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314 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
Comparative Evaluation of Microscopic
Car-Following Behavior
Sakda Panwai and Hussein Dia
Abstract—Microscopic traffic-simulation tools are increasingly
being applied to evaluate the impacts of a wide variety of intel-
ligent transport systems (ITS) applications and other dynamic
problems that are difficult to solve using traditional analytical
models. The accuracy of a traffic-simulation system depends
highly on the quality of the traffic-flow model at its core, with
the two main critical components being the car-following and
lane-changing models. This paper presents findings from a com-
parative evaluation of car-following behavior in a number of
traffic simulators [advanced interactive microscopic simulator for
urban and nonurban networks (AIMSUN), parallel microscopic
simulation (PARAMICS), and Verkehr in Stadten—simulation
(VISSIM)]. The car-following algorithms used in these simulators
have been developed from a variety of theoretical backgrounds
and are reported to have been calibrated on a number of different
data sets. Very few independent studies have attempted to eval-
uate the performance of the underlying algorithms based on the
same data set. The results reported in this study are based on
a car-following experiment that used instrumented vehicles to
record the speed and relative distance between follower and leader
vehicles on a one-lane road. The experiment was replicated in
each tool and the simulated car-following behavior was com-
pared to the field data using a number of error tests. The results
showed lower error values for the Gipps-based models imple-
mented in AIMSUN and similar error values for the psychophysi-
cal spacing models used in VISSIM and PARAMICS. A qualitative
“drift and goal-seeking behavior” test, which essentially shows
how the distance headway between leader and follower vehicles
should oscillate around a stable distance, also confirmed the
findings.
Index Terms—Car-following models, microscopic traffic
simulation.
I. INTRODUCTION
M
ICROSCOPIC traffic-simulation tools are increasingly
being applied by traffic engineers and transport profes-
sionals to deal with dynamic and operational traffic problems
and to evaluate a range of new intelligent transport systems
(ITS) applications. There are many problems such as adaptive
traffic management, traveller information, and incident man-
agement systems that are difficult to evaluate using traditional
analytical tools due to the complex nature of the underlying
system dynamics in these applications. Microscopic traffic-
Manuscript received August 30, 2004; revised December 6, 2004. The
Associate Editor for this paper was M. Kuwahara.
S. Panwai is with the Department of Civil Engineering, The University of
Queensland, St Lucia QLD 4072, Australia (e-mail: sakda@uq.edu.au).
H. Dia is with the ITS Research Laboratory, Department of Civil Engineer-
ing, The University of Queensland, St Lucia QLD 4072, Australia (e-mail:
H.Dia@uq.edu.au).
Digital Object Identifier 10.1109/TITS.2005.853705
simulation tools provide an environment where different sce-
narios can be introduced and evaluated in a controlled setting
without disrupting traffic conditions on the road. These traffic-
simulation tools are based on different theories of microscopic
traffic behavior such as car following and lane changing. Car-
following behavior, in particular, has a significant impact on the
accuracy of the simulation model in replicating traffic behavior
on the road.
This paper outlines the microscopic traffic-behavior char-
acteristics of a number of traffic-simulation tools. The paper
first describes the car-following models in three of the most
commonly used traffic-simulation tools: advanced interac-
tive microscopic simulator for urban and nonurban networks
(AIMSUN), Verkehr in Stadten—simulation (VISSIM), and
parallel microscopic simulation (PARAMICS). A methodology
for assessing the microscopic traffic behavior is then described
and the results from a comparative evaluation of the perfor-
mance of the three models in replicating field car-following
behavior are presented.
II. B
RIEF REVIEW OF CAR-FOLLOWING MODELS
Car-following behavior, which describes how a pair of ve-
hicles interact with each other, is an important consideration
in traffic-simulation models. Understanding driving behavior
is a key issue in evaluating model performance. A number
of factors have been found to influence car-following behav-
ior. These factors can be classified into two categories [1].
The first category is i ndividual differences consisting of age,
gender, risk-taking behavior, driving skill, vehicle size, and
vehicle performance characteristics. The second category is
situational factors involving both the environment and the
individual. These include factors such as time of day, day
of week, and weather and road conditions. Individual factors
include situations of distraction, impairment due to alcohol,
drugs, stress and fatigue, trip purpose, and length of driving.
Headways have been found to increase with driver age and
males are reported to choose shorter headways than females [2].
In addition, drivers aged 59 or more preferred a headway 1.83 s,
about 23% more than the normal driver (age range from 23
to 37) [3].
A study by Brackstone and McDonald [4] classified car-
following models into five groups as follows: Gazis–Herman–
Rothery (GHR) model, collision-avoidance model (CA), linear
model, psychophysical or action-point model (AP), and fuzzy-
logic-based model. These models (and the desired-spacing
model not covered in their review) are briefly described next.
1524-9050/$20.00 © 2005 IEEE
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 315
A. The GHR Model
The first formulation of this model was proposed in 1958
at the General Motors research laboratory in Detroit [5]. The
model is based on (1), which relates acceleration to the speed of
the leader vehicle, relative speed and spacing between follower
and leader vehicles, and driver reaction time.
a
n
(t)=cv
m
n
(t)
∆v(t − T )
∆x
l
(t − T )
(1)
where
a
n
(t) is the acceleration of vehicle n implemented at
time t;
v
n
is the speed of nth vehicle;
∆x is the relative distance between vehicle n and
(n − 1);
∆v is the relative speed between vehicle n and
(n − 1);
T is the driver reaction time; and
l, m, and c are constants.
The application of this model requires that the parameters
l and m to be calibrated for a particular network. This has been
reported to limit the application of the model. In addition, a
large number of contradictory findings of the correct values of
m and l have also been reported [4].
B. CA Model
This model was firstly presented by [6]. A number of variants
of the model are also reported in the literature [6]–[8]. The
model is based on (2), which describes the safe following
distance (required to avoid collision with the vehicle ahead) as
a function of the speeds of the follower and leader vehicles and
the driver’s reaction time.
∆x(t − T )=av
2
n−1
(t − T )+β
1
v
2
n
(t)+βv
n
(t)+b
0
(2)
where
v
n
is the speed of nth vehicle;
v
n−1
is the speed of (n − 1)th vehicle;
∆x is the relative distance between vehicle n
and (n − 1);
T is the driver reaction time;
α, β, β
l
, and b
o
are calibration constants.
The Gipps model [9], which is widely used in microscopic
traffic simulation, is based on the CA model. One of the factors
for the popularity of the model is the realistic behavior reported
for situations involving either a pair of vehicles or platoons. In
addition, the model can be calibrated using basic [9] assump-
tions about driver behavior and can be readily verified from
field observations.
C. Linear Model
The basic form of this model (3) relates the acceleration of
the follower vehicle to desired following distance, speed of the
follower vehicle, relative distance and speed between follower
and leader vehicles, and driver’s reaction time. This model had
its origins in the GHR model described previously and was
further improved by Helly [10], who introduced the desired
following distance factor. The model was found to present
a good fit to observed data. The main difficulty is with the
calibration of constant parameters for a particular study.
a
n
(t)=C
1
∆v(t − T )+C
2
{∆x(t − T ) − D
n
(t)}
D
n
(t)=α + βv(t − T )+γa
n
(t − T ) (3)
where
a
n
(t) is the acceleration of vehicle n imple-
mented at time t;
D
n
(t) is a desired following distance at
time t;
v is the speed of nth vehicle;
∆x is the relative distance between vehicle
n and n − 1;
∆v is the relative speed between vehicle n
and n − 1;
T is the driver reaction time; and
α, β, γ, C
1
, and C
2
are calibration constants.
D. Psychophysical or AP Model
This model is based on the assumption that a driver will
perform an action when a threshold, expressed as a function
of speed difference and distance, is reached. Three different
types of threshold are implemented [11]. For example, when the
value d/dt (∼ ∆v/∆x
2
) is exceeded, drivers would decelerate
until the relative speed between follower and leader vehicles
becomes zero. The second type of threshold is a spacing-
based threshold (∆x), which is particularly relevant at close
headways. Thus, for any change to be noticeable, ∆x must vary
by a “just noticeable distance” (JND). The third threshold is
obtained from a series of perception-based experiments that re-
quire passengers in test vehicles to observe a target vehicle and
make a decision whether the car-following gaps are widening or
shortening. Clearly, the ability to perceive speed differences and
estimate distances varies widely among drivers and hence, the
difficulty in estimating and calibrating the individual thresholds
associated with this model.
E. Fuzzy-Logic-Based Model
This model is based on fuzzy-set theory, which describes
how adequately a variable fits the description of a term. The
application of fuzzy-logic principles to the GHR model was
reported in [12]. The model divides the selected inputs into a
number of fuzzy sets and logical operators are then used to
produce fuzzy output sets or rule-based car-following behav-
ior. For example, two principal inputs to the decision-making
process can be relative speed and the separation divergence (or
the ratio of vehicle separation to the driver’s desired following
distance). A typical fuzzy rule for t he car-following model
would then have the form: If Distance Divergence is “Too Far”
and relative speed is “closing,” then the driver’s response is “No
Action.” The main difficulty in the application of this model is
316 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
the determination of membership functions, which are crucial
to the operation of the model.
F. Desired-Spacing Models
The desired-spacing models [13], [14] are based on a desired-
spacing criterion, which is assumed as a linear function of the
speed. The models are based on the premise that desired spacing
is an individual-driver characteristic and that drivers have dif-
ferent desired-spacing criteria in acceleration and deceleration.
These models eliminate the problems associated with reaction
times used in other models because they describe car following
based on desired spacing between vehicles without attempting
to explain the behavioral aspects of car following. A more de-
tailed discussion of these models can be found in [14] and [15].
III. C
AR-FOLLOWING MODELS IN
COMMONLY USED TOOLS
The car-following models of three commonly used traffic-
simulation tools is evaluated in this study. A brief description
of the car-following behavior implemented in each tool is pre-
sented next.
A. AIMSUN
AIMSUN is a microscopic traffic simulator developed at
the Laboratorio de Investigación Operativa y Simulación, a re-
search group in the Department of Statistics and Operations
Research of the Universit at Politècnica de Catalunya [16].
The car-following models implemented in AIMSUN are
based on the Gipps model [9], [17], [18]. Vehicles accelerate
to achieve the desired speed and decelerate when drivers have
to avoid a collision while trying to maintain the desired speed.
The maximum speed depends on acceleration as expressed
in (4).
V
a
(n, t + T )=V (n, t)+2.5a(n)T
×
1 −
V (n, t)
V
∗
(n)
0.025 +
V (n, t)
V
∗
(n)
(4)
where
V (n, t) is the speed of vehicle n at time t;
V
∗
(n) is the desired speed of vehicle n for the current
section;
a(n) is the maximum acceleration for vehicle n;
T is the reaction time (this is equal to simulation
step).
Fig. 1. Car-following phase-space diagram (v
j
=20m/s, b
m
=0.2m/s
2
)
[19].
The speed is also influenced by vehicle characteristics and
the limitation imposed by the leader vehicle, as shown in (5) at
the bottom of the page
where
d(n) is the maximum deceleration desired by ve-
hicle n;
x(n, t) is the position of vehicle n at time t;
x(n − 1,t) is the position of preceding vehicle (n − 1) at
time t;
s(n − 1) is the effective length of vehicle (n − 1);
d
(n − 1) is an estimate of the desired deceleration of
vehicle (n − 1).
The maximum desired speed during simulation is the lower
value returned by (4) and (5). Further details about the model
can be found in [17].
B. PARAMICS
The car-following model in PARAMICS is based on the
psychophysical model reported in [19]. The basic concept is
that the car-following plane is divided into five phases (or
regions) representing different modes of car following as shown
in Fig. 1. This figure depicts a two-vehicle car-following case
where the lead vehicle i s traveling at 20 m/s. The five phases
are denoted as: Following I, Following II, Danger, Closing In,
and Driving Freely. These phases are determined using the
following thresholds.
1) Perception-Threshold Negative (PTN) is defined as the
negative relative speed of a pair of vehicles (∆v =
v
j−leader
− v
i−follower
).
V
b
(n, t + T )=d(n)T +
d(n)
2
T
2
− d(n)
2 {x(n − 1,t) − s(n − 1) − x(n, t)}−V (n, t)T −
V (n − 1,t)
2
d
(n − 1)
(5)
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 317
TAB LE I
R
EGIONS OF THE CAR-FOLLOWING PHASE SPAC E
2) Perception-Threshold Positive (PTP) is defined as the
positive relative speed of a pair vehicles.
3) Desired-Distance (AD) threshold represents a comfort-
able distance headway of the vehicles, which is related
to speed of the follower vehicle.
4) Risky-Distance (AR) threshold represents conditions
when the distance headway is too close for comfortable
driving.
5) Safe-Distance (AS) threshold represents conditions when
a driver cannot decelerate quickly enough to avoid a risky
situation, as defined by the risky distance threshold (AR).
6) Braking-Distance (AB) threshold is an additional thresh-
old used to avoid collisions that may occur because of
higher speeds or late deceleration.
Table I summarizes the conditions that govern the determi-
nation of the five regions of the car-following model.
A variant of this model is used in the PARAMICS simulation
software. However, the differences or similarities between the
published version of the Fritzsche model and the version used
in PARAMICS are unknown [20].
C. VISSIM
The car-following model in VISSIM is based on the psy-
chophysical models reported in [21] and [22]. The basic as-
sumption in these models is that a driver can be in one of four
driving modes.
1) Free-driving mode, where no influence is exerted from
leading vehicles. In this mode, the driver attempts to reach
and maintain a desired speed.
2) Approaching mode, when the driver of the follower vehi-
cle consciously observes that she is approaching a slower
vehicle in front.
3) Following mode, where the headway for a pair of vehicles
is between the maximum following headway and the safe
headway. I n this mode, the follower vehicle is able to
accelerate or decelerate in accordance with the vehicle in
front.
4) Braking mode, when the headway between vehicles drops
below a desired safety distance.
The VISSIM traffic model comprises a psychophysical car-
following model for longitudinal vehicle movement and a rule-
based algorithm for lateral movements (lane changing). The
car-following behavior switches from one mode to another
Fig. 2. Car-following model by Wiedemann [21].
according to predetermined perceptual threshold levels that
form the basis of the psychophysical models. These thresholds
are defined as a combination of speed and headway differences
[21], [22]. In VISSIM, each driver–vehicle unit is described as
a driver–vehicle element (DVE). Fig. 2 shows the interaction
between two vehicles where DVEj is moving faster than
and approaching a slower vehicle DVEi.Driverj begins to
decelerate until an individual threshold, which is a function of
acceptable speed difference and spacing, is reached. Driver j
then maintains a speed at or below the current speed of DVEi,
until other thresholds are reached and the driver then accelerates
again [23].
One of the challenges of a psychophysical model rests with
the distributions of thresholds. Continuous measurements of
different traffic conditions are required to calibrate the model
in a realistic manner. The thresholds in Fig. 2 are defined
below [24]. Driver-specific perception abilities and individual
risk behavior is modeled by adding random values to each of
the parameters.
AX Desired distance between the front sides of two
successive vehicles in a standing queue.
ABX Desired minimum following distance, which is a
function of AX, a safety distance, and speed.
SDV Action point when a driver consciously observes
approaching a slower vehicle. SDV increases with
increasing speed differences. In the original work of
Wiedemann [21], an additional threshold is applied
to model additional deceleration by usage of brakes.
OPDV Action point when drivers of follower vehicles no-
tice that they are traveling slower than the leading
vehicles and start to accelerate again.
SDX Perception threshold t o model the maximum fol-
lowing distance, which is about 1.5–2.5 times ABX.
A driver reacts to the leading vehicle when the distance
between the two vehicles approaches 150 m. The minimum
acceleration and deceleration rate is set to be 0.2 m/s
2
.
Maximum rates of acceleration depend on vehicles’ technical
features. The model also includes a rule for exceeding the
maximum deceleration rate in case of emergency.
318 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
Fig. 3. (a) Speed profile of leader vehicle.
Fig. 3. (b) Profile of headway to leader vehicle.
IV. RADAR SPEED DATA F O R EVA L UAT I O N STUDIES
A number of studies on evaluating car-following models are
reported in the literature. The Robert Bosch GmbH Research
Group [25] collected speed data under stop-and-go traffic con-
ditions on a single lane in Stuttgart, Germany during an af-
ternoon peak. These data were used to evaluate a number of
car-following models [16], [25], [26]. The results reported in
this paper are also based on the same data and will be used to
evaluate the most recent versions of car-following models in a
number of traffic-simulation tools. A description of the data is
presented next.
A. Characteristics of the Radar Speed Data
The Robert Bosch GmbH Research Group [25] used an
instrumented vehicle to record the difference in speed and
headway between the instrumented vehicle and the vehicle
immediately in front. The response of the follower vehicle (the
instrumented vehicle), in terms of acceleration or deceleration,
was also recorded. These data were recorded in 100-ms inter-
vals for a total duration of 300 s for a single run on a single-lane
road in Stuttgart, Germany.
Fig. 3(a)–(d) depict the driving behavior between the fol-
lower and leader vehicles. Fig. 3(a) shows the speed profile
of the leader vehicle. The speed range during the experiment
was between 0 and 60 km/h. The vehicle came to a complete
stop on three occasions during the experiment [as shown in
Fig. 3(a)]. The relative distance to the leader vehicle (headway),
is presented in Fig. 3(b). The plot shows that the initial distance
to the leader vehicle was 81.1 m. The follower vehicle was then
able to drive at a free-flow speed until approximately 25 s into
the experiment when the headway started to decrease.
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 319
Fig. 3. (Continued.) (c) Profile of relative speed between vehicles.
Fig. 3. (Continued.) (d) Acceleration of instrumented vehicle.
Fig. 3(c) shows the relative speed between the follower and
leader vehicles. The absolute values of relative speed ranged
between 12 and 15 km/h. The response of the instrumented
vehicle when the leader vehicle accelerated or decelerated is
shown in Fig. 3(d). The plot shows that the response of the
instrumented vehicle ranged between −4.0 mi/s (deceleration)
to around +2.0 mi/s (acceleration).
B. Summary of Results Obtained in Previous Studies
The time-series data collected by the Robert Bosch GmbH
Research Group were applied to six car-following models [25].
1) MITSIM model. This model was developed by the traffic
simulation laboratory (SIMLAB) at Massachusetts In-
stitute of Technology (MIT) for evaluation of dynamic
traffic-management systems. The MITSIM model is
based on Herman’s car-following model [27].
2) Wied/Pel model. This model is based on the Wiedemann
model developed at the Technical University of Aachen
[28].
3) Wied/Vis model. This model, which is also based on the
Wiedemann model, is implemented in the commercial
tool VISSIM (v2.4) [23].
4) Nagel/Schreckenberg model (NSM). This model is based
on a cellular-automata approach describing single-lane
traffic flow on a ring road [29].
5) Optimal velocity model (OVM). This is a dynamic model
of traffic congestion based on equations of motion for
each vehicle. The model assumes that drivers adapt their
acceleration/deceleration response according to the dif-
ference between an optimal speed and current speed and
as a function of distance headway [30].
6) T
3
Model. This model, which is similar to the OVM
model, is based on regression analysis of measurement
320 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
TAB LE II
EM R
ESULTS FOR SELECTED MODELS
data. A detailed discussion of this model appeared in a
more recent publication by Fellendorf and Vortisch [31].
The function determining a driver’s acceleration is cho-
sen by using a polynomial function [32]. Speeds of the
follower and leader vehicles and distance headway are
used as input values to produce an output value, the
acceleration rate.
The study used an error metric (EM) on distance as a key per-
formance measure. The distance to the leader vehicle observed
in the field (d
f
) was compared to the values obtained from each
traffic simulator (d
s
). To avoid overrating on discrepancies for
large distance, the EM was weighted by logarithm and squared,
as shown below [25]:
EM =
log
d
s
d
f
2
. (6)
In a separate study [16], [26], the same methodology was ap-
plied to evaluate the car-following behavior in the commercial
tool AIMSUN. Table II summarizes the EM results obtained by
these studies.
V. E
VA L U AT I O N O F CAR-FOLLOWING BEHAVIOR
The results reported in this paper are based on an inde-
pendent evaluation of recent versions of the commonly used
traffic-simulation tools: AIMSUN (v4.15), VISSIM (v3.70),
and PARAMICS (v4.1). It should be noted that the evalua-
tion studies reported before were based on earlier versions of
AIMSUN and VISSIM. These models are continually being
developed and it is unknown if the underlying algorithms
have changed or not. Furthermore, this study also includes an
evaluation of PARAMICS, which was not included in previous
studies.
A. Evaluation Approach
Each simulator was used to model the car-following exper-
iment from which the radar speed data were collected. To set
up the experiment, firstly, the initial distance and speed of the
leader vehicle was set in accordance with the speed data. The
leader vehicle was first placed at a distance of 85.6 m from
the start of the section. The leader speed of 29.6 km/h was also
set out according to the observed data. To replicate the behavior
of the leader vehicle, two parameters (time and speed) were
controlled every time step. Secondly, the follower vehicle was
programmed to enter at the start of the section and control was
passed over to the car-following model in each simulator for
the remainder of the simulation period. Finally, each simulator’s
output (speed, time, and distance headway of both vehicles) was
captured and compared to the field measurements.
To achieve the above task, it was necessary to replicate the
behavior of the leader vehicle in each simulator. This task was
implemented in AIMSUN using the Generic Environment for
Traffic Analysis and Modelling (GETRAM) extension module,
which provides facilities to interface external applications to the
simulator. In every time step, the extensions module communi-
cates with the AIMSUN simulator using a dynamic link library
(DLL) file, which overrides the speed behavior of the leader
vehicle according to values stored in an external database.
Further details about the GETRAM extension module can be
found in [17]. VISSIM executes this task using an external
vehicle-course file, which also controls the driving behavior
of the leader vehicle in every time step during the simulation
period. Further details about this facility can be found in [33].
For PARAMICS, the speed of the leader vehicle is controlled
using PARAMICS Programmer, which provides an application
programming interface (API) to facilitate communication be-
tween the simulator and external applications. Further details
about Programmer can be found in [34].
It should be emphasized here that the leader vehicle’s arrival
into the network and its speed profile were controlled by an ex-
ternal module and were not allowed to vary in order to replicate
the exact behavior of the leader vehicle in the field. Similarly,
the follower vehicle’s arrival into the network was also con-
trolled by an external module to replicate the positioning of the
follower vehicle at the start of experiment in the field.
Fig. 4 illustrates the concept of overriding the driving behav-
ior in the simulation tools using external controllers. The field
experiment data gathered from the German study are stored
in the database. Each simulation step, the external controller
obtains the leader speed from the database, and implements it
in the traffic simulator. The behavior of the follower vehicle is
implemented by the car-following model in each simulator.
B. Scope and Assumption
The Bosch data show the car-following behavior of only
one driver. However, it is generally accepted that car-following
behavior is an individual characteristic and it is therefore not
expected that the default model parameters would correspond
to that particular individual’s characteristics. The models would
need to be calibrated (including acceleration/deceleration pa-
rameters) to that individual driver to produce better results. Due
to the variable requirements of each model, sensitivity analyses
of such impacts were not investigated for any of the tools
considered in this study. It is also noted that the car-following
behavior in this study was tested on a single-lane urban road.
Car-following behavior for critical driving situations, e.g., on
multiple-lane facilities, near on and off ramps on freeways, and
near entrances to roundabouts, should be further investigated.
This paper presents some basic findings of macroscopic behav-
ior (in terms of how each simulator replicates relative speeds
between follower and leader vehicles) but there is scope in
future studies to investigate a more comprehensive macroscopic
verification of microscopic behavior as described in [16] and
[25]. Finally, this study only considered car-following behav-
ior. There is also scope in future studies to consider other impor-
tant factors such as lane-changing behavior.
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 321
Fig. 4. Overriding driving behavior using external controllers.
TABLE III
S
ELECTED SIMULATION PARAMETERS
C. Controlled Parameters
The performance of each simulator will depend to a large
extent on the proper selection of a large number of parameters.
Some of the relevant parameters used in each traffic-simulation
tool are shown in Table III. It should be noted that each
simulator had been validated for a range of values as reported
in the respective manuals and publications. These values were
adopted to represent best case scenarios of performance. The
specification and investigation of ranges of values for which
the simulators have not been validated during their development
was not explored in this study.
The maximum acceleration and deceleration values are rele-
vant parameters to all three models while other parameters s uch
as vehicle and lane widths are only relevant to the VISSIM
simulator (considered in conjunction with car-following and
overtaking behavior). It should also be emphasized here that
the simulation time step, reaction time, and other parameters
for each car-following model can have a significant impact
on the performance of the model. No sensitivity analysis was
performed in this study to evaluate such impacts although there
is scope in future studies to examine calibration methodologies
such as those reported in, e.g., [35] and [36]. The simula-
tion time steps used in this study were based on default or
recommended values in the relevant simulators’ manuals or
publications.
D. Error Tests
A number of performance measures and error indicators
are used to assess the fitness of simulation output to the field
data [25], [37]. The criteria implemented in this study are
described below.
322 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
TAB LE IV
P
ERFORMANCE OF THE CAR-FOLLOWING MODEL
IN THE
SELECTED TRAFFIC SIMULATORS
1) The Root Mean Square (RMS) Error: This well-known
error test measures the divergence of the simulated result from
the observed value. The RMS error formulation used in this
study is
RMSE =
1
N
N
n=1
(d
s
− d
f
)
2
(7)
where
d
s
is the simulated car-following distance to the leader
vehicle at simulation time t;
d
f
is the field car-following distance to the leader vehicle
at time t;
N is the number of observations.
2) The EM on Distance: This error was weighted by the
logarithm and squared to avoid overrating discrepancies for
large distance [25]. The EM formulation used i n this study is
EM =
log
d
s
d
f
2
(8)
where
d
s
is the simulated car-following distance to the leader
vehicle at simulation time t;
d
f
is the field car-following distance to the leader vehicle
at time t.
VI. E
VA L U AT I O N RESULTS
Car following is essentially a control process that a driver
of a following vehicle uses to maintain a safe distance to the
vehicle ahead by using either acceleration or deceleration, ac-
cording to the actions of the leader vehicle. To verify whether
a traffic-simulation tool reasonably replicates that behavior,
a quantitative statistical test on the car-following distance as
recommended in [25] and a qualitative drift and goal-seeking
behavior, as recommended by Chakroborty and Kikuchi [38],
are presented next.
A. Quantitative Statistical Results
The EM and RMS error, which were described in Sec-
tion V-D, are used as the key performance measures in the
quantitative analysis. The results for the three models are shown
in Table IV. The EM indicates similar values for the psy-
chophysical spacing models used in VISSIM and PARAMICS
with better values reported for the Gipps-based models imple-
mented in AIMSUN. These results are also depicted in Fig. 5,
which shows the distance to the leader vehicle (in meters) as
replicated by each of the simulation tools. As can be seen
in Table IV and Fig. 5, the three models replicated field car-
following behavior with varying degrees of accuracy.
This study also explored a basic macroscopic characteristic
of the simulators, namely, how each simulator replicates the
relative speed between the leader and follower vehicles, as
shown in Fig. 6 below. The figure shows a substantially
different speed behavior for PARAMICS than the other two
simulators. As was mentioned before, there is scope in future
studies to investigate a comprehensive macroscopic verification
of microscopic behavior such as speed–flow, flow–density, or
any similar fundamental relationship.
B. Qualitative Drift and Goal-Seeking Behavior
The drift and goal-seeking behavior of a pair of vehicles is
essentially related to how the distance headway between leader
and follower vehicles oscillates (drifts) around what might be
termed as a stable distance headway [38]. This behavior hap-
pens because the driver of the follower vehicle cannot judge the
leader vehicle’s speed accurately or cannot maintain their own
speed precisely.
Drift behavior can be illustrated by plotting relative distance
against relative speed, as shown in Fig. 7. The x-axis shows
the relative speed of the vehicles while the y-axis represents the
distance to the vehicle ahead. The data points appearing in the
negative regions correspond to the follower vehicle traveling
at speeds greater than the leader vehicle. Fig. 6 depicts how
the car-following model for each simulator reproduces the real-
world interaction between the follower and leader vehicles.
These figures only provide a qualitative measure of the de-
gree to which each simulator replicates the measured drift be-
havior. The figures, however, clearly show that both AIMSUN
and VISSIM produced a very similar curve to the measurements
when compared to the PARAMICS curve, which reproduced
the relative speed between vehicles with much larger oscilla-
tions. These differences in drift behavior are clearly a reflection
of the various driving modes implemented in each car-following
algorithm implemented in each simulator.
VII. F
INDINGS AND CONCLUSION
The accuracy of a traffic-simulation system depends highly
on the quality of the traffic-flow model at its core. The two
main components at the heart of the traffic-flow model are the
car-following and lane-changing models. This study aimed to
evaluate only the car-following models in a number of traffic
simulators.
Speed data obtained from instrumented vehicles traveling on
an urban road in Germany were provided by the Robert Bosch
GmbH Research Group. A methodology to investigate the car-
following models in the traffic simulators was described. The
car-following behavior for each simulator was compared to the
field data using a number of error tests. The EM on distance
was used as the key performance indicator. The results showed
similar EM values for the psychophysical spacing models used
in VISSIM and PARAMICS with better values reported for the
Gipps-based models implemented in AIMSUN. The RMS error
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 323
Fig. 5. Distance to leader vehicle as replicated by each simulator.
Fig. 6. Relative speed between leader and follower vehicles as replicated by simulators.
and the qualitative drift and goal-seeking analyses also showed
a substantially different car-following behavior for PARAMICS
than the other two models.
There is scope in future studies to extend this evaluation
framework to include car-following behavior for critical driving
situations (e.g., near on and off ramps on freeways) and to
conduct sensitivity analyses to evaluate the impacts of some
of the critical parameters in each model, such as the sim-
ulation time step and reaction time. Furthermore, this study
only considered car-following behavior. The adoption of any
traffic-simulation tool for research and development purposes,
however, will need to take into consideration other impor-
tant factors such as lane-changing behavior and the ease of
interfacing the traffic-simulation system to external applica-
tions (e.g., driving simulators, adaptive traffic-management sys-
tems, optimization, and artificial-intelligence software tools).
This requirement is becoming increasingly important for
conducting research into modeling the impacts of ITS and
evaluating applications of advanced technologies to surface
transportation.
A
CKNOWLEDGMENT
The authors wish to thank the Robert Bosch GmbH Research
Group in Germany for providing the radar speed data used in
this study. The authors also wish to thank the Editor and the
three anonymous reviewers for their valuable comments and
suggestions.
This paper presents t he opinion of the authors based on their
research results and does not necessarily represent the views
or policy of the ITS Research Laboratory at the University of
Queensland. This paper does not constitute a recommendation
or standard, and it is for general information only and should
not be relied upon situationally or circumstantially. Neither the
authors nor the University are responsible for the use that might
be made of these results.
324 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 6, NO. 3, SEPTEMBER 2005
Fig. 7. Drift and goal-seeking behavior in car following.
REFERENCES
[1] T. A. Ranney, “Psychological factors that influence car-following and
car-following model development,” Transp. Res., Part F: Traffic Psychol.
Behav., vol. 2, no. 4, pp. 213–219, 1999.
[2] L. Evans and P. Waasieleweki, “Risky driving related to driver and vehicle
characteristics,” Accident Anal. Prev., vol. 15, no. 2, pp. 121–136, 1983.
[3] J. Wu, M. Brackstone, and M. McDonald, “The validation of a micro-
scopic simulation model: A methodological case study,” Transp. Res.,
Part C: Emerg. Technol., vol. 11, no. 6, pp. 463–479, 2003.
[4] M. Brackstone and M. McDonald, “Car-following: A historical review,”
Transp. Res., Part F: Traffic Psychol. Behav., vol. 2, no. 4, pp. 181–196,
1999.
[5] R. E. Chandler, R. Herman, and E. W. Montroll, “Traffic dynamics: Stud-
ies in car following,” Oper. Res., vol. 6, no. 2, pp. 165–184, 1958.
[6] E. Kometani and T. Sasaki, “Dynamic behaviour of traffic with a non-
linear spacing–speed relationship,” in Symp. Theory Traffic Flow,Re-
search Laboratories, General Motors, New York, 1959, pp. 105–109.
[7] A.D.May,Traffic Flow Fundamentals. Englewood Cliffs, NJ: Prentice-
Hall, 1990.
[8] R. Benekohal and J. Treiterer, “CARSIM: Car-following model for simu-
lation of traffic in normal and stop-and-go conditions,” Transp. Res. Rec.,
vol. 1994, no. 1994, pp. 99–111, 1998.
[9] P. G. Gipps, “A behavioural car following model for computer simula-
tion,” Transp. Res. Board, vol. 15-B, no. 2, pp. 403–414, 1981.
[10] W. Helly, “Simulation of bottlenecks in single lane traffic flow,” in Symp.
Theory Traffic Flow, Research Laboratories, General Motors, New York,
1959, pp. 207–238.
[11] R. M. Michaels, “Perceptual factors in car following,” in 2nd Int. Symp.
Theory Road Traffic Flow, Paris, France, 1963, pp. 44–59.
[12] S. Kikuchi and P. Chakroborty, “Car f ollowing model based on a fuzzy
inference system,” Transp. Res. Rec., vol. 1365, no. 1365, pp. 82–91,
1992.
[13] M. T. Parker, “The effect of heavy goods vehicles and following behaviour
on capacity at motorway roadwork sites,” Traffic Eng. Control, vol. 37,
no. 9, pp. 524–531, 1996.
[14] P. Hidas, “A car-following model for urban traffic simulation,” Traffic Eng.
Control, vol. 39, no. 5, pp. 300–305, 1998.
[15] ——, “Modelling vehicle interactions in microscopic simulation o f merg-
ing and weaving,” Transp. Res., Part C: Emerg. Technol., 2004, to be
published.
[16] J. Barceló and J. Casas, “Dynamic network simulation with AIMSUN,”
in Int. Symp. Transport Simulation, Yokohama, Japan, 2002, pp. 1–25.
[17] GETRAM/AIMSUN version 4.1 User’s Manuals, Transport Simulation
Systems ( TSS), 2002.
[18] P. G. Gipps, “MULTSIM: A model for simulating vehicular traffic on
multi-lane arterial road,” Math. Comput. Simul., vol. 28, no. 4, pp. 291–
295, 1986.
[19] H. Fritzsche, “A model for traffic simulation,” Traffic Eng. Control,
vol. 35, no. 5, pp. 317–321, 1994.
[20] E. Brockfeld, R. D. Kiihne, A. Skabardonis, and P. Wagner. “Towards
a benchmarking of microscopic traffic flow models.” Transportation
research record. No. 1852, 2003, pp. 124–129.
[21] R. Wiedemann, “Simulation des Straßenverkehrsflusses,” vol. Heft 8,
Karlsruhe, Germany: Instituts für Verkehrswesen der Universität
Karlsruhe, 1974.
PANWAI AND DIA: COMPARATIVE EVALUATION OF MICROSCOPIC CAR-FOLLOWING BEHAVIOR 325
[22] ——, “Modelling of RTI-elements on multi-lane roads,” Advanced
Telematics in Road Transport edited by the Commission of the European
Community, vol. DG XIII, 1991.
[23] M. Fellendorf, “VISSIM: A microscopic simulation tool to evaluate actu-
ated signal control including bus priority,” in 64th Institute Transportation
Engineers (ITE) Annu. Meeting, Dallas, TX, 1994, pp. 1–9.
[24] ——, “Static assignment versus dynamic simulation,” in Conf. Computa-
tional Engineering Systems Application, Hannover, Germany, 1998.
[25] D. Manstetten, W. Krautter, and T. Schwab, “Traffic simulation support-
ing urban control system development,” in 4th World Congr. Intelligent
Transport System, Berlin, Germany, 1997, pp. 1–8.
[26] J. Barceló, Microscopic Traffic Simulation: A Tool for the Analysis and
Assessment of ITS Systems. [Online]. Available: http://www.aimsun.com/
microsimulation_for_itsbis.pdf
[27] R. Herman, “Traffic dynamics through human interaction,” J. Econ.
Behav. Organ., vol. 15, no. 2, pp. 303–311, 1991.
[28] J. Ludmann, “Investigation o f intelligent traffic system by means of sim-
ulation,” presented at the 4th World Congr. Intelligent Transport System
(ITS), Berlin, Germany, 1997.
[29] M. Schreckenberg, A. Schadschneider, and K. Nagel, “Discrete stochastic
models for traffic flow,” Phys. Rev., E, vol. 51, no. 4, pp. 2939–2949,
1995.
[30] M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama,
“Dynamical model of traffic congestion and numerical simulation,” Phys.
Rev., E, vol. 51, no. 2, pp. 1035–1042, 1995.
[31] M. Fellendorf and P. Vortisch. (2003). Validation of the microscopic traffic
flow model VISSIM in different real-world situations [Online]. 2003.
Available: http://www.itc-world.com/library/2001%20TRB%20VISSIM%
20Validation.pdf
[32] T. Bleile, “A new microscopic model for car following behaviour in urban
traffic,” presented at the 4th World Congr. Intelligent Transport Systems
(ITS), Berlin, Germany, 1997.
[33] VISSIM User Manual Version 3.70, PTV AG, Karlsruhe, Germany, 2003.
[34] Quadstone Ltd., PARAMICS Programmer V4.0: User Guide and Refer-
ence Manual. Scotland, U.K.: Edinburgh, EH3 7RA, 2003.
[35] B. B. Park and J. D. Schneeberger, “Microscopic simulation model cal-
ibration and validation: A case study of VISSIM for a coordinated ac-
tuated signal system,” in Transportation Research Board Annu. Meeting,
Washington D.C., 2003, pp.1–18.
[36] J. Hourdakis, P. G. Michalopoulos, and J. Kottommannil, “A practical pro-
cedure for calibrating microscopic traffic simulation models,” presented
at the Transportation Research Board Annu. Meeting, Washington DC,
2003.
[37] G. H. Bham and R. F. Benekohal, “A high fidelity traffic simulation model
based on cellular automata and car-following concepts,” Transp. Res.,
Part C: Emerg. Technol., vol. 12, no. 1, pp. 1–32, 2004.
[38] P. Chakroborty and S. Kikuchi, “Evaluation of the General Motors based
car-following models and a proposed fuzzy inference model,” Transp.
Res., Part C: Emerg. Technol., vol. 7, no. 4, pp. 209–235, 1999.
Sakda Panwai received the B.S.I.E. degree in
civil engineering (first class honors) from King
Mongkut’s Institute of Technology, Thonburi, Thai-
land in 1996, and the M.E. degree in transporta-
tion engineering from Asian Institute of Technology,
Thailand, in 1998. He is currently working towards
the Ph.D. degree at the University of Queensland,
Australia.
He has worked for the Expressway and Rapid
Transit Authority of Thailand (ETA) for over
10 years, where he was responsible for feasibility
studies and highway design as a Senior Transportation Engineer. He also
lectured at the King Mongkut’ s Institute of Technology Thonburi from 1998
to 2002. His research interests lie in the area of intelligent transportation sys-
tems (ITS) including traffic simulation, modeling driver behavior, and advanced
traveler information system.
Mr. Panwai was given an ETA Scholarship for a Masters degree in 1996
and received an International Road Federation (IRF) Fellowship award in
2002/2003. He also received a Royal Thai Government (RTG) Scholarship
for doctoral study in 2003.
Hussein Dia received the B.S. and the M.S. de-
grees in civil engineering from Purdue University,
Westville, IN, in 1983 and 1985, respectively, and
the Ph.D. degree from Monash University, Australia,
in 1997.
He is the Director of the ITS Research Laboratory
at the University of Queensland, Australia. He has
18 years of experience in both public- and private-
sector organizations, both in Australia and overseas.
He has previously worked in consulting, research
and Information Technology organizations and acad-
emia, where he consulted and conducted research in Transportation and De-
cision Support Systems. He has extensive and demonstrated involvement in
ITS education, professional development, research and consulting. His main
professional interests are in the areas of traffic simulation and modeling of ITS
impacts and the development of real-time algorithms for traffic-management
applications.
Mr. Dia is a Chartered Professional Engineer and is affiliated with a number
of professional organizations such as the Institute of Transportation Engineers
(ITE), the Institution of Engineers Australia (IEAust) and the American Society
of Civil Engineers (ASCE).
