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Received: 16 September 2022 Revised: 2 April 2023 Accepted: 21 April 2023 IET Intelligent Transport Systems
DOI: 10.1049/itr2.12375
ORIGINAL RESEARCH
Exploring the effects of measures of performance and calibration
strategies on calibrating traffic microsimulation model: A
quantitative analysis approach
Haoran Li1Zhenzhou Yuan1Siyuan Chen1Chuang Zhu2
1Key Laboratory of Transport Industry of Big Data
Application Technologies for Comprehensive
Transport, Ministry of Transport, School of Traffic
and Transportation, Beijing Jiaotong University,
Beijing, China
2State Key Laboratory of Rail Traffic Control and
Safety, Beijing Jiaotong University, Beijing, China
Correspondence
Zhenzhou Yuan, Key Laboratory of Transport
Industry of Big Data Application Technologies for
Comprehensive Transport, Ministry of Transport,
School of Traffic and Transportation, Beijing
Jiaotong University, No.3, Shangyuan Village,
Haidian District, Beijing 100044, China.
Email: zzyuan@bjtu.edu.cn
Funding information
Beijing Natural Science Foundation, Grant/Award
Number: J210001
Abstract
In the subject of traffic microsimulation model (TMM) calibration, measure of perfor-
mance (MoP) plays an essential role. However, due to the diversity of MoP types, choosing
a MoP or MoP combination (usually used for multi-criteria calibration strategy) that can
represent the characteristics of field traffic operation has become the key to the calibration
problem. This paper proposed a quantitative analysis approach (suitable, in general, for
any TMM) with three aspects. Through this approach, more detailed and representative
MoPs can be studied. At the same time, the effect of different calibration strategies with
various MoP combinations on TMM calibration can also be compared comprehensively.
The methodology is tested on a specific case study (a signalized link with a cyclic inter-
rupted flow) by VISSIM, where various MoPs and calibration strategies (single-criteria, the
a priori-based multi-criteria, and the a posteriori-based multi-criteria calibration strategy)
are implemented for comprehensive inspection and comparison. The results show that the
TMM performance is clearly dependent on the MoPs and calibration strategies. Moreover,
the a posteriori-based multi-criteria calibration strategy is more stable than the other two
strategies for better performance TMM. The findings of this study provide new insights
into the effects of MoPs and calibration strategies on TMM calibration.
1 INTRODUCTION
Currently, an increasing number of microscopic traffic sce-
narios need to be applied to commercial traffic simulation
software (such as VISSIM, SUMO, CORSIM, and AIMSUN)
for analysis and evaluation. Each simulation software sets many
default parameters according to its submodels (such as the
car-following and lane change models). However, the default
parameters are unsuitable and cannot correctly reflect the traffic
conditions for most scenarios. Users need to configure param-
eters according to specific simulation scenarios to make the
simulation scenario as similar as possible to the actual scene
[1]. The accuracy of parameter values will seriously affect the
reliability of the traffic microsimulation model (TMM) and
its applicability in traffic engineering practice [2]. The analy-
sis results obtained by the software are often inconsistent with
reality.
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Simulation optimization is a necessary process to obtain a
reliable TMM. In other words, it is a calibration process to
find the best decision variables (or parameter values) for the
simulation system [3]. The optimized TMM is also the basis
for all simulation analysis, especially at a time of increasing
research on connected and autonomous vehicle simulation. An
effective TMM can reflect the actual traffic operation con-
ditions, reproduce the real traffic phenomena, and provide
valuable information for analysts on the performance of exist-
ing transportation systems and potential improvements [4].
Typically, the calibration process mainly includes the following
steps:
1. Determine the scenario and code correctly;
2. Select the subset of driving behaviour model parameters;
3. Select a measure of performance (MoP) to describe traffic
characteristics;
1200 wileyonlinelibrary.com/iet-its IET Intell. Transp. Syst. 2023;17:1200–1219.
LI ET AL.1201
4. Select a reasonable goodness-of-fit (GoF) for comparing
field and simulated traffic measures;
5. Establish the objective programming model and design an
optimization algorithm.
It can be seen that MoP is the basis of the simulation model
calibration. An effective MoP will make the TMM more realistic,
while an ineffective MoP will make the model misfit. Exist-
ing studies generally use aggregated data or distribution data as
MoP. The aggregated data mainly includes the average speed
[5–9], the average travel time [10–14], the average delay time
[15, 16], and the average or maximum queue length [17–19].
Another mainly includes the travel time distribution [20, 21]and
the time headway distribution [22–24]. Many scholars choose
one MoP to calibrate the TMM (in the following, we call it the
single-criteria calibration strategy) and solve the single-objective
function with a stochastic optimization algorithm. In recent
years, researchers have attempted to use two MoPs to calibrate
TMM (in the following, we call it the multi-criteria calibration
strategy). For instance, Yu et al. [25] and Mahmood et al. [26]
consider the actual flow and speed as the MoP combination.
Wang et al. [27] considered travel time and headway as the MoP
combination. However, most solve this problem by the a pri-
ori method (that is, the multi-objective function is aggregated
into a single-objective function through the weight coefficient).
Although the a priori method is simple and fast, the weight coef-
ficient is subjectively determined. It leads to the information
exchange between multiple objective functions being ignored
and unsatisfactory results [28]. Cobos et al. [29] proposed a
posteriori method to solve the multi-criteria calibration prob-
lem in TMM. Karimi et al. [22] used a multi-objective paper
swarm optimization algorithm based on the a posteriori method
and three a priori algorithms to calibrate the TMM. The results
show that the a posteriori method can make the solution closer
to the optimal solution.
Although different MoPs are used, the effectiveness of MoPs
for calibration still needs to be taken seriously. In the sub-
ject of car-following (CF) model calibration, which is similar
to the subject of TMM calibration, researchers have found
that the MoPs strongly correlate with the CF models’ per-
formance[30–33]. For instance, the fitting effect of speed
profile is better when calibrating on the space headway, but
not vice versa [33]. However, such valuable findings for cal-
ibrating TMM’s driving behaviour parameters are rare. To
the best of our knowledge, Punzo et al. [34] first compared
the effects of average speed and traffic volume on the cal-
ibration results. The results show that average speed is an
appropriate MoP in calibration. Wang et al. [27] took one
hour as the aggregate interval to compare the effects of aver-
age travel time, average queue length, headway distribution,
and conflict counts on TMM calibration. The results show
that conflict counts may not be the optimal MoP for TMM
calibration.
Although a few studies have compared the effects of some
MoPs on the calibration TMM, the effects of aggregated data
and distribution data on calibration have been neglected. Li
mentioned that it is not ensured that the microscopic traffic
characteristics of the TMM are actual when calibrated using
aggregated or distribution data [35]. Ossen et al. [36] men-
tioned that without understanding the specific microscopic
behaviour of the vehicle, the conclusion based on the fit-
ting error obtained by the MoP might be very misleading.
For example, many analysts used the average travel time as
MoP to calibrate the TMM. However, different traffic oper-
ation statues may lead to the same average travel time value.
Therefore, the data form should be considered simultaneously
when studying the influence of various MoPs on calibration
results.
For the above reasons, although scholars have preliminary
explored MoP effect in TMM calibration, some crucial gaps
still need to be identified and further investigated. First, pre-
vious studies often used field observation data, which leads to
the real global optimal solution being unknown. In this way, it
is unclear whether the obtained solution is globally optimal, and
the effects of different MoPs cannot be accurately compared.
Second, aggregating data at 1-h intervals may not accurately
reflect the microscopic traffic characteristics and actual vehicle
interactions [37]. The interval for the aggregation of measure-
ments could be reduced. Third, the measurement location is
directly related to the traffic condition, and even for the same
type of MoP, different measurement locations may affect the
calibration results. Therefore, the effect of measurement loca-
tions on calibration also needs to be investigated. Fourth, due
to the complexity of space headway data, few studies use space
headway as the MoP to calibrate TMM. However, the space
headway distribution contains much car-following behaviour
information. It is a bridge connecting the microscopic and
macroscopic traffic flow models [38], so it seems necessary
to try applying space headway to TMM calibration and com-
pared with other MoPs. Last but not least, different MoP
combinations’ effectiveness need to be investigated with the
popularisation of multi-criteria calibration strategy. Moreover,
it is even worth exploring whether the multi-criteria strategy is
effective. In the subject of CF model calibration, Punzo et al.
[39] pointed out that the calibration results of the combina-
tion function considering two MoPs (speed and space headway)
seemed to be less effective than that of the single MoP (space
headway). However, few researchers compared the effectiveness
of different calibration strategies in TMM calibration. There-
fore, it is worth increasing the depth and breadth of research
on the impact of various MoPs and calibration strategies on
TMM.
In short, to date, aggregated or distribution measures cannot
be avoided as MoPs to calibrate TMM, which will inevitably lead
to the risk of limited expression of calibrated TMM [40]. In this
context, when some MoPs are used for calibration, the TMM
fitting results are good but cannot reflect the actual microscopic
traffic operation state [20], which could mislead researchers to
use this model for further research. From the above points of
view, although previous studies often mention that inappropri-
ate MoP will affect the validity of the calibrated model due to
the diversity of MoP and the complexity of the experiment,
few scholars directly study MoP in detail. Thus, the research
analyses and discusses the influence of various MoPs on TMM
1202 LI ET AL.
performance. Furthermore, although the multi-criteria cali-
bration strategies are widely used, whether this method can
improve the accuracy of the calibration results remains to be
discussed. Therefore, this study explores the calibration strate-
gies based on the a prior/posterior and the influence of different
MoP combinations on the calibration results. The analysis and
discussion of the above problems are implemented through the
quantitative analysis method proposed in this paper. The results
of this study complement prior efforts and offer a basis for
researchers, traffic and transit practitioners, and authorities to
assess the potential of calibration strategies and avoid the poten-
tial pitfalls of MoPs. The main contributions of this paper are
as follows:
1. A systematic quantitative analysis approach is developed to
measure the effects of various MoP and calibration strate-
gies on TMM performance, which represents actual traffic
conditions and vehicle interactions from three aspects: the
fit of parameters, fit of total measurements, and the fit
of relative measurements. The effects of various MoPs on
TMM calibration can be quantified through these three
aspects.
2. Effects of different measurement locations (same study site
but different data acquisition locations) of the same MoP
type on TMM performance are investigated. Previous stud-
ies tended to compare different MoP types (e.g. speed, time
headway, and travel time). This paper not only studies the
influence of different MoP types on the calibration results
but also considers the impact of measurement locations on
calibration results.
3. The space headway distribution is used as a new MoP to
calibrate the TMM. Since the space headway data cannot
be directly used to calibrate TMM, we propose to use data
distribution forms to processed it into MoP which is suit-
able for TMM calibration. The analysis results show that
both the single-criteria and multi-criteria calibration strate-
gies have good results if using the space headway distribution
to calibrate the TMM.
4. The effects and differences of various MoPs on the calibra-
tion of the TMM under three different calibration strategies
are compared, which are significant impact on calibration
of TMM. In addition, each strategy’s influence mechanism
and reliability on the TMM calibration results are explored,
and suggestions on using MoP and calibration strategies are
provided for the analysis results.
The remainder of this paper is organized as follows. In Sec-
tion 2, a quantitative analysis approach is proposed to analyse
the effects of MoPs and calibration strategies. Section 3intro-
duces the data collection and processing of the MoP used in this
study. Section 4details the case study with specific reference
to the traffic scenario, the simulation mode, and the synthetic
data used as MoP. Section 5provides a detailed comparative dis-
cussion of the research results. Finally, Section 6concludes the
paper and discusses future work.
2QUANTITATIVE ANALYSIS
APPROACH BASED ON CALIBRATED
TMM PERFORMANCE
Generally, the TMM can be regarded as a system, and its perfor-
mance is affected by controllable and uncontrollable parameters
[41]. The system can be formulated in the following [42]
Ysim =S(cp1,…,cpG,np1,…,npH)(1)
s.t.
lnp,h≤npi≤unp,h(2)
where S(⋅) is the TMM; cpg(g=1,…,G) represent the control-
lable parameters that are usually difficult to observe from the
field directly, that is, the driving behaviour parameters; nph(h=
1,…,H) represent the uncontrollable parameters that can be
obtained directly from the field, such as the traffic volume and
road geometry; Ysim is the output of the TMM, that is, the
simulated traffic measurements.
For a reliable TMM calibration, it is necessary to encode the
road network according to the uncontrollable parameters first.
Then, the values of the uncontrollable parameters need to be
found through optimization simulation [5]. The optimization
simulation aims to make the output measurements of the sys-
tem similar to the field observation measurements. The basic
form of the objective function is
min Zk=f(Yobs,Ysim )(3)
where f(⋅) is the GoF function which is introduced in Sec-
tion 2.1,krepresents the nth objective function, and Yobs
represents the observed traffic measurements.
2.1 GoF function
The GoF function is used to compare the simulated and
observed traffic measurements, such as squared error (SE),
mean square error (MSE), mean absolute error (MAE), root
mean square error (RMSE) or mean average percentage error
(MAPE). According to the no free lunch (NFL) theorem in traf-
fic microsimulation models calibration [5], it is impossible to
prove which combination of GoF and optimization algorithms
will perform best in any scenario. In view of this, considering
that it is necessary to conduct dimensionless treatment for dif-
ferent MoP and have a convenient benchmark for comparison
to display the fitting effect, the mean average percentage error
(MAPE) is chosen as the GoF function. Accordingly, we have
ob jMoP =1
p
p
∑
l=1
1
m
m
∑
t=1
|
|
|Yobs
l(t)−Ysim
l(t)|
|
|
Yobs
l(t)(4)
LI ET AL.1203
where ob jMoP represents the objective function when using a
MoP as a calibration target. trepresents the profile’s interval.
lidentifies the different locations of the road where the detec-
tors are installed. Therefore, Yobs
l(t)andYsim
l(t) demonstrate
the observed and simulated MoP profiles in location lat interval
t;
2.2 Calibration strategy and optimization
algorithm
The optimization algorithm is used to find the solution of
controllable parameters to minimize the objective function. It
should be noted that the submodels in many commercial sim-
ulation software are unclear, making it impossible to analyse
the specific objective function gradient. Taking VISSIM as an
example, the car-following submodel is an improved Wiede-
mann model, and the difference between it and the original
Wiedemann model is not opening [43]. Hence, such problems
have black box characteristics. The computational complexity
of this problem increases exponentially in terms of the num-
ber of parameters, and even for relatively few parameters, it is
not feasible to search for global optimization [33]. Therefore,
the stochastic optimization algorithms are widely used in this
problem. The logical idea of this method is to systematically
divide the feasible area into small areas and then use the known
information randomly searched to transfer from one area to
another according to specific rules [44], such as genetic algo-
rithm, simulated annealing, particle swarm optimization and so
on.
Selection of optimization algorithm is also related to calibra-
tion strategy. In the subject of TMM calibration, the calibration
strategies can be categorized into two groups: the single-criteria
strategy and the multi-criteria strategy. A criterion represents an
objective function. Moreover, there are the a priori and the a
posteriori methods in multi-criteria calibration strategy. Among
them, the a priori method uses weight coefficients to aggregate
multiple objective functions into a single objective function for
optimization. The a prior method is used in most of the existing
research on multi-criteria calibration strategy, and each objec-
tive function’s weight coefficient is the same. The a posterior
method considers the optimal values of multiple objective func-
tions separately and finds a set of Pareto optimal solutions. In
detail, if solution A is not inferior to solution B in all objective
functions and is superior to solution B in a certain objective,
then called A dominates B. If A and B cannot dominate each
other, they are called non-dominated. If the selected solutions
are non-dominated, the solution is Pareto optimal solution. The
posteriori optimization algorithm can retain the non-dominated
solutions in the solution set and delete the dominated solu-
tions for the next iteration at each iteration. The non-dominated
solution retained after the iteration stops is the required Pareto
optimal solution set. The set of objective function values cor-
responding to these solutions is called Pareto optimal front.
Here we calibrate the TMM and study the effect of various
MoPs under three different calibration strategies: (1) Msingle(⋅),
implying that the model is obtained using the single-criteria
calibration strategy. For example, Msingle(SHT ) is the model
obtained using the single-criteria calibration strategy, in which
MoP is the SHT. (2) Mpriori(⋅, ⋅), implying that the model is
obtained using the a priori-based multi-criteria calibration strat-
egy. (3) Mposteriori(⋅, ⋅), implying that the model is obtained
using the a posteriori-based multi-criteria calibration strategy.
Genetic algorithm is used to solve single-criteria and multi-
criteria calibration strategies. Since the general GA is the a priori
method, it cannot solve the a posteriori-based problem [22].
Therefore, NSGA-II [45], similar to GA in solving logic, is used
as the a posteriori-based method. A detailed description of the a
priori and the a posteriori method in the TMM can be seen [46].
As we all know, the initial population will affect the effi-
ciency and accuracy of the stochastic optimization algorithm. To
obtain a stable and reliable initial population, we combine Latin
hypercube sampling (LHS) [47] with the cobweb graph. As
shown in Figure 1, first, the LHS is used to generate parameter
set candidates. After each parameter set candidate is imported
into the TMM and the model fully runs, each MoP’s MAPE is
calculated and arranged in ascending order. The smaller MAPE
parameter set candidates in each MoP, determined by the initial
population number, is called the better parameter set, which will
be used as the initial population of the stochastic optimization
algorithm. At the same time, the spider diagram of the better
parameter set is plotted, describing the distribution of the better
parameter set values under different MoPs and can be compared
with the real parameter values. It can be used to preliminarily
analyse the influence of different MoPs on the calibration results
of the model.
2.3 Methodology of TMM performance
appraisal based on MoP impact
This paper evaluates the performance of the TMM from three
aspects. The first aspect is the similarity between the calibrated
and the true parameter values. Here, the fit of parameters
is defined to quantify the distance between the optimized
parameter values and the true parameter values:
fp=
q
∑
j=1
|
|
|Xi,j−Xture,j|
|
|
UB j−LBj
(5)
where qis the number of parameters to be optimized. Xi,jis
the jth parameter value optimized under the ith MoP/MoP
combination. Xture,jis the true value of the jth parameter. UB j
and LBjare the upper and lower bounds of the jth model
parameter.
The second aspect is from the perspective of the calibrated
model performance, that is, the comparison based on the multi-
functionality of the model. In other words, it can be understood
as the fit of total measurements. Toledo et al. [48] and Park et al.
[49] proposed that multiple MoPs should be used to verify the
model comprehensively. Therefore, here, once the model is cal-
ibrated using an MoP/MoP combination (called the calibration
MoP), MAPE for other MoPs (called verification MoPs) are also
1204 LI ET AL.
FIGURE 1 Flow chart of the calibration and analysis approach.
calculated. Finally, all errors of verification MoPs are integrated
according to Equation (4). The fit of total measurements can be
calculated as follows:
ft=
n
∑
k=1
p
∑
l=1
1
m
m
∑
t=1
|
|
|Yobs
kl (t)−Ysim
kl (t)|
|
|
Yobs
kl (t)(6)
where the lower the ftis, the better the overall performance of
the model.
To more intuitively view the reduced degree of model
error after optimization and analyse the influence relationship
between MoPs, we use the fit of relative measurements ( fr)
to measure the improvement in verification MoP of each opti-
mized model relative to the uncalibrated model. The closer the
frvalue is to 1, indicating a significant improvement in this veri-
fication MoP for the calibrated model. The closer the frvalue is
to 0, the worse the improvement of this verification MoP. The
value of the frdefined as follows:
fr=⎧
⎪
⎨
⎪
⎩
1−Rsim
Rde f
Rsim
Rde f
≤1
0 otherwise
(7)
Rsim =
p
∑
l=1
m
∑
t=1
|
|
|Yobs
l(t)−Ysim
l(t)|
|
|
Yobs
l(t)(8)
Rde f =
p
∑
l=1
m
∑
t=1
|
|
|Yobs
l(t)−Yde f
l(t)|
|
|
Yobs
l(t)(9)
It is worth mentioning that the analytical approach estab-
lished in this paper can also be applied to the effectiveness
research of TMM calibration in any software and scenario.
LI ET AL.1205
2.4 Calibration and analysis methodology
The procedure of the proposed approach is shown in Figure 1.
Sensitivity analysis is needed to select the most significant con-
trollable parameters before optimizing the simulation model
(there are many studies on parameter sensitivity analysis meth-
ods of TMM, such as [11, 50–51], which lay the foundation for
us to select controllable parameters). After specifying the cali-
bration strategies and MoPs, the TMM effectiveness verification
procedure based on calibration using synthetic data can be car-
ried out. For each TMM calibrated by the specified calibration
strategy and MoP, the fit of parameters, fit of total measure-
ments, and fit of relative measurements are calculated once the
algorithm search is completed. The procedure is done when the
combinations between calibration strategies and MoPs are used.
Notably, most studies on TMM calibration usually use field
observation data, which cannot be used to verify the accu-
racy of the proposed method. Because researchers cannot know
the true parameter values, it is impossible to know whether
simulation optimization falls into a local or global optimum.
Second, since TMM cannot take all the potential driving fac-
tors into account in reality and the traffic process is random, the
traffic phenomenon obtained by simulation cannot completely
restore the real scene. These will interfere with the researchers’
judgment of the relevant mechanism and affect the research
conclusion. The application of synthetic data [52] is a solution
to the above problems. Therefore, to exclude other external
factors and study the influence of different MoPs on the cal-
ibration results more accurately, the “observed data” used in
this paper are synthetic data based on the real scene. It should
be mentioned that to improve the possibility of searching for
true parameters and suppressing the randomness of interfer-
ence from other factors except for MoP, this paper uses the
same random seeds and simulation times in generating synthetic
data and subsequent calibration.
3DETAILED DESCRIPTION OF MoP
Previous studies on MoP are often limited to the MoP types
(e.g. speed, time headway, and travel time). However, the MoP
collected by different measurement locations distinguishes even
the same type. For example, when practitioners want to use time
headway as MoP to calibrate an intersection model, the next
thing to do is to collect data on the site. However, the data
acquisition location can be different: they can collect the time
headway dedicated for uninterrupted traffic flow measurement,
the departure time headway in front of traffic signals, or the
time headway of the two locations at the same time. The micro-
scopic traffic behaviour in these two data is different, and the
calibrated model may also differ. Since previous studies on MoP
have emphasized this little, our study will consider this factor
here.
Therefore, the measurement locations are considered in this
paper. Another point to note is that the difficulties of data
collection are ignored in this paper. In other words, if the
MoP can be obtained through manual measurement, sensors,
or even video data in reality or through data processing tools,
it will be included in the comparison sets. In fact, even regular
smartphones could also provide a much richer sample of hetero-
geneous data for practitioners to get distribution data [53]. This
section mainly summarizes and describes the MoP types, and
the specific measurement locations will be presented in the case
study in Section 4. Note that this paper does not consider the
queue length as a MoP, which is explained in Section 3.4.The
set of MoPs used to depict traffic behaviour and conditions in
this research is composed of the following.
3.1 Speed
The time series of the average speed at detectors have been used
in many TMM calibration methods. However, the locations of
cross-sections may affect the accuracy of calibration. This paper
selects cross-sections of different traffic flow operation states
on the road section. Multiple detectors are set to measure the
time series of average speed.
3.2 Travel time
MoP related to travel time can be divided into two forms. The
first is the travel time distribution of all vehicles on the road,
that is, to obtain each vehicle’s travel time and get the probabil-
ity density function (PDF) or cumulative distribution function
(CDF) of the data. The other is according to a specific time
interval to aggregate the average travel time and then get the
time series of average travel time. This paper uses the time series
of average travel time and the CDF of travel time as MoPs to
calibrate the model.
3.3 Time headway
At present, only a few studies choose the time headway as a
MoP, but it is undeniable that the time headway can better
show the microscopic characteristics of traffic flow. Li et al. [38]
mentioned that the time headway distribution reflects the fun-
damental uncertainty of the driver’s car-following behaviour and
provides a straightforward method to describe the stochastic
characteristics of traffic flow. Therefore, we select two loca-
tions to construct two cumulative distribution functions of the
time headway. One is the time headway dedicated for uninter-
rupted traffic flow measurement, called headway. The other is
the departure time headway in front of traffic signals, called the
departure headway.
3.4 Space headway
The space headway can well reflect the microscopic traffic
flow state, which is applied to many studies on the calibra-
tion of the CF model. However, space headway data cannot be
directly applied to TMM calibration unless the leader vehicle’s
1206 LI ET AL.
FIGURE 2 Schematic representation of the experimental site.
trajectory is controlled and the followers cannot be affected by
other vehicles in the software. Few people use space headway
to calibrate the TMM because it takes so much time to imple-
ment this method that it does not apply to common simulation
projects. Generally, the MoP used to calibrate the TMM must
be an aggregation or distribution measurement. Therefore, we
consider two methods to process space headway data. One is
the CDF of the space headway of all vehicles on each specified
road segment lane, which is car-following without significant
acceleration or deceleration behaviour (i.e. acceleration less than
1m/s
2); the other is the CDF of the space headway of all vehi-
cles on each intersection entrance lane. It should be pointed out
that the average queue length is used as the MoP in many stud-
ies [27, 54] because it reflects the spatial behaviour of vehicles
to a certain extent. However, the queue length is susceptible to
the arrival distribution of vehicles in each signal cycle. Unless
the arrival time of each vehicle in the simulation is the same as
that observed in the field, the queue length will cause a signif-
icant error. The space headway distribution at the intersection
entrance includes the spatial behaviour of the vehicles at stop-
ping and running and can reduce the influence of the vehicle
arrival distribution.
4CASE STUDY
The study area is the intersection of Yuetan North Road and
Sanlihe East Road in Beijing. The selected arterial section is
a six-lane divided roadway, and only traffic in one direction
(southbound) is considered in this study. The length of the sur-
veyed section is approximately 450 m and extends from three
to four lanes 50 m from the stop line. Due to the interaction
between vehicles and the impact on the road environment, dif-
ferent traffic conditions coexist. A schematic representation of
the study section is shown in Figure 2.
The simulation model of this paper is established based on
VISSIM. The car-following model is Wiedemann 74, which
is one of the most basic submodels of VISSIM. Studies have
shown that the model is even powerful enough to simulate
the driving behaviour of connected vehicles on urban roads
if it can be accurately calibrated [55]. In addition, it should
be emphasized that the research scenario of this paper is fully
human-driven environment, which is different from the simu-
lation model of mixed traffic environment. Firstly, there may
be more than one driving behaviour model in the mixed traf-
fic of autonomous vehicles and human-driven vehicles. For
example, in the scenario of CACC car-following model adopted
by CAV and IDM car-following model adopted by human-
driven vehicles, researchers often need to take into account the
calibration of these two models [58]. Secondly, as the pene-
tration rates of autonomous vehicles change, the headway in
mixed traffic flow will also change [56, 57]. Since the mixed
traffic flow environment is not the focus of this study, more
calibration of mixed traffic flow scenarios can refer to some
corresponding studies [58, 59]. The lane change submodel is
free lane selection. According to the previous literature [46, 60,
61], the six most sensitive parameters are used to determine the
driving behaviour model, including average standstill distance
(ASSD), additive factor for safety distance (AFSD), dimension-
less multiplicative factor for safety distance (MFSD), observed
preceding vehicles (OV), safety distance reduction factor (SRF),
and minimum headway (MH). The specific definition of the
parameters is given in the appendix. Therefore, we have np =
[ASSD;AESD;MFSD;OV ;SRF ;MH ]; each parameter’s
true value was set and nptrue =[1.5;1.75;2.5;3;0.7;0.7].
After determining the nptrue, the field observation data are
generated. It is significant to note that VISSIM needs to set
expected speed distributions for different vehicle types rather
than for a single vehicle type [62]. Studies have shown that the
expected speed distribution significantly impacts driving speed
and affects traffic performance [63, 64]. Bhattacharyya et al. [37]
found that the different expected speeds of different vehicles
in the TMM remarkably correlate with the calibration’s correct-
ness. However, this paper focuses on the influence of various
MoPs on driving behaviour parameters. To minimize the impact
of other factors, we have preset the following: first, the vehicle
composition in this experimental scene is mainly unit car, and
only the expected speed distribution for the unit car is set; sec-
ond, the expected speed distribution and expected acceleration
distribution in this study is preset in advance. Specific meth-
ods for calibrating the expected speed distribution and expected
acceleration distribution can refer to Maksymilian’s study [65].
It is worth noting that in any simulation software, the range of
parameter values will directly affect the calibration results of the
LI ET AL.1207
microscopic simulation model. Excessive parameter range will
significantly affect the calculation time and accuracy of the algo-
rithm. Too small parameter range may not contain the optimal
solution and lead to poor performance of the calibrated model.
Therefore, the correct determination of parameter range will
play a crucial role in parameter calibration. Here, we refer to
previous studies [22, 46, 60] to set the upper and lower bounds
of the parameters. In particular, lnp =[1;0.5;1;1;0.2;0.3],
unp =[3;3;5;4;1;1].
Figure 3shows the processed field observation data. Each
data collection and processing method is as follows:
In terms of the series of average speed, ten detectors are
selected in three positions. The traffic conditions of each posi-
tion are different: detectors 1–3 are set on the lane of the
upstream section of the intersection, which shows “free-flow”
conditions. Detectors 4–6 are set on the upper lane of the inter-
section, and the vehicle will be interfered with by the vehicle
queuing from time to time caused by signal control. Detectors
7–10 are located at the entrance lane not far from the stop
line, where the intersection has been channelized, and vehi-
cles cannot change lanes at will. In terms of the average travel
time and travel time distribution, all vehicles’ travel time passing
through cross-section 3(starting) and cross-section 2(ending)
was collected.
In terms of the time headway distribution, the time headway
and departure headway are obtained from cross-section 1and
cross-section 2, respectively.
In terms of space headway distribution, Wiedemann [66]
believes that the vehicle is car-following when space headway ≤
150m. Therefore, in this paper, 150 m is used to judge whether
the vehicle is car-following. The space headway for each lane in
area 1 and area 2 are collected according to the rules introduced
in Section 3.4.
This study establishes various single-objective and multi-
objective functions based on various MoPs and the combination
of two MoPs, respectively. Meanwhile, the a priori and the
a posteriori optimization algorithms are used to optimize the
multi-objective function. The a priori optimization algorithm
sets the weight coefficient to the same value. The population
size is 20, and the stopping criteria are 50 iterations. The opti-
mization algorithms are carefully fine-tuned based on previous
studies [8, 15, 25, 37].
To facilitate the description of the experimental results, we
simplify the name of each MoP. Table 1introduces the specific
MoP types, abbreviations, and corresponding descriptions.
5RESULTS
In this research, all simulation work was carried out with VIS-
SIM 9.0 on a personal computer, which has a 4.9-GHz Intel
Core and 32 GB of RAM. The resolution of the simulator is
0.1 s. Because this is a small-scale case and the traffic flow is
controlled interrupted flow, the running state of traffic flow in
each signal cycle is similar under the premise of fixed traffic
demand; at the same time, our research focuses on comparing
the effects of various MoPs horizontally. Therefore, we set the
TAB LE 1 Types and nomenclature of MoP.
MoP types Abbreviation Description
Speed S1 Time series of 1-min average speed curve by
detectors 1–3.
S2 Time series of 1-min average speed curve by
detectors 4–6.
S3 Time series of 1-min average speed curve by
detectors 7–10.
ST Time series of 1-min average speed curve by
detectors 1–10.
Travel time TTS The series of 3-min average travel times.
TTD Cumulative probability distribution curve of
travel time at 5-s intervals.
Time headway TH1 Cumulative probability distribution curve of
time headway at cross-section 1.
TH2 Cumulative probability distribution curve of
time headway at cross-section 2.
THT Cumulative probability distribution curve of
time headway at cross-section 1 and
cross-section 2.
Space headway SH1 Cumulative probability distribution curve of
headway at section 1.
SH2 Cumulative probability distribution curve of
headway at section 2.
SHT Cumulative probability distribution curve of
headway at section 1 and 2.
simulation time to 1800 s. It is sufficient to provide microscopic
traffic-related information to calibrate the driving behaviour of
small-scale interrupted flow simulation models. Due to the need
to record the vehicle trajectory, it takes 20 h for each MoP to
calibrate the TMM (each run contains three random seeds and
a full warm-up period).
5.1 Results of the initial population based
on LHS
After generating 300 parameter set candidates, each parameter
set candidate is input into the simulation model for complete
running. MAPE measures the distance between the simulated
and observed values of each MoP. The 300 parameter set candi-
dates are arranged in ascending order, and the top 20 parameter
sets are selected. Cobweb plots can preliminarily judge the effec-
tiveness of MoP, as shown in Figure 4. The horizontal axis
represents the name of the six variables to be optimized, and
the vertical axis represents the parameters’ value. Because of the
different ranges of each parameter, the normalization method
is selected to fix the value of each parameter’s value between 0
and 1. The first 20 parameter set candidates are drawn with red
lines, and the true values are drawn with black lines. Suppose
the red line is relatively concentrated and the concentrated red
line is close to the black line. In that case, it shows that ob jMop
can be more easily found the global optimal solution, that is,
the MoP can represent the field traffic conditions. If the red
1208 LI ET AL.
FIGURE 3 The processed field observation data. (a) Average travel time in the form of series, (b) space headway in section 1, (c) space headway in section 2,
(d) time headway at cross-section 1, (e) time headway at cross-section 2, (f) travel time in the form of distribution, (g) average speed at detectors 1–3, (h) average
speed at detectors 4–6, (i) average speed at detectors 7–10.
LI ET AL.1209
FIGURE 4 Cobweb plots of the better parameter set candidates.
line is dispersed, different parameter values will cause similar
performance, which requires further algorithm optimization. If
the red line is concentrated and the concentrated red line is far-
ther away from the black line, it shows that the MoP cannot
truly reflect field traffic conditions. Figure 4shows the following
characteristics:
1. Regardless of the MoP, each variable’s parameter set candi-
date values are mainly distributed on both sides of the true
value. The range of parameter set candidates covers the true
value, indicating that using the parameter set candidates as
the initial population is conducive to finding an acceptable
solution.
2. The cobweb plots of ST, S1, S2, and S3 are relatively simi-
lar, the cobweb plots of TH1, TH2, and THT are relatively
similar, and the cobweb plots of SH1, SH2, and SHT are
relatively similar. Although the measurement locations are
different, the initial parameters for the same MoP types are
similar.
Another point to note is that there is a phenomenon in the
experiments that some parameter sets closer to the true value,
and those further away from the true value may lead to simi-
lar objective function values. Taking ob jS3as an example, some
of the parameter set candidates with the corresponding objec-
tive function values are shown in Table 2. It can be seen that
when the speed series collected at the intersection entrance is
used as the MoP to calibrate the model, the parameter sets with
a large difference will lead to similar objective function values
between 12.05 and 12.07. This indicates that there may be a
risk when using only this MoP to calibrate the model, that is,
to make the TMM fit in the wrong direction. In fact, Table 2
is just one example, and similar situations can occur with some
other MoPs.
TAB LE 2 The parameter set candidates with the corresponding ob js3
values.
ASSD AFSD MFSD OV SRF MH ob jS3
1.30 1.65 1.75 4 0.65 0.90 12.050
2.0 1.55 2.20 3 0.20 1.00 12.065
1.50 0.5 3.55 4 0.55 0.80 12.066
1.10 1.25 3.75 4 0.50 0.80 12.076
Interesting questions can be raised and are worth discussing
in the results: (1) There is little difference in the better param-
eter sets for different measurement locations but the same
MoP types (such as TH1, TH2, and THT). Will the MoP
collected at different measurement locations affect the cali-
bration results? (2) Some widely varying sets of parameters
lead to similar objective function values. However, according
to common sense, the closer the parameter set is, the smaller
the error is. Does this phenomenon exist in the final calibra-
tion results and how to explain it? Therefore, these two issues
will also be discussed according to the calibration results in
Section 5.2.
5.2 Results of calibration
After ending the algorithm, for each MoP experiment, ten
simulations were run with distinct random seeds [67]. Ten sim-
ulations were considered adequate since the variations across
separate simulations never exceeded 5% [68]. In terms of
convergence, due to space limitations, we take Msin gle (ST ),
Msin gle (SHT ), Mpriori (SHT ,ST ), and Mposteriori (SHT ,ST )as
examples to introduce the convergence of single-criteria and
multi-criteria calibration strategies. Figure 5represents the
1210 LI ET AL.
FIGURE 5 Objective values during the optimisation process.
FIGURE 6 Search history of the a posteriori optimization.
convergence process of the objective function when the GA
algorithm is used to optimize the objective function. It can be
seen that the objective function value decreases the fastest in the
first few iterations and then gradually levels off. 50 iterations
are enough for them. Also, it should be noted that although
the objective function value of Msin gle(SHT ) in the figure is
lower than that of Msin gle (ST )andMpriori (SHT ,ST ), this does
not mean that the model using SHT as the calibration tar-
get performs better than the other two because their objective
functions are different. Therefore, our main purpose here is to
introduce the convergence of the models. In the following, we
will analyse the performance of the models in detail. Figure 6
shows the search process results in each iteration when using the
NSGA-II algorithm for the a posterior optimization. The hori-
zontal axis and vertical axis in the graph represent two objective
function values, respectively. The red triangle represents the
objective function value corresponding to the Pareto optimal
solution, and the black circle represents the objective func-
tion value corresponding to the non-dominated solution in the
solution process. Then, the fit of parameters and fit of total mea-
surements values are calculated to measure the impact of various
MoPs on the calibration results from a macro perspective. The
fit of relative measurements is calculated to measure the error
reduction of the optimized TMM from a micro perspective.
The effects of calibration strategies and MoPs on TMM are
discussed in Sections 5.2.1, 5.2.2,and5.2.3.
5.2.1 Results of the effects of various MoPs on
model performance under different calibration
strategies
The quantified TMM performance results in different cali-
bration strategies are presented in Figure 7. The following
considerations can be made.
1. In the single-criteria calibration strategy
SHT (i.e. space headway) and ST (i.e. speed) are considered
the most effective MoP. TTD (i.e. travel time in the form of
distribution) and THT (i.e. time headway) are the less effec-
tive MoP in the single-criteria calibration strategy. Figure 7a
shows the overall performance (i.e. fit of total measurements) of
TMM calibrated with various MoPs and the difference between
driving behaviour parameters and real values (i.e. fit of param-
eters). In particular, the fit of total measurements and the fit
of parameters of uncalibrated models are also presented. It can
be seen that the fit of total measurements of Msin gle (SHT )is
optimal compared with other models, which is 14.31%. The fit
of total measurements of Msin gle (ST ) is second to Msin gle (SHT )
with 16.71%. The fit of total measurements of Msin gle (TTD)and
Msin gle (S2) are relatively bad compared with other models but
better than uncalibrated models, which are 28.38% and 29.05%,
respectively. Most of the other models have the fit of total mea-
surements around 20.00%, and it can be seen that even widely
differing fit of parameters may lead to a similar fit of total mea-
surements. This shows that in VISSIM, models close to the
true parameter value do not necessarily perform better than
models far from the true value. In other words, the relation-
ship between model performance and parameter values is not
linear.
The differences in model performance can be observed in
more detail in Figure 7b. Different MoPs have different effects
on improving TMM; the lighter the colour, the better the
improvement to the verification MoP. Thus, much information
can be uncovered in Figure 7b. The model calibrated with space
headway collected in two measurement locations (i.e. SHT) has
the most comprehensive improvement effect among all mod-
els in all aspects. The model calibrated with space headway in
the intersection entrance (i.e. SH2) shows poor performance
in terms of time headway and space headway in the “free-
flow” area. The model calibrated with space headway in the
“free-flow” area (i.e. SH1) shows poor performance in terms
of time headway in the “free-flow” area and speed in the inter-
section entrance. The models calibrated with speed (i.e. S1, S2,
S3, and ST) perform poorly in terms of time headway and
space headway in the “free-flow” area. The models calibrated
with time headway (i.e. TH1, TH2, and THT) show poor per-
formance in terms of speed and space headway. In particular,
although both travel time in the form of distribution and travel
time in the form of series are processed from travel time data,
Msin gle (TTS ) does not perform well regarding time headway and
space headway in the “free-flow” area. Msin gle (TTD ) performs
LI ET AL.1211
FIGURE 7 Comparison of results based on different MoPs and calibration strategies. (a) Fit of parameters and fit of total measurements of each model with
the single-criteria calibration strategy. (b) Fit of relative measurements of verification MoPs in each model with the single-criteria calibration strategy. (c) Fit of
parameters and fit of total measurements of each model with the a priori-based multi-criteria calibration strategy. (d) Fit of relative measurements of verification
MoPs in each model with the a priori-based multi-criteria calibration strategy. (e) Fit of parameters and fit of total measurements of each model with the a
posteriori-based multi-criteria calibration strategy. (f) fit of relative measurements value of verification MoPs in each model with the a posteriori-based multi-criteria
calibration strategy (we chose the one in the Pareto solution that minimizes the fit of total measurements of the TMM).
worse in terms of speed and space headway in the intersection
entrance and time headway in the “free-flow” area. In order
to facilitate readers to quickly check the influence of different
MoPs on the calibration results in the single-criteria calibra-
tion strategy, we summarize the above main results, as shown in
Table 3.
In addition, it should be noted that the impact between MoPs
is not bidirectional. For example, the TTD can be well fitted
in Msin gle (SH1). However, the SH1 cannot be well fitted in
Msin gle (TTD).
2. In the a priori-based multi-criteria calibration strategy
1212 LI ET AL.
TAB LE 3 Performance overview of models calibrated with different
MoPs in the single-criteria calibration strategy.
The MoP used in
calibration
Deficiencies or advantage of the corresponding
calibrated model
Space headway
collected in two
measurement
locations (SHT)
More comprehensive performance improvement
than models calibrated using other MoPs.
Space headway in the
intersection
entrance (SH2)
Showing poor performance in terms of time
headway and space headway in the “free-flow”
area.
Space headway in
free-flow area
(SH1)
Showing poor performance in terms of time
headway in the “free-flow” area and speed in the
intersection entrance.
Speed Showing poor performance in terms of time
headway and space headway in the “free-flow”
area.
Time headway Showing poor performance in terms of speed and
space headway.
Travel time in the
form of
distribution
Showing poor performance in terms of speed and
space headway in the intersection entrance, and
time headway in the “free-flow” area.
Travel time in the
form of series
Showing poor performance in terms of time
headway and space headway in the “free-flow”
area.
Figure 7c shows the fit of parameters and fit of total
measurements of each model in the a priori-based multi-
criteria strategy. The Mpriori (THT ,ST ) (i.e. calibrated with time
headway and speed) shows the best performance, whose fit
of total measurements is 13.05%. The Mpriori (TTD,TTS ) (i.e.
calibrated with travel time in the form of distribution and
travel time in the form of series) shows the worst perfor-
mance, whose fit of total measurements is 30.48%. Most
models’ fit of total measurements ranged from 13.00% to
20.00%. Mpriori (SHT ,THT ) (i.e. calibrated with space headway
and time headway), Mpriori (TTS,ST ), and Mpriori (TTD,THT )
have similar overall performance and their fit of total mea-
surements is around 15.00%. Moreover, we observed the
peculiarity of Mpriori (SHT ,TTS ), although the fit of param-
eters of Mpriori (SHT ,TTS ) are much lower than that of
Mpriori (THT ,ST ), its overall performance is worse. This further
illustrates the complex relationship between parameter values
and model performance. This will be further explored in Sec-
tion 5.2.3, and this section focuses mainly on the performance
of the calibrated models.
The performance of the models can be viewed in more
detail based on the fit of relative measurements in Figure 7d.
It can be seen that although each fit of relative measurements
in Mpriori (THT ,ST ) may not be the lowest, the improve-
ment of the model is satisfactory compared with other models.
Mpriori (THT ,TTD)andMpriori (SHT ,THT ) do not perform well
in terms of speed compared to other models. Mpriori (TTS ,ST ),
Mpriori (SHT ,ST ), and Mpriori (SHT ,TTD) perform poorly in
terms of time headway in the “free-flow” area. Moreover,
Mpriori (TTS ,ST ), and Mpriori(TTD,ST ) also show worse per-
formance in terms of space headway in the “free-flow” area.
Meanwhile, the performance of Mpriori (TTD,TTS ) in terms of
speed, space headway and time headway is hardly improved.
In order to facilitate readers to quickly check the influence of
different MoP combinations on the calibration results in the
a priori-based multi-criteria calibration strategy, we summarize
the above main results, as shown in Table 4.
3. In the a posteriori-based multi-criteria calibration strategy
Figure 7e shows the fit of parameters and fit of total mea-
surements of each model in the a posteriori-based multi-criteria
strategy. Each MoP combination corresponds to multiple
models because the solution obtained by the algorithm is
non-dominated. It can be seen that most models’ fit of total
measurements is between 13.00% and 16.00%. The fit of total
measurements of the lowest one in Mposteriori (THT ,ST ) (i.e.
calibrated with time headway and speed) is 11.60%, which
is the best performance among all models. The fit of total
measurements of the best-performing Mposteriori (TTD,TTS ) (i.e.
calibrated with travel time in the form of distribution and travel
time in the form of series) is 27.78%, which is much higher than
the other models. Moreover, it can be seen by the fit of param-
eters that the parameter values of each model are closer to the
true values compared to the models in the other two strategies.
The fit of relative measurements of the models with the
best fit of total measurements in each MoP combination
are shown in Figure 7f. It can be observed that, except
for Mposteriori (TTD,TTS ), the difference among the models is
mainly in the speed collected at detectors 4–6, time headway,
and space headway in the “free-flow” area. Specifically, the
Mposteriori (TTS,ST )andMposteriori(TTD,ST ) showed the worst
performance in time headway and space headway, but still
improved by about 40.00% to 50.00% over the uncalibrated
model. Mposteriori (THT ,TTD) has the worst performance in
speed compared to the other models. Most of the models
showed acceptable improvements in all aspects of performance.
In order to facilitate readers to quickly check the influence
of different MoP combinations on the calibration results in
the a posteriori-based multi-criteria calibration strategy, we
summarize the above main results, as shown in Table 5.
5.2.2 Results of the effects of different
calibration strategies on model performance
Many studies believe that the a priori-based multi-criteria strat-
egy is superior to the single-criteria strategy because the form
of MoP combinations can effectively compensate for the defect
that a single MoP cannot fully reflect the traffic characteristics.
However, this conclusion does not always hold in our exper-
imental results. Combining different MoPs leads to different
model performances in the a priori-based multi-criteria strategy.
Some models perform better than the single-criteria calibration
strategy, while others perform poorly. This can be observed
more clearly in Figure 8. Only the models calibrated with
the combination of (time headway, travel time in the form of
LI ET AL.1213
TAB LE 4 Performance overview of models calibrated with different MoP combinations in the a priori-based multi-criteria calibration strategy.
The MoP combinations used in calibration Deficiencies or advantage of the corresponding calibrated model
(Time headway, speed) More comprehensive performance improvement than models calibrated
using other MoP combinations.
(Space headway, travel time in the form of series)
(Time headway, travel time in the form of distribution) Showing poor performance in terms of speed.
(Space headway, time headway)
(Space headway, speed) Showing poor performance in terms of time headway in the “free-flow” area.
(Space headway, travel time in the form of distribution)
(Travel time in the form of series, speed) Showing poor performance in terms of time headway and space headway in
the “free-flow” area.
(Travel time in the form of distribution, speed)
(Travel time in the form of distribution, travel time in the form
of series)
Showing poor performance in terms of speed, space headway and time
headway.
TAB LE 5 Performance overview of models calibrated with different MoP combinations in the a posteriori-based multi-criteria calibration strategy.
The MoP combinations used in calibration Deficiencies or advantage of the corresponding calibrated model
(Travel time in the form of series, speed) Showing the worst performance in terms of time headway and space headway
than others.
(Travel time in the form of distribution, speed)
(Space headway, travel time in the form of distribution) Showing the worst performance in terms of speed than others.
(Travel time in the form of distribution, travel time in the form
of series)
Showing poor performance in terms of speed, space headway and time
headway in the “free-flow” area.
The others The difference among the models is mainly in the speed collected at detectors
4–6, time headway and space headway in the “free-flow” area.
FIGURE 8 Comparison of model performance when using different
calibration strategies. Take TTS,ST as an example, each bar represents,
Msin gle (ST ), Mpriori (TTS,ST )andMposteriori (TTS,ST )inorderfromlefttoright.
distribution), (time headway, travel time in the form of series),
(time headway, speed), and (travel time in the form of series,
speed) perform better than their corresponding models cali-
brated with a single MoP. Most models calibrated with MoP
combinations do not perform better than their corresponding
models calibrated with single MoP. Moreover, the models
calibrated with the combination of (travel time in the form
of distribution, travel time in the form of series) and (space
headway, speed) perform even worse than their corresponding
models calibrated with single MoP. This reflects that using
the a priori-based multi-criteria strategy is still risky, as it is
not necessarily superior to the single-criteria strategy. Overall,
in this study, the most significant advantage of the a priori-
based multi-criteria calibration method is only observed in
Mposteriori (THT ,TTD) (i.e. calibrated with time headway and
travel time in the form of distribution), Mposteriori (THT ,TTS )
(i.e. calibrated with time headway and travel time in the form
of series), Mposteriori (THT ,ST ) (i.e. calibrated with time headway
and speed) and Mposteriori (TTS,ST ) (i.e. calibrated with travel
time in the form of series and speed).
Although the a priori-based multi-criteria strategy does not
achieve the desired results, it does not mean that the multi-
criteria strategy is failed. As seen from Figure 8, for either MoP,
the models obtained in the a posteriori-based strategy (except
Mposteriori (TTS,TTD )) perform better than the corresponding
models calibrated in single-criteria strategy and the a priori-
based strategy. It is clear that the a posteriori method could
improve the performance of the calibrated model better than
the a priori method. A reasonable explanation for this result
is that in the a priori-based method, the weights of the two
objective functions need to be determined in advance, weak-
ening the most effective influence of the MoP. In contrast,
the a posteriori method considers the objectives separately and
could take advantage of each. Although this result is consistent
with Karimi’s conclusion [46] that a posteriori-based methods
are more effective than a priori-based methods in calibrating
1214 LI ET AL.
FIGURE 9 The absolute deviation of each model under different calibration strategies. (a) Under the single-criteria strategy. (b) Under the priori-based
multi-criteria strategy. (c) Under the posteriori-based multi-criteria strategy.
TMMs. However, he only compared the difference between the
two methods using the same MoP combination, whereas, in this
paper, different MoP combinations were taken for the experi-
ments. The results show that similar patterns exist for all other
MoP combinations in this experiment. It is an essential addition
to Karimi’s conclusion.
To further summarize the results and provide a reference for
practitioners, the role played by the calibration strategy when
calibrating the TMM with various MoPs should be investigated.
We use absolute deviation (Di) and average absolute devia-
tion (MD) to evaluate the stability of each calibration strategy
affected by different MoPs, that is, describe the dispersion of
the model performance in each strategy.
Di=|
|
|MEIi−MEI |
|
|(10)
MD=1
n
n
∑
i=1
Di(11)
Figure 9describes the fit of total measurements and its aver-
age value of all models in different strategies. The absolute
deviation and mean absolute deviation of each model is also
drawn. The red line represents the average value of fit of total
measurements of all models under this strategy, and the closer
it is to the horizontal axis, the higher the performance of the
model obtained using this strategy; the dark blue line represents
the fit of total measurements of each model under this strat-
egy; the light blue line represents the mean absolute deviation of
all calibrated models under this strategy; the yellow bar means
the difference between ( ft)and(ft) of each model. The smaller
the value is, the closer the calibrated model is to the average
level. It can be seen that the smallest average values of fit of
total measurements are in the a posteriori-based multi-criteria
strategy.
Moreover, the Diof each model in the a posteriori-based
multi-criteria strategy is not significantly different and the
MDis the smallest among the three strategies. This indicates
that the a posteriori-based multi-criteria strategy is least influ-
enced by various MoPs and has more potential to get a TMM
with better performance. Other than that, it can be seen that
the Diin the single-criteria strategy varies considerably, and
the MDis the largest of the three strategies. This indicates
that although, theoretically, similar performance TMM can be
obtained in different calibration strategies (e.g. Msingl e (SHT ),
Mpriori (SHT ,TTS ), and Mposteriori (TTS ,ST )), the single-criteria
calibration strategy is more affected by the MoPs. That is, with-
out a reliable MoP, obtaining a model with better performance
in the single-criteria calibration strategy is difficult. However, in
actual projects, it is almost impossible to know the reliability of
LI ET AL.1215
an MoP in advance. The results reveal the potential riskiness
of using the single-criteria strategy to calibrate the TMM. It is
an important implication for practitioners because the variety
of MoPs that can be obtained is very limited in many practical
projects.
5.2.3 Further discussion on MoPs in
experimental results
1. TMM performance cannot be verified by fitting results of a
single MoP alone
Some researchers often rely solely on the fitting results of a
single MoP (especially the travel time in the form of distribu-
tion or travel time in the form of series) to indicate whether the
TMM is properly calibrated. However, a good fitting of a sin-
gle MoP is necessary but not sufficient for a good performing
TMM. As an example of travel time distribution and average
travel time series, the fit of relative measurements of travel time
in the form of distribution and fit of relative measurements of
travel time in the form of series in Mposteriori (TTD,ST ) (i.e., cal-
ibrated with travel time in the form of distribution and speed)
are 0.8 and 0.83, and the minimum fit of total measurements of
Mposteriori (TTD,ST ) is 12.70%, which performs better than most
other models in Figure 7f. This is consistent with the common
sense of most researchers. However, although the fit of rela-
tive measurements of TTD and fit of relative measurements of
TTS in Mposteriori (TTD,TTS ) (i.e. calibrated with travel time in
the form of distribution and travel time in the form of series)
are even smaller than those of Mposteriori (TTD ,ST ), which are 0.9
and 0.85, the minimum fit of total measurements of the model
is 27.70%. This is not an isolated case; similar results exist for
other models such as Mposteriori (TTD ,ST ).
2. Further exploration of the relationship between parameter
values and model performance
In Section 5.2.1, we found that the parameters close to the
true values do not always result in better model performance;
parameters far from the true values can also result in better
model performance. To analyse this observation, we visualized
the object functions ob jMoP with respect to [AFSD; MFSD]
(since it is impossible to plot the change in the objective func-
tion value under the action of six parameters, we simplify to two
parameters) in steps of 0.05. The values of the two parameters
range from [0.7,2.5] and [1.25,4.25], which cover the values of
the parameters for each model in our experimental results. The
results are shown in Figure 10. Specifically, in each subgraph,
the horizontal axis represents MFSD and the vertical axis rep-
resents AFSD. Each block in the figure represents a parameter
set, and the colour of the block represents the objective func-
tion value corresponding to the MoP. The darker the block’s
colour (purple), the smaller the objective function value, that is,
the smaller the gap between the simulation output value and the
observation value. The lighter the colour of the block (yellow),
the bigger the objective function value.
It can be observed from Figure 10 that there are a large and
widely distributed number of local optimums in each ob jMoP,
which explains why even widely different parameters lead to
similar model performance. This is consistent with the phe-
nomenon in Section 5.1. Moreover, it can be seen that the
distribution of local optimums for different ob jMoP is not the
same. In this case, it is not easy to find the solution that makes
each ob jMoP relatively better by only one ob jMoP unless the global
optimal solution is found. This corresponds to the discussion
of the single-criteria calibration strategy above. Last but not
least, it can be seen that a solution close to the true value does
not always correspond to a smaller value of the objective func-
tion. However, in some of the literature where TMM calibration
has been studied using synthetic data, the difference between
the calibrated and the true values has become an important
basis for researchers to judge the effectiveness of the proposed
method (whether a new algorithm or a new calibration frame-
work). On the contrary, our results show that it is risky to
measure the effectiveness of the calibration method only by the
distance between the feasible solution and the real parameter
values.
3. Effect of measurement locations on TMM calibration
The influence of MoP obtained from different measurement
locations on TMM calibration has rarely been considered in
previous studies. In Section 5.1, we find that different mea-
surement locations have little influence on the parameter set
candidates. However, different measurement locations imply
different traffic conditions, which may affect the calibration
results. Therefore, to compare the effect of different measure-
ment locations on the calibration results, the fit of relative
measurements of the models calibrated with different measure-
ment locations MoPs are plotted in Figure 11. Each pole axis
represents the performance of the calibrated model on this
microscopic traffic variable. On the axis, the farther away from
the centre point indicates that the model performs better on
this microscopic traffic variable, that is, the model has been well
calibrated in this respect. Therefore, the detailed performance
of each calibrated model can be well expressed and compared
with other calibrated models. It can be seen from Figure 11
that those models calibrated with different measurement loca-
tions MoPs have different advantages. And, no measurement
location is always superior to other measurement locations. Tak-
ing Figure 11a as an example, Msin gle (S1) (i.e. calibrated with
speed in the “free-flow” area) performs better than Msin gle (S3)
(i.e. calibrated with speed in the intersection entrance) when
speed is selected to calibrate the model. However, the perfor-
mance of Msin gle (S1) in terms of time headway is inferior to
Msin gle (S3). Similar phenomena are common in Figure 11b,c.It
is worth emphasizing here that while models calibrated using
multi-point measurement locations do not necessarily perform
best on each microscopic traffic variable, it seems an acceptable
compromise.
4. Defects of using (TTD,TTS ) combination as calibration
targets
1216 LI ET AL.
FIGURE 10 The objective function with different MoP. (a) ob jsT,(b)ob js1,(c)ob js2,(d)ob js3,(e)ob jTH 1,(f)ob jTH 2,(g)ob jTHT ,(h)ob jSH1,(i)ob jSH 2,(j)ob jSHT ,
(k) ob jTTS ,(l)ob jTTD .
FIGURE 11 Comparison of the specific performance of models calibrated with the same type of MoP but at different measurement locations. (a) Models
calibrated with speed, (b) models calibrated with time headway, (c) models calibrated with space headway.
It can be seen from Sections 5.2.1 and 5.2.2 that the fit
of total measurements of the models using (TTD,TTS ) (i.e.
calibrated with travel time in the form of distribution and
travel time in the form of series) calibration are much higher
than the other models, both in the a priori-based multi-criteria
calibration strategy and in the a posteriori-based multi-criteria
calibration strategy. Therefore, it is necessary to investigate the
causes of this observation. It can be seen in Figure 7b that the
LI ET AL.1217
TTD and TTS of Mpriori (TTD,TTS )andMpoteriori (TTD,TTS )are
significantly improved, while the improvements in their other
aspects are not obvious. The reason for this can be roughly
conjectured from Figure 8. There are more locally optimal solu-
tions in ob jTTD and ob jTTS than in the other objective functions,
and these locally optimal solutions are widely distributed. This
makes it easier for the algorithm to search for “locally optimal”
for ob jTTD and ob jTTS but may not be “locally optimal” for the
other objective functions.
6 CONCLUSIONS AND FUTURE
RESEARCH
This paper describes a quantitative analysis approach using
TMM performance as the entry point to evaluate the effect of
MoPs and calibration strategies on TMM calibration.
The approach is implemented to a road section in Beijing. In
particular, the effect on the calibration of different MoP types,
measurement locations, and calibration strategies has been anal-
ysed. Results have presented the methodology and indicators
used are useful in order to understand the critical points of the
problem. The main conclusions of this paper are as follows: (1)
The performance of the TMMs calibrated with different MoPs
showed significant differences, as analysed in the results above.
(2) The TMM with space headway calibration performs bet-
ter in both single and multi-criteria calibration strategies. Space
headway distribution is considered a potential new MoP. (3)
The MoP obtained by the multi-point measurement is better
for TMM calibration than that obtained by single-point mea-
surement. (4) In TMM calibration, a good fitting of only one
MoP does not mean that the model can reflect the actual traf-
fic conditions, but the fitting results of several MoPs need to
be verified. (5) The multi-criteria calibration strategy based on
the a posteriori method shows excellent stability for different
MoP combinations. In contrast, the single-criteria calibration
strategy is susceptible to MoP, and the influence of differ-
ent MoPs on the calibration results of the model is quite
different.
It should be noted that although our calibration method and
indicators mentioned in this paper are applicable to any scenario
and driving behaviour model, the case we tested is a small-scale
interrupted flow scenario (an isolated intersection). Therefore,
the limitations of the discussion results need to be clarified.
First, this paper focuses on the interrupted flow on urban roads
(the car-following model used is Wiedemann 74). Due to the dif-
ferent characteristics of traffic flow, the results discussed in this
paper may not be suitable for highway scenarios with uninter-
rupted flow (the car-following model to be used is Wiedemann
99 in VISSIM [69]). In fact, Punzo [34] and Abuamer [70]have
discussed the performance of the microsimulation model in
terms of speed when using traffic volume as MoP for highway
scenarios. Second, due to the interaction between intersections
and the complexity of driving behaviour characteristics, the
results obtained by applying this approach to large-scale sce-
narios may not be exactly the same as the results of this study.
Moreover, the calibration method based on distribution [71]
may be a method to further accurately calibrate the large-scale
network model because it allows the researchers to study simul-
taneously various driving behaviour patterns. Therefore, future
research can be based on the research ideas and indicators
proposed in this paper combined with the distribution-based
calibration method to explore the effect of MoP on calibration
results in large-scale scenarios.
AUTHOR CONTRIBUTIONS
Haoran Li: Conceptualization; Resources; Software; Visual-
ization; Writing - original draft; Writing - review & edit-
ing. Zhenzhou Yuan: Conceptualization; Funding acquisition;
Supervision; Validation; Writing - review & editing. Siyuan
Chen: Conceptualization; Visualization; Writing - original draft;
Writing - review & editing. Chuang Zhu: Conceptualization;
Visualization; Writing - original draft; Writing - review & editing.
ACKNOWLEDGEMENTS
This research was supported by the Beijing Natural Science
Foundation of China (Grant No. J210001).
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
DATA AVAILABILITY STATEMENT
Research data are not shared.
ORCID
Haoran Li https://orcid.org/0000-0001-9764-6323
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How to cite this article: Li, H., Yuan, Z., Chen, S.,
Zhu, C.: Exploring the effects of measures of
performance and calibration strategies on calibrating
traffic microsimulation model: A quantitative analysis
approach. IET Intell. Transp. Syst. 17, 1200–1219
(2023). https://doi.org/10.1049/itr2.12375
APPENDIX
The detailed parameter definition can refer to the VISSIM man-
ual [58]. A brief description of each parameter is provided
below:
1. Average standstill distance (ASSD): This parameter defines
the average expected distance between two vehicles.
2. Additive factor for safety distance (AFSD) and dimension-
less multiplicative factor for safety distance (MFSD): These
parameters determine the calculation of the expected min-
imum following distance during the low speed differences
and are used to determine the range of the expected safe
distance.
3. Observed preceding vehicles (OV): This parameter defines
the number of vehicles in front that the driver can see while
driving.
4. Safety distance reduction factor (SRF): This parameter
adjusts the safe distance of the vehicle during the lane
change. Once the lane change process ends, the original
safety distance needs to be reconsidered.
5. Minimum headway (MH): This parameter defines the min-
imum distance to the preceding vehicle required for the
desired lane change.