification using virtual data）
This process confirms that the program produced in 2.3 can reproduce the traffic phenomena
considered in 2.1 (Model Specifications) thereby verifying that the operation principle of 2.2 isjustified. In this case, an object of comparison with the simulation result is the traffic engineering
theory already established, which often explains phenomena by means of macro indices. This
process may be said to be an obligation of the developer in model development. Generally,
verification involves extraction and verification of individual highlighted phenomena, one by one,while using virtual data with ideal conditions so that they can be free from various actual restraints,
such as data accuracy, availability, etc.

5)

Validation…（Verification using actual data）
This is a process used to evaluate the practical applicability of the model. Validation is carriedout in terms of the adequacy of actual set model specifications or the accuracy of model output
items using data available in the actual world. Assume that the adequacy of the model operation
principle has been verified as described in 2.4 above.

The model is not considered to bepractically applicable, however, if the model specification itself is incomplete or if actual traffic
conditions can not be fully reproduced due to problems, such as actual input data accuracy oraccessibility.

Furthermore, model performance as a system must also be confirmed.

This

includes determining whether or not the model can be implemented within a practically applicabletime span or with hardware of an appropriate scale.

Validation requires data on simulation inputs

including traffic demand and operation as well as highly reliable data representing traffic
conditions to be compared with the simulation result. Such data gathering has been a substantial
burden for model developers, hindering validation.

Against this background, construction of thebenchmark data set to verify reproducibility is under way to make it available for common
utilization of model developers. Because of the advantage that it allows models to be comparedon a common basis, the Standard Benchmark Data Set, whose reliability as accurate measurement
data is widely recognized, is expected to be used by developers for validation.

4

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３．Traffic Phenomena to be Modeled through Simulation
This section discusses applications in which the modeling of basic traffic phenomena described below
proves important.

In addition, correspondence with the theory describing individual phenomena iscited and used as a key to establish the specific procedure for the standard verification processdescribed in the next chapter.
1)

Generation of vehicles
To implement simulation, it is necessary to generate the traffic at the entry end according to thearrival distribution of vehicles from outside the study area. The type of pattern to be assumed forarrival distribution when generating vehicles should be selected according to the type of roadconcerned and traffic volume. Generally, the following patterns may be considered:a) Random arrival of vehicles…When the study area is an expressway, the arrival pattern of traffic
not channeled outside the area may have spacing distributed randomly.

In a situation with low

traffic volume and vehicles running independently without affecting one another, the spacing ofrandomly arriving vehicles is distributed exponentially.

As the traffic volume grows,

approaching near-saturation, the prerequisite for independent spacing is lost. In this case,
Erlang distribution is said to apply.

Even for ordinary streets, many models employ thispattern because of differences in lag time that vehicles suffer at intersections adjacent to theentry end depending on whether or not random arrival is taken into account.
b) Arrival of vehicles at a given interval…When traffic is assumed to arrive after artificial
channeling or due to bottlenecks outside the area, spacing is distributed uniformly. Certain
models employ uniform arrival because there is no need to use the random number series and it
is easy to implement.
c) Arrival of vehicle groups at a certain interval…When the vehicle group is assumed to arrive at a
certain interval under influence of a signalized intersection in a vicinity outside the area, there isno such theory as random arrival. There are models that consider this kind of arrival pattern byusing a unique mathematical model.
2)

Bottleneck capacity／saturation flow rate at link’s downstream end
Generally, a given flow rate or bottleneck capacity is steadily observed on the direct downstreamside of the bottleneck section at the head of breakdown in the sag or lane blockage section, merge
area. Substantial contribution of the reproducibility of bottleneck capacity to the reproduction
accuracy of the lag time caused by breakdown can be explained by a simple model represented by
the point-queue1 of Fig. 2.

Namely, when the demand with peak arrives at the bottleneck, themaximum slope of cumulative curve for the traffic volume outgoing from this bottleneck is
restricted by the bottleneck capacity. Accordingly, this curve diverges from that of the arrival
1

Model, in which a link is assumed to be a virtual point-queue without length, and the flow is controlled only withrestrictions of the FIFO (first-in-first-out) principle and maximum flow rate. Since this model has no length concept, an
infinitely large number of vehicles can exist in the link and drawing of breakdown is not considered.

5

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traffic volume.

The area of this diverging portion is the total lag time caused by the bottleneck,which is evidently substantially dependent on the bottleneck capacity. For the simulation model,
it is essential that the bottleneck capacity is reproduced in a stable manner.

Cumulative traffic
volumeEntry
Travel timein free flow

Arrival at bottleneck

Outflow

Area of this portion＝Total lag
time
Bottleneck capacityTime

Fig.2 Conceptual view of lag time evaluation using Point-queue
For streets, on the other hand, signalized intersections become mostly bottlenecks.

In theseintersections, when vehicles retained during the red phase are about to outflow at the green phase,
it is observed that they outflow at a certain rate, that is, the saturation flow rate after elapse of afew seconds. Fig. 3 shows the outflow pattern after the beginning of the green phase in an
ordinary intersection. Outflow continues at the saturation flow rate till vehicles retained during
the red phase are gotten rid of, and subsequently at the flow rate of arrival from the upstream side.
The flow rate decreases gradually as the yellow phase begins, and becomes zero, that is, the traffic
flow stops, at the red phase.

Since the reproducibility of the saturation flow rate at thedownstream end link contributes greatly to the reproduction accuracy of the lag time at asignalized intersection, it is important to clarify how these phenomena are modeled in thesimulation model.

6

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Cumulative traffic volume
Smoothed cumulative curveTime at which
retained vehilces
have passed

Acutal throughtraffic volume

Saturation flow rate
Blue

Yellow
Red

Time

Fig.3 Conceptual view of one-cycle outflow pattern at a signalized intersection
3)

Drawing and elimination of breakdown and shock wave propagation speed
When a breakdown beginning at a bottleneck is drawn to the upstream link, traffic that need notpass through this bottleneck is also affected (Fig. 4). Reproduction of this phenomenon requires
handling of the physical-queue to control the density of breakdown flow according to theappropriate flow characteristic, that is, the traffic-density function, during simulation. In the caseof physical-queue, the speed of drawing/eliminating breakdown can be expressed by the
relationship between the demand arriving from the upstream side and the bottleneck capacity, as
shown in Fig.5, while using the shock wave theory.

As a difference in the breakdown

drawing/elimination speed results in a difference in the degree of influence on the traffic that has
nothing to do with the bottleneck, it is important that the simulation model can reproduce change
in this breakdown correctly.

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Vehicles not pasing throughbottleneck
Vehicles passing throughbottleneck

Bottlenecka) In the physical-queue, when breakdown is drawn to the
upstream side of merge area, vehicles that are not to passthrough bottleneck are contained in breakdown, suffering lag time.

Virtual point
Bottleneckb) In the point-queue, drawing of breakdown toward upstreamside is not considered, vehicles not to pass through bottleneck
are not included in breakdown

Fig.4 Difference between point-queue and physical-queue

8Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)
Bottleneck capacity:
small

Free
flow
sectionBreakdown
sectionBottleneck capacity:
large

Traffic
flowFree flow

Breakdown

sectionsectionFlow-density curve

ArriveddemandBottleneck capacity:
large
Breakjdown
drawing rate

Bottleneck capacity:small

On the flow -density curve, the inclination of a line connecting
the traffic situlation in the breakdown section and that of thefree flow section is the travel speed at the end of breakdown(shock wave). The negative inclination of indicates thatbreakdown isdrawn.

Density

toward upstream side

Fig.5 Calculation of breakdown drawing/elimination rate according to the shock wave theory
4)

Capacity of merge/diverge area and merge/diverge ratio
The merge area is the most remarkable bottleneck of expressways. Bottleneck at the merge area
causes either breakdown on both the main line and the merge branch or breakdown on either ofthem depending on the ratio of demand from the upstream side. Namely, assuming that the demandof main line a is Qa，demand of a branch b is Qb，the bottleneck capacity is C*，and the merge ratios
when breakdown occurs on both main line a and branch b are ma，and mb (ma+mb=1) respectively:a) When Qa+Qb>C* and Qa/ma>C* and Qb/mb>C* , breakdown occurs on both main line a andmerge branch b.
b) When Qa+Qb>C* and Qa/ma>C* and Qb/mb<C* , breakdown occurs only on the main line a.
With the simulation model, it is required to demonstrate the reproducibility of the bottleneck
capacity and merge ratio at the merge area and the breakdown situation on both merging andmerged sides while changing the distribution ratio of demand from the upstream side.

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Merge demand：Q b
Merge side throughvolume：Qb *Main line
demand：Q a

Bottleneck capacity：CC＊*
Merge area through＊ c* =Cvolume：QｃQ=C＊ *volume：Main side throughQQaａ*＊
volume：Merge ratio during＊＊*:=
breakdown:mａ＊m:maｂ:mb =QQ:Qｂb＊*,(m
, (m
a +m
b =1)
brekdown：
ａa:Q
ａ:m
ｂ:=1)
Whenbreakdown
breakdownisisdrawn
drawnononbothbothmainmaina)a)Whenline and merge line
a+Q
+Qｂ
b＞
>CC* ＊andかつQQａa/m
/mａa＞
>C
かつ
Q/m
b /m
b >C＊*QQａ
C＊* and
Qｂ
ｂ＞C

Merge
demand：Q b

Merge side throughvolume：Qb *Main line
demand：Q a

Bottleneck capacity：*CC＊
Merge area throughvolume：Qc* =C*

Main line side throughMerge ratio at*volume：Q a＊*＊*
breakdown：
mａ: am:mbreakdown:m:Qｂbｂb≠≠QQ
ａa:Q
bapplied※ ※ma,
mａ, mｂmbof ofa) aa)isis appliedb) When breakdown is drawn on the main line only＊*
QQａa+Q
C*＊andC＊*and
Qｂ/m
+Qｂb＞
>C
andQQ
a /m
a >C
and
Qb /m
b <C
ａ/m
ａ＞
ｂ＞C

Fig.6 Difference of breakdown drawing at merge area depending on the capacity and merge/diverge ratio

On the other hand, in the diverge area, capacity varies according to the distribution ratio of demand
from the upstream side to the main line and diverge branch, that is, the diverge ratio. Namely,
assuming that the demand for main line a is Qa，the demand for branch b is Qb，the main line
capacity downstream of the branch is Ca* ; the diverge branch capacity is Cb* ; and the distribution
ratio of demand to main line a and diverge branch b is ra and rb (ra+rb=1)，respectively. The
capacity of the diverge branch C* then becomes:
C*=min(Ca*/ ra, Cb*/ rb)(Fig. 7)． During simulation, it is necessary to check if the above relationship can be established.
In the case of a model handling the traffic flow discretely, it is necessary2 to check if the intended
diverge ratio can be achieved through elimination of error3 due to discretion when there exists an
extreme deviation in the diverge ratio and the demand from the upstream side is relatively small.

2

In a model where the demand is provided for each 0D instead of setting the diverge ratio, a similar problem occurs when asubstantial deviation exists in the route selection probability in a simple network with a 10D2 route.
3
For example, assume here that there is the demand of 10 units per five minutes from the upstream side when the diverge
ratio is 0.99:0.01. Since the discrete method can not divide the demand into 9.9 units and 0.1 unit, a certain contrivance isnecessary.

10Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Diverge area***
capacity:C =min(Ca /ra , Cb /rb )Demand to mainline：Qa
Demand to diverge
branch：Q b

Diverge branchcapacity：C b *Main line
capacity：C a *Divergeratio：r a :rb = Qa :Qb , (ra +rb =1)a) Breakdown in diverse branch determines the diverge area capacity
C* =Cb */rb and Qb >Cb *Diverge area***
capacity：C =min(Ca /ra , Cb /rb )Demand to mainline：Q a
Demand to diverge b
branch：Q

Diverge branchcapacity:C b *暴線容量：Ca *Divergeratio：ra :rb = Qa :Qb , (ra +rb =1)b) No breakdown even t the same demand level
Qa ' <Ca * and Qb '<Cb *Fig.7 Difference in breakdown depending on difference in capacity and diverge ratio in the diverge area
5)

Decrease in the right-turn capacity due to opposing traffic in a signalized intersection
In ordinary streets, it is a daily observation that vehicles waiting for right-tun in a signalizedintersection hinder travel of following vehicles, resulting in a breakdown. Such vehicles are
waiting to find a gap in the opposing straight-through traffic in the green phase.

As a result, theright-turn traffic capacity in this intersection is reduced by the opposing straight-through volume.
Model verification is made by comparing the model describing this phenomenon macroscopicallywith the simulation result. As an example of macroscopic description, a calculation equation4 forright-turn capacity by the Japan Society of Traffic Engineers is shown in Equation (1) below.
SR=1800 f (S G – q C)/(S – q) C + 3600K/C…(1)

SR…Capacity of exclusive right-turn lane [units/hour]
S…Saturation flow rate in the entry section of opposing straight-through traffic[units/effective green one-hour]
q…Volume in the entry section of opposing straight-through traffic [units/hour]
C…Cycle length [second]
G…Effective green time [second]
K…No. of units discharged at change of signal [units/cycle]
4“Plan and Design of Level Crossing – Fundamentals”; The Japan Society of Traffic Engineers, 198411

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f…Gap acceptance probability determined from the following relationship:f=6)

1.00 (q=0),0.81 (q=200),

0.65 (q=400),

0.54 (q=600),

0.45 (q=800),

0.37 (q=1000),

0.0 (q>1000),Interpolation made for the median q value．

Route selection behavior
Modeling for users’ route selection behavior considered in simulation is classified as follows:a) Dynamic route selection model not incorporated…This is a type in which each vehicle, without
any information on a destination, selects the next link according to the distribution ratio set foreach diverse area. Since the OD volume need not be given as a demand, the input data is easy
to obtain. When the network includes loop, however, the link volume is larger than the actual
volume because there are vehicles that go around the loop.
b) Dynamic User Optimal (DUO) allocation incorporated…DUO is “to select the optimum routeaccording to the route cost in the instant it is presented till the user reaches the destination.”As the simulation itself represents the current situation through accumulation of situations at
respective time points, modeling is relatively easy. This also represents the framework oftravel information presentation in the actual world. Accordingly, many models incorporate aroute selection model based on the DUO principle. Note however that the quality of the “route
cost in the instant it is presented” is not defined in DUO. If the route cost is, for example, the“average required time up to the destination, which was observed five minutes ago,” theselected route is not necessarily the optimum route to reach the destination.

Namely, aso-called hunting phenomenon may occur.
c) Dynamic User Equilibrium (DUE) allocation incorporated…DUE is “to select the optimum
route according to the route cost that a user actually experiences till he/she reaches thedestination.”

Since the future traffic situation not known at time of selection must be projected,

a complicated network may make theoretical solution difficult.

Therefore, at present, there is

no practically applicable simulation model that can achieve DUE in the strict sense of the word.
Models approximating achievement of DUE are as follows: One is (c1) a model for selection
through feedback of simulation result concurrently with advance projection of the traffic
situation up to the near future by independent modules on the basis of the current traffic
situation reproduced through simulation. The other is (c2) a model that repeats simulation topredict and converge the future route cost empirically from the previous simulation result.
d) Probabilistic route selection…In the case of b) and c) above, the minimum of presented route
cost is always selected. Contrary to the above, this model assumes that human recognition
error is distributed probabilistically, and the route with the minimum cost is not necessarily
selected. Depending on the distribution pattern of recognition error, models are classified intoa Logit model, a probit model, etc.
Of these models, the one using a) above is considered applicable for evaluation of short-term
traffic operation policies that do not have to consider routes of road users. It can also be applied
to networks without allowance for route selection.
12

Verification of these models is not specificallyStandard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

necessary because it is equivalent to the previous verification of the merge/diverge ratio in that it
involves verification of whether or not the set diverge ratio is actually achieved.
On the other hand, the simulation model using standards such as b) DUO or c) DUE adopts aframework in which users select routes on the basis of presented route cost.

This type of model ismostly used to evaluate the dispersing of traffic spatially by means of information services androad construction. Generally, verification of these models is made using a simplified networkwith two routes because of the increased difficulty of determining flow patterns to achieve DUO
and DUE as the network becomes complicated. Fig. 8 shows the flow pattern and route costwhen DUE is to be achieved using the travel time as a cost for the two-route network. Namely,
all vehicles select route 1 initially when the cost is small. As breakdown occurs at the bottleneck
downstream of the merge area, and the cost of route 1 becomes equivalent to that of route 2, thetraffic flows to both routes. The diverge ratio at this time point is equal to the capacity ratio in
the merge area.

Route1
Demand A
(t)
Start
point

Q1 (t)

Q1 ' (t)Q2 (t)

Q2 ' (t)Merge ratio：
1 :m2
m
End
point
Bottleneck capacity：*
C

Route2

Fig.8 1OD2 route network
Figs. 9 and 10 show the flow pattern based on point-queue when the demand including peak A(t)exists in a simple 10D2 route network and the merge area becomes a bottleneck. Specifically,
they show the flow pattern for two cases: one with DUO allocation on the basis of the current route
required time and the other where DUE is achieved. In the case of DUO based on the current
route required time:i) Initially, all vehicles select route 1 when the cost is small.
ii) At a time t2, the cost or the travel time t2 - t1 of vehicles outgoing at this time point becomesequal to the initial cost p20 of route 2.
iii) The cost of route 1 in the next instant is the travel time of vehicles that suffer larger delay thanthose outgoing immediately before this instant and thus becomes higher than that the cost ofroute 2. As a result, all vehicles select route 2 after t2iv) At a time t3, part of the traffic volume outflows from route 2 to the merge area. At this time
point, breakdown remains on the side of route 1, so that the run-off volume from both routes is
equivalent to the bottleneck capacity allocated on the basis of the merge ratio.
v) Breakdown of route 1 is eliminated at a time t4． Since no vehicles are left on route 1, the route
cost decreases discontinuously to p10. Therefore, after this time point, all vehicles select route
1 again.
In this case, the inflow volume for each route, Q1(t)，Q2(t), increases in stages, step-by-step.
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Cumulative
volumeDemand A(t)
Bottleneck
throughvolumeQ1 '(t)+Q 2 '(t)Capacity*C

Time

Cumulative
volumeQ1 (t)

Q1 ' (t)Capacity*C
Q2 (t)
Q2 ' (t)Time

Route cost
p2 0

Route 2 cost

p1 0

Route 1 cost

0

Time
ｔ
１ ｔ
2 ｔ
3 ｔ
4 ｔ
5

Fig.9 Flow pattern with DUO allocation based on current route required timeOn the other hand, the flow pattern in which DUE is achieved for the same demand is substantiallydifferent from the case of DUO.

Namely:i) Initially, all vehicles select route 1 where the required time is short.
ii) At a time t1, the cost becomes equal for routes 1 and 2, so that vehicles may select either route.
The ratio of volumes for the respective routes becomes equal to the merge ratio during
breakdown in the merge area, and the cost of each route changes equally.
iii) At a time t3, vehicles moved into route 2 run off at a time t4 when breakdown in the route 2
disappears. Therefore the cost becomes p20. Since the cost of route 2 does not decrease
further, all vehicles subsequently select route 1.

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Demand A

Cumulative
volume(t)
Bottleneck
throughvolumeQ1 '(t)+Q2 '(t)CapacityC*
Time
Cumulative
volumeQ1 (t)

Q1 ' (t)CapacityC*
Q 2 (t)Q 2' (t)Time

Route cost

Route 2 cost

p2 0

Route 1 cost

p1 0

Time

0

ｔ
1 ｔ
2

ｔ
3 ｔ
4 ｔ
5

Fig.10 Flow pattern achieving DUE
In the case of DUE, the FIFO (first-in-first-out) principle is established in the bottleneck whenboth routes are selectable.
is taken.

This is because the required time is the same regardless of which route

Therefore, it is known that the bottleneck through volume is quite similar to thebreakdown phenomenon on a single route.
Figs. 9 and 10 show the theoretical value when point-queue is used without considering the effect(drawing) of a breakdown.

In the simulation handling physical-queue, the figures may bedifferent when a breakdown affects the diverge area.
comparison with these theoretical values for evaluation.

15

In any case, verification involves

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

４．Simulation Model Standard Verification Process - Verification
This chapter describes the verification process used while referring to the virtual data set. Here, thefundamental concept of verification is to compare “the established theory to described phenomena”
and “the observed and accumulated results of dynamic traffic conditions represented by simulation.”
Verification is not dependent on exact agreement of the simulation result with these theoretical values.
The objective of verification is to define the model characteristics while confirming correlation withor difference from the theory.

At the same time, it is considered important to define the relationshipbetween certain model parameters and model behavior.
Verification steps are required to clarify conceptually how each model represents traffic phenomena
concerned. In this case, the required verification procedure differs for the following two models
because of substantial difference, in set parameters. They are a model which reproduces the flow by
taking into account the follow-up behavior of individual vehicles (a car-following model) and a model
to control the flow with the vehicle list by providing externally traffic flow characteristics such as theflow – density (Q-K) function. (a Q-K type model).
Verification steps corresponding to traffic phenomena described in the previous chapter are explained
below step-by-step separately for Q-K and car-following models.

As is said commonly for all items,

it is necessary to describe in as much detail as possible how these phenomena are modeled. It is also
necessary to describe clearly related parameters and settings. Unless otherwise described, the link is
considered to be one lane. Namely, it is intended to perform verification while eliminating theeffects of lane changes on capacity in a multi-lane situation.

(1) A．Q-K type model verification procedure
The Q-K model is a generic name for models that perform flow control with a list by providing
macroscopic traffic flow characteristics. This type of model includes those establishing not only
Q-K relationships, but also S-V (spacing – velocity) and Q – V (volume – velocity) relationships
derived from them. These models are verified according to the procedures 1) through 6) described
below. Note that certain models handle specific phenomena by partially providing microscopic
characteristics (vehicle behavior, etc.).

In this case, refer to the verification procedure for the

car-following model that is described later.
1)

Generation of vehicles
To verify the vehicle generation function of a simulation model the following points must be
determined.
a) Whether the generation pattern assumed in the model is achieved.
b) Whether there exists substantial divergence from the assumed pattern due to a random number
series.
c) Whether the quantity of vehicles is completely the same as the traffic demand set within a given
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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

time period or within what range they increase/decrease.
d) Whether, in a situation with a breakdown within the study area being drawn outside the network,
arriving vehicles are added to the end of breakdown outside the area, and finally, the entire set
demand flows into the area.
Specific verification procedure examples are described below first for a) through c).
i) A network comprising the generation point shown in Fig. 11 and the link running off therefrom.
The links are assumed to have a capacity of 2200 [units/hour].

Demand = 500, 1000, 2000 [veh./hr]

Link
Capacity = 2,200 [veh./hr]

Generation point

Fig.11 Example of verification data set for vehicle generation modelii) Given three stages of traffic demand, 500，1000，and 2000[units/hour], simulation is made forhour and the time interval headway from a preceding vehicle when vehicles are generated isrecorded. For a model in which vehicle generation timing is difficult to record, observe theheadway at the link upstream end. For a model approximating the fluid, the generated trips
are recorded at a unit scan interval.
iii) As shown in Fig. 12, the appropriately discretized headway or the generated trips within a unit
scan time is represented in the form of a histogram. For the purpose of comparison, theprobability density distribution of a theoretical arrival pattern is also shown in this figure5.
Appearance
frequency

Prability density function

0

1

2

3

4

5 6 7 8Spacing interval

910

Fig.12 Histogram and theoretical value of headwayiv) Verification is made also on whether the total generated trips in one hour are larger or smaller
than the set volume of 500，1000，and 2000 units.
v) For a model in which random generation is made using random numbers, steps ii) to iv) are5

Verification focuses not on exact representation of theoretical values, but on definition of model behavior. It is therefore
unnecessary to perform as much statistical calibration. It may be enough to check the graph visually.

17

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

repeated five times while changing the random series for each traffic demand.
Now verification of d) is described below.
i) Given the traffic demand in which the demand for the initial one hour is 4400 [units/hour] andno more, vehicles are generated after that, simulation is made till the volume at the link
downstream end becomes zero as shown in Fig. 13.

Demand = 4400 [veh./hr]0 [veh./hr]

Generation point…Initial one hour
…Next one hour

Linkク
Capacity = 2,200 [veh./hr]

Fig.13 Volume conservation verification data set when cars in a jam are spread out outside the networkii) The cumulative curve of through volume that is observed at the link upstream end is illustrated
to see if 4,400 vehicles flow into the network finally. The curve expected here is as shown in
Fig. 14.

Cumulative
volume4400

Set demand

Link throughvolume

2200

0

1

2

Time

Fig.14 Volume cumulative curve expected when the demand of 4400[units/hour] is given
2)

Bottleneck capacity／Saturation flow rate at link downstream end
First, reproducibility of the bottleneck capacity is verified. Given the sufficiently large demand tothe bottleneck according to the procedure6 described below, verification is made to determine
whether the rate of flow on the downstream side is stable for the bottleneck capacity.
i) The network to be used consists of links whose downstream ends become bottlenecks as shownin Fig. 15. Set the model parameter so that the bottleneck capacity becomes 800，1000，and
1200[units/hour]. The capacity is set to be around 2200 [units/hour] for other sections.

6

For a model based on car-following travel, the procedure is approximately similar to the procedure to determine the Q-K
curve on the breakdown flow side in the Appendix.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Demand = 1,500 [veh./hr]Bottleneck capacity= 800, 1000, 1200 [veh./hr]

Link capacity = 2,200 [veh./hr]

Fig.15 Bottleneck capacity reproducibility verification data setii) The traffic demand of 1500 [units/hour] is provided so that breakdown occurs always in thebottleneck.
iii) Simulation is made for one hour using respective model parameters and the through volume on
the downstream side of the bottleneck is recorded.
iv) As shown in Fig. 16, the through volume cumulative curve is plotted7, and verification is madeto see if the bottleneck capacity is achieved.

Cumulative
volumeCase with bottleneck capacity of 1000
[units/hour]Set demand

1500

Link throughvolume

1000

0

1

Time

Fig.16 Verification on whether or not the bottleneck capacity is reproduced in a stable manner
Verification on the saturation flow rate at the link downstream end is made as follows. Namely,
for a simulation model applied to ordinary streets including signalized intersections, verification ismade to check the manner in which vehicles retained during the red phase run off during the green
phase.
i) As shown in Fig. 17, a network is formed from one-lane links controlled by the signal at thedownstream end. The signal is under the fixed-time control with a cycle length of 120[seconds], a split of 50%, and a lost time of 10 [seconds/cycle].

7

Be sure to enter the link through volume in one hour to the graph.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)
Cycle 120 sec
Split 50%
Lost time 10sec

Demand = 600 [veh./ hr]
800 [veh./hr]1000 [veh./hr]

Link capacity = 2,200 [veh./hr]Saturation flow rate
= 1400，1600，1800 [veh./effective green one hour]

Fig.17 Verification data set on reproducibility of saturation flow rate at link downstream endii) Set the model parameter so that the saturation flow rate at the link downstream end becomes
1400，1600，and 1800[units/effective for green phase in one hour]. Simulation is made forone hour on this case while changing the arrival demand from upstream to 600，800，and
1000[units/hour].
iii) When ten cycles are completed after the start of simulation, observe run-off from the link forabout ten cycles. The observation time interval is equal to the unit scan time of the model.
iv) The run-off volume per cycle after start of the green phase is plotted into the cumulative curve.
As shown in Fig. 18, cumulative curves of ten cycles are overlapped and indicated. 8
Verification is made to confirm that the flow rate is reproduced in a stable manner in all cycles
while the traffic flow is saturated.

Cumulative
volumeGreen

Yellow

Red

Through volume per
cycle
Saturation flow rate
0

55

60

Time [sec]Fig.18 Saturation flow rate observed at link downstream end
3)

Spreading out cars, eliminating jams and shock wave propagation rate
This verification is made on a basic segment including bottleneck in terms of followings:e) Condition in which the demand exceeds the bottleneck capacity and breakdown is drawn to the
upstream sidef) Condition in which the demand is smaller than the bottleneck capacity and breakdown is

8

For the sake of reference, a straight line with a gradient of saturation flow rate is entered in the graph.

20

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

dissipated downward from the upstream side.
This is done to verify that drawing and dissipation of breakdown are reproduced according to thetheory. For a model that handles traffic flow controlled by signals, further verification is made on
the following points:g) Condition in which breakdown is eliminated upward from the downstream side when the signal
phase changes from red to green.
Specific procedure is described first for a) and b).
i) A basic-segment network is formed from multiple links with bottleneck section on thedownstream side, as shown in Fig. 19.

Demand =750 [veh./hr] -- 0 - 5 minutes
900 [veh./hr] -- 5 - 15 minutes
1,500 [veh./hr] -- 15 - 25 minutes
750 [veh./hr] -- 25 - 60 minutes

Bottleneck capacity= 800, 1000, 1200 [veh./hr]

Link 1

Link 2

Link 3

Link 4

Link 5

500m

500m

500m

500m

500m

Link capacity = 1,800 [veh./hr]

Fig.19 Verification data set for spreading cars out and eliminating traffic jamsii) Three cases are set up, each with the bottleneck capacity of 800，1000，and 1200[unit/hour].
The capacity for other sections is set to 1800[unit/hour].
iii) Provide the demand that has a peak in such a manner that breakdown occurs at bottleneck andis dissipated subsequently. Provide the demand as follows after simulation start:
・0〜5 minutes…750[units/hour]
・5〜15 minutes…900[units/hour]
・15〜25 minutes…1500[units/hour]
・25〜60 minutes…750[units/hour]iv) As shown in Fig. 209，the shock wave propagation rate is determined10 from the Q-K curve
provided to the model. Then, the traffic condition transition diagram on the downstream sideof the bottleneck is prepared as shown in Fig. 21.
v) Simulation is made for each bottleneck capacity to handle the traffic jam by observing therun-off volume from each link.
vi) As shown in Fig. 21, the traffic condition transition diagram is overlapped on the run-off

9

For the sake of simplification, this figure shows an example approximating the Q-K curve as a triangle. This does notnecessarily pertain to certain models. In this case, five forward waves (FW1 through 5) and one backward wave BW1
occur.
10
In a model which defines the relationship of not Q-K, but S-V, the shock wave propagation rate is determined byconverting this relationship into the Q-K relationship.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

volume cumulative curve of each link, and verifying is made11 on whether the jam is spread out
or eliminated at this rate.

Volume [veh./hr]-10.3 [km/hr]

1800

FW1 - FW5 : Forward wave
BW1
: Backward wave

1500
36.0 [km/hr]
BW1
FW3, FW4

900
750

1000
FW5

3.6 [km/hr]

FW1, FW2

20.8

41.7 5090

Density
140 [veh./km]

Fig.20 Shock wave propagation rate when the bottleneck capacity is 2000[units/hour]

11

Considering the purport of verification, it is enough here to see visually on the graph if the time point at which the linkrun-off rate changes on the cumulative curve agree with that at which the shock wave is propagated theoretically. As the
run-off rate is not stable during simulation, it is difficult to indicate, exactly by using numerals, the time point at which theshock wave is propagated22Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Cumulative volume
900

Link-1
800

Demand [veh./hr]
700

750

900

Link-21500

Link-3750

600

Link-4500

Link-5400

300

Bottleneck capacity
1000[units/hour]

200
100

0

0

5

10

15

20

25

30

35

40

45

50

55

60

4'10"
Distance from bottleneck[m]

0

9'10"

Link-519'10"

500
BW1

51'11"

FW5

Link-41,000

1468.2m
26'43"

1,500

Link-3
Link-2

FW2

FW1

2,000

FW3

FW4

Link-1
2,500
0

5

10

15

20

25

30

35

40

45

50

55

60

[minutes]Fig.21 Traffic condition transition diagram on the bottleneck downstream (lower) and observed volume
cumulative curve (upper)
The procedure concerning c) is described below. Verification is made here for the simulation
model for ordinary streets including signalized intersections − specifically, on the manner inwhich vehicles retained during the red phase run off in the green phase.

Verification is made onwhether or not start and stop wave propagation rates according to the signal agree with theoreticalvalues determined from the shock wave theory.
i) A network is formed from one-lane links with signal control on the downstream end, as shownin Fig. 22. The signal is under the fixed-time control with a cycle length of 120 [seconds],
split of 50%, and lost time of 10 [seconds/cycle].

23

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)
Cycle 120 sec
Split 50 sec
Lost time 10sec

Demand = 600 [veh./ hr]
100m

Volume observation
section

80

60

40

20

0

Saturation flow rate
= 1400，1600，1800 [veh./effective green one hour]Fig.22 Verification data set for reproducibility of start/stop wave according to signalii) Set the model parameter so that the saturation flow rate is 1400，1600，
and 1800[units/effective,
green one hour] and carry out simulation of these three cases.
iii) Provide the demand of 600 [units/hour] so that it is not saturated for a signalized intersection.
In this case, it is desirable that vehicle generation is assumed to be for uniform arrival because
excessive random arrival causes hindrance to verification of whether or not the stop wave is
propagated according to the theory12.
iv) Simulation is made on each parameter set to observe the through volume at points of 0, 20, 40,
60, 80, 100 m …. from the signalized intersection.

The observation time interval is the unit

scan time of model.
v) For a one-cycle time span beginning with a red phase, the cumulative curves of throughvolumes at each point are overlapped mutually in the graph. In the case of a model providing
the link capacity externally, verification is made of whether start and stop waves are propagatedat the shock wave propagation rate determined from the Q-K curve assumed by the model asshown in Fig.2313.

Namely, this curve is overlapped to the cumulative curve as shown in Fig.

24 to verify whether the inclination change time points agree14.

12

In a model not assuming uniform arrival, it is essential to take such a measure as provision of a given demand within the
shortest possible interval. For example, vehicles may be generated at a rate of 10 units every minute.
13
For the sake of simplification, similar to the previous phrase, the example of approximating the Q-K curve in a triangle isshown here.
14
Considering the purport of verification, it is enough to visually check the graph to determine whether the time point at
which the link run-off rate on the cumulative curve agrees with that at which the shock wave is propagated theoretically.
As the run-off rate is not stable during simulation, it is difficult to precisely and numerically indicate the time point at
which the shock wave is propagated24Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Volume [veh./hr]
1800
36.0 [km/hr]
Start wave
-20.0 [km/hr]
Stop wave

600-4.86 [km/hr]
16.7

Density
140 [veh./km]

50

Fig.23 Start and stop wave rate determined from the Q-K curve

Cumulative
volume[units]

120m
100m
80m
60m
40m
20m
0m

Red

Start
wave

Distance from signalizedintersection[m]

120
Stop
wave

100
80

Green

Time
[sec]

- 20.0 [km/hr]-4.86 [km/hr]

36.0 [km/hr]

60
40
107.2m

20
0

0

60

79.3

Time
[sec]

Fig.24 Start and stop wave propagation manner and cumulative volume at each point
4)

Capacity and merge ratios in the merge section
For the merge area, verification is made to see if the achieved capacity and merge ratio are as set
by changing the demand ratio between the main line and merge sides. The behavior verification
procedure for the merge area is described below.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

i) A network is formed from two (a and b) merge branches with a capacity of 1800 [veh/hr] asshown in Fig. 25. The capacity of the section directly downstream of the merge area isassumed to be 2200 [veh/hr], which is smaller than the sum of the merge branch capacities.

Generation point

Merge branch a
Capacity 1800
[units/hour] Merge area
Capacity 2200
[units/hour]

Total demand= 2000，2500 [units/
hour]

Generation point

Merge branchbCapacity1800[units/hour]

a/b merge ratio
0.1:0.9，0.3:0.7，0.5:0.5

Fig.25 Verification data set for reproducibility of merge capacityii) In the model giving externally the merge ratio during a traffic jam, the a/b merge ratio is set in
two ways at 0.3:0.7 and at 0.5:0.5. Simulation is made for each of them.
iii) For each parameter set, the total demand to the merge area is assumed to be 2000 and
2500[veh/hr] and the demand distribution ratio from branches a and b is set to three stages:
0.1:0.9，0.3:0.7，and 0.5:0.5. With a total of six patterns, 12 simulation times are derived.
Each simulation may take about one hour.
iv) The demand for each merge branch and the cumulative through volume at the downstream end
are graphed for each case to determine whether a jam has occurred. The jam situation is
expected to result as shown in Tables 1 and 2. Concurrently, the cumulative through volume
on the downstream side of merge area is also entered in the graph to determine whether the set
capacity is achieved.
Table1 Traffic jams in each merge branch when the merge ratio is 0.3:0.7
Total demand
0.1:0.9
0.3:0.7
0.5:0.5｜a/b distribution ratio
2000[veh/hr]
No jam
No jam
No jam2500[veh/hr]
Jam in b
Jam in both
Jam in a
Table2 Traffic jams in each merge branch when the merge ratio is 0.5:0.5
Total demand｜a/b
0.1:0.9
0.3:0.7
0.5:0.5
distribution ratio
2000[veh/hr]
No jam
No jam
No jam2500[veh/hr]
Jam in b
Jam in b
Jam in both
For the diverge area, verification is conducted as follows to confirm that the diverge ratio changes
according to the capacity.

26

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

i) A network is formed from two (a and b) branches with a capacity of 900 [veh/hr]. The
capacity before the diversion area is assumed to be 2200 [veh/hr].

Total demand = 1200 ，2000[units/hour]
Link capacity 2200
[units/hour]

Merge branchaCapacity 900[units/hour]

Generation point
a/b diverge ratio
0.1:0.9，0.3:0.7，0.5:0.5

Merge branchbCapacity 900[units/hour]Fig.26 Verification data set for reproducibility of diverge area capacityii) Total demand at the diverge area is assumed to be 1200 and 2000[veh/hr]. Then, simulation iscarried out six times for each demand level while changing the distribution ratio or diverge
ratio of demand to each of the a and b branches in three patterns of 0.1:0.9，0.3:0.7，and 0.5:0.5.
iii) For each case, judgment is made from the through volume of diverge area on whether or not a
jam has occurred and the capacity is observed. The result shown in Table 3 is expected.
Table3 Traffic situation in the diverge area
Total demand｜a/b
0.1:0.9
distribution ratio
Jam
1200[veh/hr](Capacity1000[veh/hr])
Jam
2000[veh/hr](Capacity
1000[veh/hr])
5)

0.3:0.7

0.5:0.5

No jam

No jamJam(Capacity
1286[veh/hr])Jam(Capacity
1800[veh/hr])Decrease in right-turn capacity due to straight through traffic in the signalizedintersection
To verify the right-turn capacity, the result is compared with the right-turn capacity calculation
equation15 of the Japan Society of Traffic Engineers. The verification procedure is described
below:i) As shown in Fig. 27, a network, including one signalized intersection is formed.

The

saturation flow rate of opposing straight through traffic is set to 2000 [units/effective green onehour] or to an equivalent level. The basic right-turn capacity is set to 1800 [veh/hr]. The
number of vehicles that can stay in the intersection waiting for a right-turn is assumed to be
two units.
15

This equation is used not to present theoretical values, but only for reference.

27

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Straight throughdemandSaturation flow rate of opposing
straight through traffic

Right-turn basic capacity
1800 [veh/hr]= 200 〜1200 [veh./hr]
2000[veh./effective
green one hour]

Cycle 120 sec
Effective green time 40，60，
80 secRight-turn demand
2000[veh/hr]

Fig.27 Verification data set for decrease in right-turn capacityii) For the signal parameter, the cycle is set to 120 seconds and the effective green time is changedin three stages to 40，60，and 80.
iii) With each signal parameter set, the right-turn volume is observed while changing the demandof opposing straight through traffic in six stages to 200，400，600，800，1000，and 1200. In
order to ensure supply of vehicles at all times, the traffic demand for right turns in theintersection is set at approximately 2000 [veh/hr].
iv) The simulation observation result is compared with equation (1) of Section 5, Chapter 3.
Namely,
SR=1800 f (S G – q C)/(S – q) C + 3600K/C…(1)

SR…Capacity of an exclusive right-turn lane [veh/hr]
S … Saturation flow rate at approach of opposing straight through traffic[veh/effective green one hour]
q…Volume at the approach of opposing straight through traffic [veh/hr]
C…Cycle length [sec]G…Effective green time [sec]K…No. of vehicles that can be discharged at change of signal [veh/cycle]
f…Gap acceptance probability determined from the following relationshipf=

1.00 (q=0),0.81 (q=200),

0.65 (q=400),

0.54 (q=600),

0.45 (q=800),

0.37 (q=1000),

0.0 (q>1000),Interpolation for median q value

When comparing simulation results, plot the opposing straight through volume on an abscissa andthe right-turn capacity (= through traffic volume) on an ordinate for each signal parameter set, asshown in Fig. 28.

28

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Right-turnthrough volume[veh/hr]Cycle length 120 sec
Effective green
time 60 sec
Simulation result

Equation
(1)
200

400

600

800

1000

Opposing straight
through volume
1200 [veh/hr]

Fig.28 Comparison of right-turn capacity simulation results and theoretical values
6)

Route selection behavior
This verification is used to confirm the route selection model the simulation model assumes andhow truly the theoretical value is reproduced. The theory in this case is either DUO or DUE.
Since an excessively complicated network makes calculation of the theoretical value itself
impossible, a simple network comprising a 10D2 route is used for verification. Verification iscarried out as follows:i) The 10D2 route network shown in Fig. 29 is used.

The capacity is set to 900 veh/hr or anequivalent so that the merge area becomes a bottleneck and to 1800 veh/hr for other sections.
The merge ratio during a jam is assumed to be 0.5:0.5.

Merge ratio during
jam 0.5:0.5

Demand1200 [veh/hr] - 0〜60minutes
600[veh/hr] - 60 〜120 min
Link 0
1500m

Start
point

Capacity of links 0〜2= 1800[veh/hr]

Link 1

1500m
Route1

Route23000m

Link 33
1500m

End
point

Bottleneck capacity
900[veh/hr]

Link 2

Fig.29 Verification data set for reproducibility of route selection behaviorii) Prepare three model setting patterns 16 for each of the model selection standards (DUO/DUE,
shortest cost selection/probability selection, etc.) and route cost renewal time interval, androute selection timing.
iii) For each setting pattern, simulation is for two hours. Set the demand to 1200 veh/hr for the
initial one hour and 600 veh/hr for subsequent one hour.
16

Parameters and set items vary greatly depending on the model and are thus not specifically given here. Each model user
must define pertinent parameters and set appropriate values

29

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

iv) Observe the cumulative volume of incoming and run-off for links 1 and 2 in each case andcompare the observed results with the theoretical flow pattern. For reference, the flow patternwhen DUE is achieved with a free flow rate of 36 km/h (= 10 m/sec)17 is shown in Fig. 30. It
should be noted that, to avoid complication, the link volume is handled with point-queue andspreading out cars from the traffic jam to the diverge area is not considered.

122.5

Cumulative volume
1800

Demand setting
Link 1 inflow
Link 2 inflow
Link 1 outflow
Link 2 outflow

600 [units/hour]
900 [units/hour]
1200

600 [units/hour]

1200 [units/hour]

990
910

300 [units/hour]

760
650
600 [units/hour]

5001200 [units/hour]

450 [units/hour]

150

5
2.5

10 15

60

900

Fig.30 Flow pattern of a case in which DUE is achieved

17

The difference in free travel time between both routes is 2.5 minutes.

30

112

[minutes]
120
117

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)(2) B．Car-following Type Model Verification Procedure
The car-following type model is a model that simulates travel in the lane according to set parametersconcerning driving behaviors such as reaction delay, maximum acceleration, and target headway, etc.
Verification of these models proceeds according to steps 1) through 7) below.
1)

Generation of vehicles
In this step, the function of a simulation model to generate vehicles is verified. The following
points are checked:h) Whether the generation pattern assumed for the model is achieved.
i) Whether or not substantial deviation has occurred from the assumed pattern due to a random
number series.
j) Whether vehicles of exactly the same quantity as the demand set for a given time span havebeen generated or to what degree the quantity increases/decreases.
k) Whether, with breakdown drawn from the inside of the study area to the outside of network,
arrived vehicles are added to the end of the jam outside the area and the finalized demand flows
into the area without elimination.
Examples of specific verification procedures are shown below, first for a) to c):i) A network is formed from a generation point and a link running off from this point, as shown in
Fig. 31. The link is assumed to have an effective width of 3.5 m and gradient of 0% so that it
can have sufficient capacity.

Demand = 500, 1000, 2000 [veh./hr]

Generation point

Link
Driveway width 3.5m ，gradient 0%

Fig.31 Example of data set for verification of the vehicle generation modelii) One-hour simulation is made for a case with three stages, each 500，1000，and 2000veh/hr, of
demand.

In this simulation, recording is made for the time interval headway from a previous

vehicle when vehicles are generated. For a model for which the vehicle generation timing isdifficult to record, headway is observed at the link upstream end. For a model approximating
fluid (?), the generated trips are recorded at the unit scan interval.
iii) As shown in Fig. 32, the generated trips at an appropriately discretized headway or within theunit scan time are represented in a histogram for respective results.

For the sake ofcomparison, the probability density distribution of the theoretical arrival pattern is also shown

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

in the figure18 below．

Appearance frequency

Probability density function

0

1

2

3

4

5

6 7
Headway8

910

Fig.32 Histogram and theoretical values for headwayiv) Verification is also carried out to determine whether the total generated trips per hour haveincreased or decreased from the set trips of 500，1000，and 2000 units.
v) For a model achieving random vehicle generation using random numbers, steps ii) through iv)
are repeated five times while changing the random number series for respective demands.
Verification of d) is described below.
i) Given demand of 4400 veh/hr for the initial one hour and totally zero after that, as shown in
Fig. 33, simulation continues until the volume at the link downstream end becomes zero.

Demand = 4400 [veh./hr]
0 [veh./hr]

Generation point…Initial one hour
…Next one hour

Link
Driveway width 3.5m ，gradient 0%

Fig.33 Verification data set for volume conservation when cars in traffic jam are drawn outside the
networkii) The cumulative curve of through volume observed at the line upstream end is illustrated toverify that 4400 vehicles have finally flowed into the network. The curve shown in Fig. 34 is
projected.

18

Verification focuses not on exact representation of theoretical values, but on definition of model behavior. It is therefore
unnecessary to perform statistical calibration. Checking the graph visually is sufficient.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Cumulative
Set demand

4400

Link through volume

Time
0

1

Fig.34 Volume cumulative curve projected when the 4400veh/hr demand is given
2)

Relationship between model parameters, flow characteristics and bottleneck capacity
In a car-following type model, the principal parameters are roughly classified into those related todriving behavior and those related to location and road section. The former includes reaction
delay, desired speed, intensity of acceleration/deceleration, etc. while the latter includes the speed
limit, lane width, gradient, etc.

Namely, the link capacity and Q-K curve necessary forverification are not given externally, but reproduced as a result of synthesis of individual vehicle
behaviors.

Therefore, the objective of this verification step is to elucidate the relationshipbetween input data and model parameters with flow characteristics. In other words, the link
capacity reproducible within the scope of actual input items and recommended parameters19 by themodel, or range of saturation flow rate must be clarified.
In this section, a car-following type model is assumed, with input items and model parameters asshown in Table 4, and with standard values and setting range, determining the Q-K curve
reproducible through simulation. Model users must first list principal input items and parametersthat similarly affect reproducibility of capacity.

Standard values and the setting range20 must be

specified.

19

This section does not deal with whether or not the recommended range of the model parameter is adequate in terms of
traffic engineering because determination of exact values is meaningless. For example, a model parameter called“reaction delay time” in a simulation appears to be similar to the reaction delay time of actual driving behavior, but it ispractically totally different from that.
20
When the adequate parameter setting range is not described in the manual, the value range that is considered generally
applicable from past experience of operation of the model must be specified.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Table4 Principal input items and parameters of an assumed model
NameStandard
Minimum
Maximuma) For driving behavior of vehiclesa-1) Reaction delay time
1.0 sec
0.7 sec
1.5 seca-2) Desired headway
2.0 sec
1.7 sec
3.0 secMax.
acceleration
22
2.5 m/sec
1.8 m/sec
2.5 m/sec2a-3) (light)
2
2
1.4 m/sec
0.8 m/sec
2.0 m/sec2(Heavy)a-4) Desired speed
60 km/sec
40 km/sec
100 km/secb) For demandb-1) Traffic demand
Set freely as requiredb-2) Heavy vehicle ratio
15 %
0%
30 %
c) For link performancec-1) Speed limit
60 km/sec
40 km/sec
100 km/secc-2) Gradient
0%
-6 %
6%
c-3) Driveway width
3.5 m
2.75 m3.5 mc-4) Min. headway
2.0 sec
1.7 sec
3.0 sec
To determine what kind of traffic characteristics a model demonstrates when certain input data andparameter settings (hereinafter called simply “parameter set”) are used, the cumulative volume isrecorded at link upstream and downstream ends in a “steady state21” of free and breakdown flows.
Then, the volume and density within a certain time span are sampled and plotted on a Q-K plane.
In this case, the average Q-K curve must also be determined from the plot for use in subsequentverification steps.
Simulation is made for a one-link network according to the procedure described below, and the
Q-K curve is determined.
i) Prepare 11 types of parameter set as shown in Table 5.

In the case of free flow, parameters

related to c) link performance are not changed to prevent bottlenecks.
Table5 Parameter set to verify traffic characteristics in free flow
Free-1All standard values
Free-2a-1) minimum, the rest are all standard values
Free-3a-1) maximum，〃Free-4a-2) minimum，〃Free-5a-2) maximum，〃Free-6a-3) minimum，〃Free-7a-3) maximum，〃Free-8a-4) minimum，〃Free-9a-4) maximum，〃Free-10b-2) minimum，〃Free-11b-2) maximum，〃ii) Set a sufficiently low traffic demand level for a certain parameter set to prevent breakdown,
and start simulation.
iii) Wait till the link becomes a “steady state” in free flow.

Observe the cumulative volumes at

upstream and downstream ends of the link that has reached the “steady state.” For heavy
21

For the concept of “steady state,” refer to Appendix A.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

vehicles, carry out counting while assuming the personal vehicle conversion factor as 1.7.
iv) For certain ten minute periods, determine the number of vehicles within a section from thedifference of cumulative volume between link upstream and downstream ends. Take theaverage and assume the average value as a vehicle density in ten minutes.
v) Assume that the number of vehicles passing through the downstream end within the same ten
minutes is the traffic volume.
vi) Plot the result on the Q-K plane.
vii) Repeat steps v) through vii) for the next ten minutes and carry out plotting similarly.
viii) Repeat the same operation ten times, that is, perform simulation for 100 minutes, and carry out
plotting on the Q-K plane.
ix) End the simulation once.

Then, increase the demand in steps and repeat steps i) through viii).

When the demand exceeds a certain level, the link through volume is saturated. This volume
is considered to be the link capacity value in this parameter set. After observation of the link
capacity, proceed to x), the next step.
x) Draw a straight line or curve to interpolate the average value plot in each parameter set.
is the Q-K curve on the free flow side in a certain parameter set.
xi) Return to i), change the parameter set, and repeat the procedure.
The procedure described above is shown in Fig. 35.

35

This

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

About 1km section concerned
DemandVolume level not causing
breakdown

Demand arrived at
upstream＝Through volume

Throughvolume atdownstream
end

Cumulative volume[pcu]
No. of section
volume during
sampling
Sample average number of vehicles
÷
length of Section concerned
Volume duringobservationtime

Q [pcu/hr]

Average density infree flow section

10min

Time
Plot on Q-K
Result on the same
volume level and for
different observation
time

VolumeResult of simulation bychanging the volumelevel
Q-K curve with certain follow
parameters on the free flow side

Density

K [pcu/km]

Fig.35 How to determine Q-K characteristics of free flow
To determine the Q-K curve on the breakdown side, a link or bottleneck is provided on thedownstream side for the above Free-1〜Free-11 parameter sets and simulation is made as follows
while changing parameters related to link performance.

36

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)i) Prepare forty-four parameter sets as shown in Table 6.
Table6 Parameter set to determine traffic characteristics in the breakdown flow
Jam-1
Jam-2
Jam-3
Jam-4
Jam-5
Jam-6
Jam-7
Jam-8
Jam-9
Jam-10Jam-11
Jam-12
Jam-13
Jam-14
Jam-15
Jam-16
Jam-17
Jam-18Jam-19Jam-20Jam-21
Jam-22
Jam-23
Jam-24Jam-25
Jam-26Jam-27
Jam-28Jam-29Jam-30Jam-31
Jam-32
Jam-33Jam-34Jam-35Jam-36Jam-37
Jam-38Jam-39Jam-40Jam-41
Jam-42Jam-43Jam-44

Change Free-1 + c-1) of downstream link from standard to lower limit
Change Free-1 + c-2) of downstream link from standard to upper limit
Change Free-1 + c-3) of downstream link from standard to lower limit
Change Free-1 + c-4) of downstream link from standard to upper limit
Change Free-2 + c-1) of downstream link from standard to lower limit
Change Free-2 + c-2) of downstream link from standard to upper limit
Change Free-2 + c-3) of downstream link from standard to lower limit
Change Free-2 + c-4) of downstream link from standard to upper limit
Change Free-3 + c-1) of downstream link from standard to lower limit
Change Free-3 + c-2) of downstream link from standard to upper limit
Change Free-3 + c-3) of downstream link from standard to lower limit
Change Free-3 + c-4) of downstream link from standard to upper limit
Change Free-4 + c-1) of downstream link from standard to lower limit
Change Free-4 + c-2) of downstream link from standard to upper limit
Change Free-4 + c-3) of downstream link from standard to lower limit
Change Free-4 + c-4) of downstream link from standard to upper limit
Change Free-5 + c-1) of downstream link from standard to lower limit
Change Free-5 + c-2) of downstream link from standard to upper limit
Change Free-5 + c-3) of downstream link from standard to lower limit
Change Free-5 + c-4) of downstream link from standard to upper limit
Change Free-6 + c-1) of downstream link from standard to lower limit
Change Free-6 + c-2) of downstream link from standard to upper limit
Change Free-6 + c-3) of downstream link from standard to lower limit
Change Free-6 + c-4) of downstream link from standard to upper limit
Change Free-7 + c-1) of downstream link from standard to lower limit
Change Free-7 + c-2) of downstream link from standard to upper limit
Change Free-7 + c-3) of downstream link from standard to lower limit
Change Free-7 + c-4) of downstream link from standard to upper limit
Change Free-8 + c-1) of downstream link from standard to lower limit
Change Free-8 + c-2) of downstream link from standard to upper limit
Change Free-8 + c-3) of downstream link from standard to lower limit
Change Free-8 + c-4) of downstream link from standard to upper limit
Change Free-9 + c-1) of downstream link from standard to lower limit
Change Free-9 + c-2) of downstream link from standard to upper limit
Change Free-9 + c-3) of downstream link from standard to lower limit
Change Free-9 + c-4) of downstream link from standard to upper limit
Change Free-10 + c-1) of downstream link from standard to lower limit
Change Free-10 + c-2) of downstream link from standard to upper limit
Change Free-10 + c-3) of downstream link from standard to lower limit
Change Free-10 + c-4) of downstream link from standard to upper limit
Change Free-11 + c-1) of downstream link from standard to lower limit
Change Free-11 + c-2) of downstream link from standard to upper limit
Change Free-11 + c-3) of downstream link from standard to lower limit
Change Free-11 + c-4) of downstream link from standard to upper limitii) Simulation is made with demand equivalent to link capacity that can cause jams at bottleneck.
iii) Wait till the upstream link becomes a “steady state” with breakdown flow. In this “steadystate”, observe the cumulative volume at the upstream and downstream ends of the upstream
link.
iv) For a certain ten minutes, determine for every minute the number of vehicles in a section fromthe difference in cumulative volume between upstream and downstream ends of the link.
Take the average and use it as the vehicle density for the ten minutes.
v) Assume also that the number of vehicles passing through the downstream end within the sameten minutes is the traffic volume.
vi) Plot the result on the Q-K plane.
vii) Repeat steps iv) through vi) in the next ten minutes and carry out plotting similarly.
37

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

viii) Repeat this operation ten times, that is, for simulation for 100 minutes, and carry out plotting
on the Q-K plane.

Variance of plotting serves as a guideline to see if the bottleneck capacity

is reproduced in a stable manner.
ix) End simulation once. Then, repeat steps ii) through viii) while changing the parameter c)concerning the performance of the downstream link. It is recommended to change the c)value in about five steps.
x) Draw a curve to interpolate these results.
the jam side.

This is the Q-K curve of a certain parameter set forSpecify the lower limit value to define the range of bottleneck capacity

reproducible only with model parameters.
xi) Close the road at the link downstream end to determine the jam density. Count the number ofvehicles that are stopped in a traffic jam.
xii) Return to step i) and repeat the same procedure while changing the parameter set.
The above procedure is shown in Fig. 36.

38

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Upstream side link

Downstreamside link

About 1km section concerned

Demand arrived
at upstream

Through volume
at upstream

Through volume
at bottleneck

Cumulative volume[pcu]
No. of vehicles in
the jam section
during sampling

Average number of vehicles during sampling÷
length of Section concerned
Volume duringobservationtime

Average density ofthe breakdown section

10min

Time
Time at which jam reaches
the upstream point
Plot on Q-K

Q [pcu/hr]

Result of simulation whilechanging location
parameters of bottleneck
Q-K curve on the breakdown sideat certain car-following parameters

VolumeLower limit of bottleneck
capacity that can be set
with model parameters

Result in a different
observation time span withthe same location parameter

Jam density
Density

K [pcu/km]

Fig.36 How to determine the Q-K characteristics in the breakdown flow
Q-K curves determined in this way for free flow and breakdown sides are overlapped to be used astraffic characteristics22 of a certain parameter set.
3)

Relationship between model parameter and saturation flow rate
Verification of reproducibility of the saturation flow rate at the link downstream end is as follows.
Namely, verification is conducted for the simulation model for ordinary streets, including
signalized intersections, by checking the manner in which vehicles retained during red phases run
off during green phases.

22

In this case, a total of 11 types of Q-K characteristics are obtained. They are “Free-1 + Jam-1, Jam-2, Jam-3, Jam-4” to“Free-11 + Jam-40, Jam-41, Jam-42, Jam-43.”

39

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

i) A network is made from a one-lane link controlled by a signal at the downstream end, as shownin Fig. 37. The signal is under a fixed-time control with a cycle length of 120 [seconds], asplit of 50%, and a lost time of 10 [seconds/cycle]

Cycle 120 sec
Split 50%
Lost time 10sec

Demand = 1000 [veh./hr]Fig.37 Verification data set for saturation flow rate at the link downstream endii) Assume that the demand arrived from the upstream is 1000veh/hr, and carry out simulation for
one hour for each of 19 parameter sets shown in Table 7.

40

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Table7 Parameter sets used for verification of saturation flow rate
SFR-1
SFR-2
SFR-3
SFR-4
SFR-5
SFR-6
SFR-7
SFR-8
SFR-9
SFR-10
SFR-11
SFR-12
SFR-13
SFR-14
SFR-15
SFR-16
SFR-17
SFR-18
SFR-19All standard valuesa-1) minimum，the rest are all standard valuesa-1) maximum，〃a-2) minimum，〃a-2) maximum，〃a-3) minimum，〃a-3) maximum，〃a-4) minimum，〃a-4) maximum，〃b-2) minimum，〃b-2) maximum，〃c-1) minimum，〃c-1) maximum，〃c-2) minimum，〃c-2) maximum，〃c-3) minimum，〃c-3) maximum，〃c-4) minimum，〃c-4) maximum，〃iii) In ten cycles after simulation start, observe run-off from the link for about ten cycles. The
observation time interval is the model unit scan time 23.
iv) With each parameter set, the run-off volume per cycle after start of green phase is represented
by the cumulative curve. Cumulative curves for ten cycles are overlapped as shown in Fig.
3824. Verification is carried out to confirm that the flow rate is reproduced in a stable mannerin any cycle while the flow is saturated.

Cumulative
volumeYellowgreen

Saturation flow
0

rate

Red

Through volume per
cycle
Time [sec]55

60

Fig.38 Saturation flow rate observed at the link downstream end

23
24

For an event scan type simulation model, observation must be made at least every second.
Draw a straight line with a slope equivalent to that of the cumulative curve while the flow is saturated in the graph. The
inclination or the saturation flow rate must be entered in the graph. Note that this is only a guideline and the exact valueof inclination is not necessarily significant.

41

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

4)

Spreading out vehicles, and eliminating traffic jams, and shock wave propagation rates
This verification is carried out for the basic segment, including bottlenecks, under the following
conditions:l) Demand exceeding the bottleneck capacity, with jammed traffic is drawn to the upstreamm) Demand below the bottleneck capacity, with jams disappearing downward from the upstreamside
Verification consists of confirming how spreading vehicles out and eliminating jams are
reproduced as compared with the shock wave theory. For the model controlled with signals,
further verification is done for the following condition:n) Condition in which jams are eliminated upward from the downstream as the signal phasechanges from red to green
The specific procedure is described first for a) and b).
i) For verification, a basic segment network with a bottleneck section on the downstream side isformed.

About three to five sections are set to observe the through traffic. To verify the

traffic flow characteristics, three types of parameters set with typical Q-K characteristics areprovided from the sets used in step 2). In these parameter sets concerning road conditions,standard values are used for the entire basic segment on the bottleneck upstream side.

Thebottleneck section reproduced with the smallest capacity is used. The section length forwhich the cumulative number of through vehicles is observed should be determined
appropriately according to the flow characteristics, so that the shock wave propagation can be
grasped25. In this model, observation sections are arranged every 500 m.

Demand = 1000 [veh./hr] -- 0 - 15 min
1600 [veh./hr] -- 15 - 25 min
1000 [veh./hr] -- 25 - 60 min

500m

500m

500m

Bottleneck section

500m

500m

Standard link parameterFig.39 Verification data set for spreading vehicles and eliminating jamsii) The demand26 is given, in which there are peaks of jams at bottleneck and elimination of jams.
In this verification, the following levels of demand are given for the bottleneck capacity after

25

Namely, the traffic condition transition diagram on the bottleneck upstream side is first prepared from the shock wave
propagation rate determined in Fig. 40. And the section length is set so that the shock wave surface is grasped at as many
sections as possible.
26
The demand to be provided must generate jams relative to the bottleneck capacity shown in Fig. 40.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

start of simulation:
・0〜15 min…1000veh/hr
・15〜25 min…1600veh/hr
・25〜60 min…1000veh/hriii) As shown in Fig. 4027，the shock wave propagation rate is determined from the Q-K curve thatthe parameter set of the model represents. And the traffic condition transition diagram on thebottleneck upstream side, shown in Fig. 41, is prepared beforehand.
iv) Simulation is made for each of three types of parameter sets. The condition of spreading out
vehicles is grasped by recording the cumulative through volume at each observation section.
v) As shown in Fig. 41, the traffic transition diagram is overlapped to the through volume
cumulative curve at each section, and verification28 is made for how spreading vehicles andeliminating jams are reproduced with reference to the theory.

27
28

In this case, four forward waves of FW1 through FW4 and one backward wave BW1 are generated.
Considering the purport of verification, it is enough here to see visually on the graph if the time point at which the flow ratechanges on the cumulative curve agrees with that at which the shock wave is theoretically propagated. As the flow rate is
not stable during simulation, it is difficult to precisely and numerically indicate the time point at which shock waves arepropagated. In addition, the Q-K curve to determine the theoretical value shows only the average and has originally been
prepared as a guideline.

43

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Q-1 curve
Volume [pcu/hr] on the free flow side
Q-K curve
on the breakdown flow
side

1800
1600
BW1

-10.0

50.0 FW2, FW3

1400

FW4

1000

10.0
FW1 - FW4 : forward wave
BW1
: Backward wave
(Numerical of the same color
indicates the propagaton rate [km/hr])

FW1 75.0

Density
140 [pcu/km]

Fig.40 Shock wave propagation rate determined from Q-K curve

Cumulative
volume [veh]900
800Demand [veh./hr]

700

1600

1000

1000

600
500

400
300
200
100
0

0

5

10

15

20

25

30

35

40

45

50

55

60

55

60

0

Distance from bottleneck [m]

2 '00"

18'00"

34'40"

500
FW4

BW1
1,000

1389m
26'20"
1,500

FW1

FW2

FW3

2,000

2,500
0

5

10

15

20

25

30

35

40

45

50

Time[sec]

Fig. 41 Traffic condition transition diagram upstream of bottleneck (below) and through volume
cumulative curve at each observation section (above)44

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Now the procedure for c) is described below. Verification is carried out here of a simulation modelof ordinary streets including signalized intersections by checking the manner in which vehicles
held up during red phase run off at green phase. In this verification, the propagation rate offorward and backward waves under control of signals is compared with the theoretical values
obtained from the shock wave theory.
v) A network is made from a basic-segment network, including signalized intersections, as shownin Fig. 42. The signal is under a fixed-time control with a cycle length of 120 [seconds], asplit of 50%, and a lost time of 10 [seconds/cycle]. Sections to observe the through volume
are arranged every 20 m on the upstream side of the signalized intersection. The observation
time interval is the model unit scan time 29.

Cycle 120 sec
Split 50%
Lost time 10sec

Demand = 600 [veh./ hr]
100m

80

60

40

20

0

Volume observation
sectionFig.42 Verification data set for start/stop wave under control of signalvi) Three typical parameter sets to give the typical saturation flow rate are prepared to verify thesaturation flow rate. Given a demand of 600 [veh/hr], simulation is made for each set. Since
highly random arrival causes difficulty in comparison because the stop wave is not propagateduniformly, it is desirable that uniform arrival is assumed for vehicle generation30.
vii) From the Q-K curve and saturation flow rate corresponding to the given parameter set, thestart/stop wave propagation rate is determined from Fig. 43.

Then, the traffic conditiontransition diagram upstream of the signalized intersection is prepared as shown in Fig.44(below).
viii)

For an appropriate one-cycle time span beginning with a red phase, the cumulative curveof through volume at each point is overlapped as shown in Fig. 44 (above). This is thenoverlapped with the traffic condition transition diagram to check if the time points at which theinclination changes agree31.

29

For an event scan type simulation, observe the volume at intervals of about 1 second.
For a model for which uniform arrival is not assumed, a contrivance must be used, such that a given demand is provided
within the shortest possible interval. For example, 10 vehicles are generated every minute.
31
Considering the purport of verification, it is enough here to see visually on the graph if the time point at which the linkrun-off rate changes on the cumulative curve agrees with that at which the start/stop wave is propagated theoretically. As
the run-off rate is not stable during simulation, it is difficult to indicate precisely and numerically the time point at which
the start/stop wave is propagated.

30

45

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Volume [pcu/hr]
1800

40 .0 [km/hr]
Start wave
-25.0 [km/hr]

600
Stop wave-4.0 [km/hr]

DensityJam density [pcu/km]

Critical density

Fig.43 Start/stop wave velocity determined from the Q-K curve

Cumulative
volume[pcu]

120m
100m
80m
60m
40m
20m
0m

Time[sec]
Red

Distance from signalizedintersection [m]

0

Green

Stop
wave

20

Start
wave

-4.0 [km/hr]-25.0 [km/hr] 40 .0 [km/hr]

40
60
79.3 m

80
0

60

71.4

Time[sec]

Fig.44 Start/stop wave propagation condition and cumulative volume at each point46

Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

5)

Capacity and merge ratio of the merge area32
For verification of the merge area, the standard values and setting ranges must be clarified not only
for the input data and parameters used to define the characteristics of car-following travel of Table
4, but also for others that may affect merge behavior. Table 8 provides examples of principal
input items and parameters for an assumed model.

Table8 Principal input items and parameters affecting merge behavior of an assumed model
Name
A
B
C
d) For driving behavior of vehicles
Gap
acceptanced-1)
1.0 sec
0.7 sec
1.5 sec
threshold33e) For the merge sectione-1) Merge section length
100m
0m
200m
Max. entry speed
e-2)
50km/h
30km/h
80km/hfrom a merge branchf) Merge branch and main lane demand ratiof-1) Total 2000[veh/hr]
3:7
1:9
5:5
f-2) Total 2500[veh/hr]
3:7
1:9
5:5
In this case, Standard values of Table 4 (i.e., Free-1 of Table 5) is used as parameters related tocar-following travel. Furthermore, input items and parameters of Table 8 are changed as shownin Table 9. The capacity and merge ratio in the merge area are verified each case.
Table9 Parameter sets used for verification of merge area
Merge-1“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-1-A”
Merge-2“Free-1” + “d-1-B” + “e-1-A” + “e-2-A” + “f-1-A”
Merge-3“Free-1” + “d-1-C” + “e-1-A” + “e-2-A” + “f-1-A”
Merge-4“Free-1” + “d-1-A” + “e-1-B” + “e-2-A” + “f-1-A”
Merge-5“Free-1” + “d-1-A” + “e-1-C” + “e-2-A” + “f-1-A”
Merge-6“Free-1” + “d-1-A” + “e-1-A” + “e-2-B” + “f-1-A”
Merge-7“Free-1” + “d-1-A” + “e-1-A” + “e-2-C” + “f-1-A”
Merge-8“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-1-B”
Merge-9“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-1-C”
Merge-10“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-2-A”
Merge-11“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-2-B”
Merge-12“Free-1” + “d-1-A” + “e-1-A” + “e-2-A” + “f-2-C”
The verification procedure for the merge area is described below.
i) With a network made up from merge branches and the main lane as shown in Fig. 45,
simulation is made for each parameter set for about one hour.

32

In the case of car-following type model, verification of the merge area is omitted because the FIFO rule is evidently
observed, and the capacity of the downstream link is synthesized according to parameter setting. Verification of thiscapacity is the same as for verification of the bottleneck in the basic element. Contrary to this, the Q-K type model
requires verification of whether or not the FIFO rule is observed in the link upstream of the diverge area and the volume isshifted so that it is subject to restrictions of the downstream link capacity.
33
In this table, a model is assumed, which judges merging by means of 0/1 while using the gap acceptance threshold as aborder. For a model based on probability determination, three types of probability distributions must be provided.

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Standard verification Model for Traffic Flow Simulation Model ~ Verification Manual (Draft) ~(Ver.99/11/25)

Generation
point
Merge
branchTotal demand= 2000，2500 [pcu/hour]

Generation
point

Through volume
observation section

Main
Through volume
line
ovservation section

Through volume
observation section

Fig.45 Verification data set for reproducibility of the merge area capacityii) The volume is observed at the downstream end of the diverge branch and main line for eachcase. The cumulative volume of each case and the total cumulative volume (= cumulative
volume of the merge area) are plotted into a graph. The cumulative demand curve is also
entered in this graph to determine if breakdown has occurred in the merge branch and main line.
The merge ratio determined from the through volume of the merge branch and main line is also
entered in the graph.
6)

Decrease in the right-turn capacity due to opposing traffic in signalized intersection
To verify the right-turn capacity, the result is compared with the right-turn capacity calculation
equation34 of the Japan Society of Traffic Engineers, which is widely employed in Japan.
Standard values and setting ranges must be clarified not only for the input data and parameters
used to define the characteristics of car-following travel of Table 4, but also for others that may
affect merge behavior. Table 10 provides examples of principal input items and parameters for anassumed model.

34

This equation is not used to produce the theoretical value. It is used only for reference during comparison.

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Table10 Principal input items and parameters affecting right-turn capacity of an assumed model
Name
A
B
C
g) For driving behavior of vehicles
Opposing straight throughg-1)
3.0 sec
5.0 sec
8.0 sec
gap acceptance threshold35h) For intersection structure
No. of vehicles retained in
h-1)
1 veh
2 veh
4 veh
the intersectionh-2) Min. right-turn headway
1.7sec
2sec
3seci) Signal parametersi-1) Cycle
120sec (common to all cases)i-2) Effective green timeThree type of 40，60，and 80secj) For demandj-1) Opposing through demand
Variable in 200 steps from 200〜1200[veh/hr]j-2) Right-turn demand
2000[veh/hr] (common to all cases)
In this case, the Standard values of Table 4 (i.e., SFR-1 of Table 7) are used as parameters related
to car-following travel. Furthermore, input items and parameters of Table 10 are changed asshown in Table 11. The achieved right-turn capacity is verified for each case.
Table11 Parameter sets used to verify the right-turn capacity
Rturn-1“SFR-1” + “g-1-A” + “h-1-A” + “h-2-A”
Rturn-2“SFR-1” + “g-1-B” + “h-1-A” + “h-2-A”
Rturn-3“SFR-1” + “g-1-C” + “h-1-A” + “h-2-A”
Rturn-4“SFR-1” + “g-1-A” + “h-1-B” + “h-2-A”
Rturn-5“SFR-1” + “g-1-A” + “h-1-C” + “h-2-A”
Rturn-6“SFR-1” + “g-1-A” + “h-1-A” + “h-2-B”
Rturn-7“SFR-1” + “g-1-A” + “h-1-A” + “h-2-C”
The verification procedure is described below as an example.
i) A network including one signalized intersection is formed as shown in Fig. 46.

Throughdemand= 200 〜1200 [veh./hr]Cycle 120 sec
Effective green time 40 ，60 ，80 sec

Right-turndemand2000[veh/hr]

Fig.46 Verification data set for right-turn capacity

35

In this table, a model is assumed, which judges merging by means of 0/1 while using the gap acceptance threshold as aborder. For a model based on probability determination, three types of probability distributions must be provided.

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ii) Set the cycle to 120 sec for the signal parameter and change the effective green time in threestages of 40，60，and 80 sec. While changing the opposing through demand in six stages of200，400，600，800，1000，and 1200 for each signal parameter, carry out simulation for about
one hour, observing the right-turn capacity.
iii) Compare the simulation observation result with the equation below:
SR=1800 f (S G – q C)/(S – q) C + 3600K/C…(1)

SR…Inverse number of min. headway of right-turn(=right-turn capacity) [veh/hr]
S … Value reproduced with SFR-1 during verification of saturation flow rate
[veh/effective green one hour]
q…Volume at approach of opposing through traffic [veh/hr]
C…Cycle length [sec]G…Effective green time [sec]K…No. of vehicles discharge at change of signal [veh/cycle]
f…Gap acceptance probability determined as follows:f=1.00 (q=0),0.81 (q=200),

0.65 (q=400),

0.54 (q=600),

0.45 (q=800),

0.37 (q=1000),

0.0 (q>1000),Interpolation made for median q value

When comparing simulation results, plot the opposing straight through volume on an abscissa andthe right-turn capacity (=through volume) on a coordinate for each signal parameter setting, asshown in Fig. 47.

Right-turnthrough volume[veh/hr]Cycle length 120sec
Effective green time 60sec
Simulation result式(1)Equation(1)

200

400

600

800

1000

Opposing straight
through volume
1200 [veh/hr]

Fig.47 Comparison of simulation result and theoretical values for right-turn capacity
7)

Route selection behavior
This verification is carried out to confirm the route selection model the simulation model assumes
and how truly the theoretical value is reproduced.

The theory in this case is based on a dynamic

allocation principle − either DUO or DUE. Since an excessively complicated network makes
calculation of the theoretical value itself impossible, a simple network comprising a 10D2 route isused for verification. Verification is carried out here as follows:50

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i) The 1OD2 route network shown in Fig. 48 is used.

The parameter on the link performance ofTable 4, c) is set so that the merge area becomes a bottleneck. Namely, use values with which
the capacity of link 3 is smaller than links 0 to 2. For the merge area, set the parameter
concerning merge behavior of Table 8 so that the merge ratio during a jam becomes 1:1.

Demand1200 [veh/hr] - 0〜60 min
600[veh/hr] - 60〜120 min
Start
point

Link 01500m

Link 1Route
1Merge ratio during
jam 1:1

1500m

Route
2
3000m

Link 33
1500m

End
point

Bottleneck

Link 2

Fig.48 Example of verification data set for reproducibility of route selection behaviorii) Prepare three model setting patterns 36 for each of the model selection standards (DUO/DUE,
shortest cost selection/probability selection, etc.) and route cost renewal time interval, androute selection timing.
iii) For each setting pattern, simulation is made while providing peak demands that cause jams.
Observe the cumulative volume of incoming and run-off for links 1 and 2 in each case, andcompare the observed result with the theoretical flow pattern. For reference, set the demand
to 1200 [veh/hr] for the initial one hour and 600 [veh/hr] for subsequent one hour. The flow
pattern when DUE is achieved with the free flow rate being 36 km/h (= 10 m/sec)37 is shown in
Fig. 49. It is also assumed that the link capacity achieved with the set model parameters is1800 [veh/hr] for links 0 to 2 and 900 [veh/hr] for link 3. It should be noted that, to avoid
complication, the link volume is handled with point-queue, and that drawing of jammed
vehicles to the diverge area is not considered.

36

No specific parameters and set items are specified here because they differ substantially from one model to another.
Model users must specify pertinent parameters and set up appropriate values.
37
The difference of free travel time between both routes is 2.5 minutes.

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Cumulative volume

122.5
1800

Demand setting
Link 1 inflow
Link 2 inflow
Link 1 outflow
Link 2 outflow

600 [units/hour]
900 [units/hour]
1200

600 [units/hour]

1200 [units/hour]

990
910

300 [units/hour]

760
650
600 [units/hour]
500
1200[units/hour]

450 [units/hour]

150[minutes]
5 10

15

900 [units/hour]

60

2.5

Fig.49 Flow pattern when DUE is achieved

52

112

120
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Appendix A
Concept of Steady State
Verification of flow characteristics represented by the car-following type model is made separately
for the free flow condition and traffic jam flows. Here, simulation with a simple one-lane basic
segment is made for a combination of a certain model parameter. When traffic conditions in acertain section becomes “steady,” the traffic density and volume of this section are plotted todetermine the Q-K curve.

In this case, the “steady” traffic condition can be defined as a conditionin which “the volume observed at any point in the section concerned shows an equivalent flow rate
within a given tolerance range regardless of the time span.” Needless to say, the size of thetolerance varies38 depending on the time span length to be determined, making determination of
specific standard values difficult. Therefore, more simplified criteria are described below:i) To determine whether or not the free flow is in a steady state, simulation is made with a given
demand39 every hour. After elapse of sufficient time 40, the cumulative volume is determined
every ten minutes at the volume generation point and at the link upstream and downstream
ends. In this case, the condition is judged to be steady when the difference in cumulative
volume between upstream and downstream ends does not increase as time passes and novehicles are retained at the generation point.
ii) To determine whether or not a jam flow is in a steady state, simulation is made by applying agiven demand exceeding the bottleneck capacity to a basic segment network made up from alink with the bottleneck at the downstream end.

After elapse of sufficient time, thecumulative volume is determined every ten minutes at the volume generation point and at thelink upstream and downstream ends.

Concurrently, the average travel speed in the linkconcerned and that in the section further downstream of the link downstream end are measured
every ten minutes. The condition is judged to be steady when the difference in cumulative
volume between the upstream and downstream ends does not increase as time passes, and when
an increasing number of vehicles are retained and can not enter the link at the generation point,
and the average travel speed of the link concerned is below that on the further downstream
side.

38

The traffic condition which may be judged “steady” for the time span of 30 minutes is no longer “steady” when the timespan is changed to 5 seconds because the volume measured during the time span varies depending on the location and time.
39
This means that the same volume is given for each time span.
40
This time is the time period till the volume arrives at the link downstream end.

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Cumulative
volumeThese differences do notincrease as time
passesTime
Generation
point

After elapase of
Upstream Downstream sufficient time
end
end

Fig.A1-1 Conceptual view when the free flow is in a steady state

Cumulative
volumeCumulative curve at generation point
diverges above the curve at the
upstream end

These differences do notincrease as time
passesTime
Generation
point

After elapse of
Upstream Downstream sufficient timeend
end

Average travel
speed

Link
concerned

Bottleneck

Furtherdownstream
sectionThe speed of the link concerned is lower
than that on the downstream side
After elapse ofTime
sufficient time

Fig.A1-2 Conceptual view when the flow in a traffic jam is in a steady state54