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Transportation Research Record: Journal of the Transportation Research Board,
No. 2623, 2017, pp. 1–9.
http://dx.doi.org/10.3141/2623-01
Adaptive cruise control (ACC) and cooperative adaptive cruise con-
trol (CACC) are important technologies for the achievement of vehicle
automation, and their effect on traffic systems generally is evaluated
with microscopic traffic simulations. A successful simulation requires
realistic vehicle behavior and minimal vehicle collisions. However, most
existing ACC-CACC simulation studies used simplified models that were
not based on real vehicle response. The studies rarely addressed collision
avoidance in the simulation. The study presented in this paper devel-
oped a realistic and collision-free car-following model for ACC-CACC
vehicles. A multiregime model combining a realistic ACC-CACC system
with driver intervention for vehicle longitudinal motions is proposed.
This model assumes that a human driver resumes vehicle control either
according to his or her assessment or after a collision warning asks the
driver to take over. The proposed model was tested in a wide range
of scenarios to explore model performance and collision possibilities.
The testing scenarios included three regular scenarios of stop-and-go,
approaching, and cut-out maneuvers, as well as two extreme safety-
concerned maneuvers of hard brake and cut-in. The simulation results
show that the proposed model is collision free in the full-speed-range
operation with leader accelerations within −1 to 1 m/s2 and in approach-
ing and cut-out scenarios. Those results indicate that the proposed
ACC-CACC car-following model can produce realistic vehicle response
without causing vehicle collisions in regular scenarios for vehicle string
operations.
Technologies for automated vehicle control have drawn great interest
since the automated highway system was introduced in the 1930s
(1). Adaptive cruise control (ACC) is one of the emerging technolo-
gies for driving assistance systems, and it was designed to enhance
driving comfort by automatically responding to a preceding vehi-
cle. Cooperative adaptive cruise control (CACC), an extension of
ACC with vehicle-to-vehicle (V2V) communication, is favored by
road operators because it has the possibility of vehicle coordination
and cooperation, which provides an opportunity to enhance traffic
efficiency.
Study of the potential impacts of ACC-CACC vehicles on traffic
efficiency is necessary because the penetration rate of ACC and CACC
vehicles is expected to increase in the near future. An early study
showed that ACC and CACC vehicles have the potential to increase
the lane capacity at 100% market penetration rate (MPR) (2). How-
ever, the conclusion for ACC vehicles does not hold in a simulation
if a realistic distribution of the desired time gap is considered (3).
The impact of CACC vehicles on lane capacity is still significant
in moderate- and high-MPR scenarios (3–5). With respect to flow
stability, CACC vehicles can smooth traffic flow and dampen shock
waves (4, 6–8), whereas ACC vehicles may worsen traffic stability
with amplified disturbances (9, 10).
Existing traffic impact analyses of ACC-CACC vehicles are based
on microscopic traffic simulations. To represent ACC-CACC vehicle
behavior in traffic simulations, default human driver car-following
models should be replaced by ACC-CACC car-following models.
According to the accuracy of simulated car-following models, liter-
ature on simulating ACC-CACC vehicles can be categorized into
four groups. The first group of studies used the desired speeds or
accelerations from ACC-CACC controllers as the actual speeds or
accelerations in the simulation (6, 11). It can be easily implemented,
but the predicted vehicle response may not be realistic since the model
ignores driveline dynamics, rolling, and aerodynamic resistance.
Studies of the second group applied a first-order lag between the
controller command (i.e., the desired speed or acceleration) and the
actual vehicle speed or acceleration to represent the driveline dynam-
ics (2, 4, 12). The response of a mechanical drivetrain is included
in the simulations, whereas the effects of external factors cannot
be captured. A full vehicle dynamic model, which includes vehicle
controller and both internal and external influential factors, was
adopted in the third group (13). Although the vehicle dynamic is
reasonably simulated, the detailed vehicle model consumes large
computation time and is barely feasible for large-scale traffic simu-
lations. The last group of studies modeled the realized speeds and
accelerations of ACC-CACC vehicles as the car-following response
using data collected during field tests (9). Empirical car-following
models based on measured vehicle response are expected to out-
perform these groups in model validity and implementation sim-
plicity. Empirical car-following models thus were selected as the
basic simulation models.
Empirical ACC and CACC models must be developed to fulfill the
requirements of large-scale traffic simulations. The first requirement
is the full-speed-range operation of ACC-CACC vehicles. Empirical
car-following models have been calibrated only within a speed range
Realistic Car-Following Models
for Microscopic Simulation
of Adaptive and Cooperative
Adaptive Cruise Control Vehicles
Lin Xiao, Meng Wang, and Bart van Arem
Department of Transport and Planning, Faculty of Civil Engineering and Geo-
sciences, Delft University of Technology, Stevinweg 1, 2628 CN Delft, Netherlands.
Corresponding author: L. Xiao, lin.xiao@tudelft.nl.
2 Transportation Research Record 2623
from 25.5 to 29.5 m/s (9); however, simulated ACC-CACC vehicles
can easily operate at a lower speed, especially when traffic conges-
tion occurs. Second, vehicles colliding in simulations may lead to an
unexpected simulation stop or deleted vehicles. The collision-free
property of a car-following model ensures proper performance
of a traffic simulator. However, the collision-free property cannot
be guaranteed in simulations because the empirical car-following
models are not designed to represent collisions, which are rare events
in practice. In emergency situations, drivers often override system
control to avoid collisions (14, 15), and car-following models must
explicitly incorporate that collision avoidance behavior (16). Previous
studies gave insufficient attention to the integrated ACC-CACC car-
following model with driver takeovers, and the resulting collision
properties have seldom been investigated.
This paper establishes ACC-CACC simulation models that origi-
nate from the empirical models, operate in a full-speed range, and
satisfy the collision-free requirement. Driver–system interaction
is considered, and a complete model with authority transition for
the full-speed range is proposed. The properties and validity of the
model, especially collision avoidance in safety-critical conditions,
were tested and assessed in a wide range of simulation scenarios.
This study fills the gap between ACC-CACC empirical car-following
models in limited scenarios and its extension and applications in
various traffic scenarios.
The rest of the paper has four parts. The first part introduces a
conceptual car-following model for ACC-CACC simulations with
model specifications. The second part builds a simulation experiment
to evaluate collision avoidance in five scenarios that ACC-CACC
vehicles may encounter in a simulation. The third part presents the
simulation results and explores the relationship between collision and
vehicle string disturbance. Conclusions and future work are discussed
in the last part.
MODEL FORMULATION
This section proposes a schematic control structure of simulated
ACC-CACC vehicles and formulates the models for their longitudinal
behavior.
Conceptual Model and Underlying Assumptions
A multiregime model for ACC-CACC longitudinal vehicle response
is proposed with two parallel control loops: a human driver control
loop and a system control loop. Each loop represents the sequential
procedures for corresponding vehicle control within a simulated
time step, and both loops are based on a three-stage control structure
from (17). Figure 1 illustrates the multiregime framework of double
loop control, where vi, xi, and ai refer to the speed, location and
acceleration of vehicle i. At each time step, the model inputs are
speed and position of preceding vehicle i − 1 and subject vehicle i at
a previous time step, as well as the desired time gap and the cruise
speed set by human drivers. These inputs are processed by either
ACC-CACC or human driver response models, and eventually the
actual kinematic data become model outputs and provide feedback
information for the next time step.
In the system control loop, the first perception stage obtains vehi-
cle kinematic data through radar sensors or V2V communication
and provides required inputs to the decision-making stage. In the
second stage, the ACC-CACC controllers receive and process the
inputs after the collision warning system does not issue a warning.
A speed or acceleration command is delivered to the lower-level
vehicle system in the third phase. The lower-level vehicle system,
which is related to throttle and brake actuation, operates vehicles to
meet commands. The final outputs are actual acceleration, speed,
and location. Depending on the ACC-CACC controller algorithms,
relevant kinematic information is collected and used as input for
decision making in the next time step.
The human driver control loop performs similar control processes.
The driver first perceives the leader’s speed and location and deter-
mines the activation or deactivation of automation or retains vehicle
control in the last time step. If the driver takeover is initiated, the
human driver response model overrules the ACC-CACC controller
and generates a desired acceleration to the vehicle model in the
third phase.
The proposed car-following model reflects the relationship between
actual vehicle speed and acceleration and the vehicle’s relative speed
and gap error in the previous time step. It is formulated as in Equa-
tion 1 and replaces the combination of the decision-making phase
and the actuation phase:
afxxvv
ik ik ik ik ik
()
=
−− −−−−
,, ,(1)
,1,1 ,1 1, 1,1
where subscript i and k represent vehicle sequence and time step,
respectively.
The driver intervention and the collision warning system determine
when to switch between the two control loops. They correspond to
two types of authority transition: discretionary overrides and man-
Collision
Warning System
ACC-CACC
Controller
Human Driver
Response
Warning on,
1-s delay
Acceleration/speed
command
Vehicle
Model
Acceleration
command
vi, xi
vi-1, xi-1
+–
Desired time gap
Desired speed
+
vi (CACC)
ai
(ACC, human)
Driver
Intervention (Remain)
deactivation
Sensor/V2V
(Re) activation
Perception
Decision Making Actuation
Driver
Perceptions
vi-1, xi-1–
++
vi, xi
Car-Following Models
FIGURE 1 Conceptual longitudinal models for ACC-CACC vehicles in simulations.
Xiao, Wang, and van Arem 3
datory overrides (14, 15). The discretionary override is initiated by
drivers, for drivers actively interacting with the automation system.
The mandatory override is activated as long as a collision warning
is given in a safety-critical situation. With respect to automation acti-
vation, it is assumed that the switch is effective only from the driver
control loop to system control loop, and the automation system
cannot switch on by itself.
ACC-CACC Car-Following Models
ACC-CACC controllers based on feedback control generally include
three subcontrollers for three motion purposes (18). The cruising
controller is designed for maintaining a user-set desired speed if a
preceding vehicle is absent. The gap regulation controller works for
car-following situations and aims to keep a constant time gap (CTG)
with its predecessor. When an ACC-CACC vehicle approaches its
leader with a high relative speed, the gap-closing controller tran-
sitions from cruising controller to gap regulation controller. In the
following, models for three operation modes are formulated.
Cruising Models
Cruising models for ACC and CACC vehicles are the same because
additional V2V information does not play a role in vehicle cruising
operation. Vehicle acceleration is modeled as a feedback control law,
which keeps the vehicle traveling at the desired speed. The general
formula is
ak
vv
ik ik
()
=−
−(2)
,set ,1
i
where the control gain k is a parameter for determining the rate of
speed error for acceleration and vset is the desired cruising speed. This
value was set as 0.3 to 0.4 s−1 in the literature (2–4, 7), and 0.4 s−1
was selected for this study.
Car-Following Models
The ACC and CACC car-following models of Milanés and Shladover
were used as the basic simulation models (9). The responses of ACC
followers were modeled as a second-order transfer function and are
described by
ak
ekvv
ik ik ik ik
()
=+ −
−− −
(3)
,1,2 1, 1,1
ii
where ei,k is the gap error of vehicle i at time step k. Equation 3
shows that vehicle acceleration depends on a gap error and a speed
difference with the preceding vehicle, where their feedback gain k1
and k2 is 0.23 s−2 and 0.07 s−1, respectively.
For CACC vehicles, the car-following behavior is represented by
a first-order model. Vehicle speed is calculated by the speed in the
previous time step (vi,k −1), the gap error (ei,k −1) in the previous time,
and its derivative, according to
vv
ke ke
ik ik pikdik
=+ +
−−−
(4)
,,1,1,1
ii
where kp and kd are 0.45 s−2 and 0.25 s−1.
Model Revision In original formulas, the gap error is determined
by the intervehicle spacing, desired time gap, and subject vehicle
speed. The intervehicle spacing was expressed as the position dif-
ference of two consecutive vehicles, where the vehicle length was
assumed to be zero. A distance variable, d0, is introduced here to
include the vehicle length in the gap error term, which is formulated as
ex xdtv
ik ik ik ik
=−−−
−− −−
(5)
,1,1 ,1 0des ,1
i
where tdes is the desired time gap.
The original simulation scenario of Milanés and Shladover was
rebuilt (9), and the simulation by the revised models was run with
an assumed 5-m vehicle length. The results showed that the model
revision does not change the car-following response of ACC-CACC
vehicles.
Dynamic Spacing Margin According to Equation 5, the desired
gap between vehicles at standstill is zero if d0 equals the vehicle
length. To prevent rear-end collisions, d0 was formulated as a function
of vehicle speed, which gives additional clearance at low speeds. A
preliminary full-speed-range simulation test on Equations 3 and 4
suggested that ACC and CACC vehicles require a different spacing
margin. ACC vehicles should have a 2-m additional clearance below
a speed of 10 m/s, whereas CACC vehicles need only a 1-m spacing
margin at speeds below 2 m/s. Thus, a maximum 2-m spacing mar-
gin was assumed for ACC vehicles, and the transitional speed range
begins at 15 m/s, where the margin gradually increases from zero.
The factor d0 is assumed to be inversely proportional to vehicle
speed with boundaries of 5 and 7 m and is formulated as
d
v
vv
v
=
≥
≤<
<
5if15m s
75 if 10.8 15 ms
7otherwise 10.8 ms
(6)
0
For CACC vehicles, a 1-m margin at speeds of 2 m/s (where the
desired gap is 1.2 m) was assumed, and a transitional speed range
starts at 10 m/s. By a linear function, the dynamic d0 policy for CACC
vehicles is
d
v
vv
=
≥
−+ <
5if10m s
0.125 6.25 otherwise10m s(7)
0
A larger spacing margin was given to the ACC model than to the
CACC model, because ACC vehicles need more spacing to com-
pensate for the gap variation caused by overshoot. The inverse
proportional function and linear function of d0 were determined
through preliminary tests to avoid rear-end collisions.
A combination of a CTG policy and a dynamic spacing margin
ensures a realistic ACC-CACC car-following response without
collisions at low-speed operations. Maintaining a CTG most likely
represents driving behavior on highways. Therefore, the CTG
policy is widely accepted by commercial ACC-CACC systems and
is the dominant gap-regulation discipline in field tests (9) and this
study for reproducing realistic vehicle response. A minimum spac-
ing between two vehicles at standstill is often required in addition
to the CTG policy of a safety margin, which is lacking in the origi-
nal model. Therefore, a dynamic spacing margin is proposed for
avoiding collisions only in simulation. The dynamic spacing margin
can extend the safety margin with a smooth vehicle performance
4 Transportation Research Record 2623
without altering the validity of the original model in the field test
speed range.
Approaching Models
The vehicle response under the gap-closing controller was not
modeled by Milanés and Shladover (9). The parameters of the
original car-following models were tuned for approaching. The
approaching model is applied once the vehicle gap is twice as large
as the desired gap and it falls into the detection range of forward-
looking sensors. For a smooth transition, the approaching model is
switched to the car-following model when the gap and speed errors
are smaller than 0.2 m and 0.1 m/s simultaneously.
Reducing the speed difference and shortening the gap are the con-
trol objectives in the approaching model. To achieve safe approach-
ing, the feedback gain on speed error was increased, and the feedback
gain on gap error was reduced. After tuning, k1 and k2 are 0.04 s−2
and 0.8 s−1 in Equation 4, and kp and kd are 0.01 s−2 and 1.6 s−1 in
Equation 5. This approaching model in combination with driver
intervention guarantees no collision when an ACC-CACC vehicle
approaches a standstill vehicle, as simulations will show.
Collision Warning System and Human Takeover
The multiregime nature of ACC-CACC operations requires modeling
transitions between different driving modes, in particular takeover
by human drivers. It is assumed that the system-initiated override
is based on a collision warning and the driver-initiated override is
activated in a particular condition.
Forward Collision Warning
A safety-critical situation can be identified by either the kinematic
approach or the perceptual approach. The kinematic approach triggers
the collision warning if the spacing is equal to or smaller than an
estimated safety spacing, whereas the perceptual approach is based
on drivers’ perception of critical situations and often uses time to
collision or its variations as indicators.
The indicator and suggested criteria in the Kiefer et al. study were
chosen to trigger the critical situation warning (19). Kiefer proposed
a probability indicator based on a so-called hardness of braking index,
which is a function of inverse time to collision and subject vehicle
speed. This indicator can be used for modeling and estimating the
drivers’ hard brake response to a variety of safety-critical conditions
and here is used to evoke the collision warning. This approach is
simple and computationally efficient.
Human Driver Car-Following Models
and Switching Assumptions
The intelligent driver model is a collision-free car-following model
for human-driven vehicles (20). Its modified version, IDM+ (7),
has been successfully applied in an open-source traffic simulator and
thus was chosen as the car-following model in the loop of human
control.
Driver-initiated deactivation depends on the driver’s subjective
evaluation of the situation. Before a vehicle leaves a string, the driver
may overrule the system to implement maneuvers that ACC-CACC
controllers are incapable of, for example, opening a safe gap at the
front or adapting the speed with the leader in an adjacent lane. More-
over, the driver may take over control when the vehicle approaches a
traffic jam, which has been observed in an ACC field operational test
in the Netherlands (21). In this case, it is assumed a driver-initiated
overrule is performed when an ACC-CACC vehicle approaches a
low-speed vehicle with a relative speed of more than 15 m/s and the
gap with the low-speed leader is less than the driver’s perception
range (150 m).
System-initiated overrule is evoked by the collision warning, and
the switch from the ACC-CACC car-following model to IDM+ has
a time delay considering the driver’s reaction time. Different from
driver-initiated overrule, the driver is assumed not prepared for the
warning, and thus the driver response is subject to a delay. The delay
includes the time for drivers to repay attention to driving tasks, the
action of braking, and the response of the vehicle mechanism. In
total, a delay of 1 s between alarm onset and vehicle actual braking
is assumed.
SIMULATION EXPERIMENTAL DESIGN
FOR MODEL VERIFICATION
The multiregime model is an approximate imitation of ACC and
CACC vehicles in the real world and should be verified to the degree
needed for applications. A series of simulation experiments was
designed and conducted to scrutinize potential collision avoidance
characteristics and the following response.
Experiment Design and General Simulation Setups
The experiment examined the impacts of several typical string dis-
turbances on the vehicle-following response and collision avoidance.
Five representative traffic scenarios were used: stop and go, hard
brake, cut-in, cut-out, and approaching.
The simulated scenarios were established and programmed in
MATLAB. The vehicle speed, acceleration, and location were used to
represent vehicle kinematic motions and were calculated and updated
every 0.05 s. The simulation starts when a vehicle string travels at a
constant speed and vehicles follow their preceding vehicles in equi-
librium status. The ACC vehicles maintain a 1.1-s time gap, and the
CACC vehicles maintain a 0.6-s time gap. Simulated disturbances
are introduced at 10 s, and simulations end when the string returns
to the equilibrium status. In each simulation, there is only one string,
and the simulated vehicle string is assumed to be homogeneous (vehi-
cle length 5 m). The length of the ACC vehicle string is restricted to
four vehicles, because of the string instability of ACC vehicles found
in the field test (9). The length of the CACC vehicle string is assumed
to be 10 vehicles, for implementation constraints in reality and model
consistency from the original model.
Scenario A. Stop and Go
The stop-and-go scenario examines the full-speed-range string
operation, as opposed to the limited speed range that the original
car-following models were calibrated and validated for. The simu-
lated vehicle string initially travels at 32 m/s, and the leader starts to
decelerate at 10 s to a full stop using decelerations of 1/80, 1/40, 1/20,
Xiao, Wang, and van Arem 5
and 1/10 g, respectively. After a stop of 10 s, the leader accelerates
to 32 m/s by a positive value of previous decelerations and remains
at 32 m/s till the end.
Scenario B. Hard Brake
In the hard brake scenario, the string leader applies large decelerations
compared with the comfortable decelerations in the first scenario.
The deceleration values and lasting time together define the string
disturbances introduced in simulations, and that was tested within
various speed ranges. The mean value of the original speed range was
chosen as the first tested initial speed, which was sequentially set to
lower values remaining at a 4 m/s speed interval. The tested decelera-
tions were from 2 to 6 m/s2, and the time for decelerating was tested
on a scale of 1 to 5 s.
Scenario C. Cut-In
The cut-in scenario was used to determine the collision impacts of a
cut-in vehicle on the ACC-CACC vehicle string. The cut-in maneuver
inevitably leads to a sudden drop in the gap to the directly following
vehicle, which creates a critical situation. The disturbance is simu-
lated as a vehicle cut-in at the second place of the string with a rela-
tive speed. The cut-in vehicle remains at the cut-in speed, and the
vehicles behind respond to this new leader. It is assumed that both
ACC-CACC string vehicles maintain a 1.1-s time gap and the cut-in
vehicle emerges at the place that left a 0.6-s time gap to its direct
follower (18). If a 5-m gap between the cut-in vehicle and its leader
is taken into account, only the simulations with initial operational
speeds greater than 20 m/s satisfy the assumptions.
Scenario D. Cut-Out
The cut-out scenario simulates a potential safety-critical process of
ACC-CACC vehicles leaving the string. A driver-initiated override
and a comfortable deceleration to open a gap are assumed for the
leaving vehicles, and the remaining vehicles have to decelerate as
well to respond, which may raise the collision risk. A maximum of
three vehicles is designed to leave the string. The second vehicle in
the string is always considered as the leaving vehicle for its extensive
influence. The other leaving vehicles are chosen by a balanced-
distributed sequence pattern or a concentrated distribution. All
leaving vehicles are assumed to start opening gaps simultaneously
at 10 s, and the remaining vehicles will catch up to their leader after
the leaving maneuver.
Scenario E. Approaching
A vehicle string that detects and approaches a leading vehicle down-
stream is simulated in the approaching scenario. The relative speed
of approaching is an influencing variable because it not only deter-
mines the activation of driver-initiated overrule but also raises high
collision risks. For relative speeds below 15 m/s, the detection range
was 120 m by ACC vehicle sensors and otherwise 150 m by human
perception. For CACC vehicles, the detection range was assumed
to be the range of V2V communication, which is 300 m. At 10 s, a
vehicle was set up downstream of a string and cruised at a constant
speed. Tested relative speeds were set from 0 m/s up to initial vehicle
speed, covering the approaching situations of standstill leaders,
low-speed leaders, and leaders with same speeds.
Table 1 lists the details of the tested variables in each scenario. To
verify the vehicle behavior, vehicle response and string performance
are evaluated by a qualitative analysis of vehicle speeds, accelera-
tions, and gaps. The collision is strictly defined as the distance gap
between two vehicles equal to or smaller than zero.
RESULTS AND DISCUSSION
Collision properties and prevented potential collision by human
takeover are the results that are relevant for verification of the con-
ceptual model. Results of the collision avoidance are presented in the
next section, followed by illustrated string performance by kinematical
parameters and model capability.
Collision Property and Human Takeover
The simulation results showed that the tested disturbance does
not lead to rear-end collisions in the full-speed-range scenario,
approaching scenario, and cut-out scenario. They verify the collision-
free property during normal string operation and provide strong
evidence to support the model applicability in traffic simulation.
Nevertheless, high collision risk still can be identified, particularly
TABLE 1 Parameter Setups for Simulated Disturbances
Reference
Milanés Model
Scenario A
Stop and Go
Scenario B
Hard Brake
Scenario C
Cut-In
Scenario D
Cut-Out
Scenario E
Approaching
Speed range (m/s) Speed range (m/s) Initial speed (m/s) Initial speed (m/s) Initial speed (m/s) Initial speed (m/s)
[25.5–29.5] [0–32] 30, 25, 20, 15, 10, 5 32, 28, 24, 20 30, 25, 20, 15, 10, 5 30, 25, 20, 15, 10, 5
Acceleration Acceleration Acceleration (m/s2)Δv = vi − vi−1 (m/s) Opening gap (s) Δv = vi − vi−1 (m/s)
±1/80 g, ±1/40 g,
±1/20 g, ±1/10 g
±1/80 g, ±1/40 g,
±1/20 g, ±1/10 g
−2, −4, −6 0, 2, 4, 6, 8, 10 1.2, 1.4, 1.6, 1.8 0, 5, 10, 15, 20, 25, 30
Deceleration time (s) Leaving position Detection range (m)
1, 1.5, 2, 2.5, ACC ACC
3, 3.5, 4, 4.5, {2}, {2,3} 120 (Δv < 15 m/s)
5 CACC 150 (Δv ≥ 15 m/s)
{2},{2,3},{2,6}, CACC
{2,5,8}, {2,3,4} 300
6 Transportation Research Record 2623
in the low-speed-range operation and approaching situations. The
potential collisions are eventually avoided by driver takeover on
time. Tables 2 and 3 list the timing at which drivers override ACC
systems in Scenario A and Scenario E, respectively.
In the stop-and-go scenario, collision-critical situations were found
at leader decelerations of 1/20 and 1/10 g. Those overrides happened at
speeds below 10 m/s, where a 2-m spacing margin was introduced.
The results implied that the proposed spacing margin and driver
intervention successfully prevent collision for a full-speed-range
string operation.
In approaching scenarios, collision warning is rarely triggered by
the approaching vehicle when the relative speed is no greater than
10 m/s. Once the relative speed goes beyond 10 m/s, the approach-
ing vehicle is overruled by either system-initiated requests or driver-
initiated requests at once (at 10.05 s), and resulting human hard
brake may activate the warnings for the other following vehicles.
High-relative-speed approaching is an extreme safety-critical situ-
ation. Especially for a standstill leader, a 120-m detection range is
insufficient for ACC vehicles to decelerate to a full stop before colli-
sions. Override timing shows the collision warning system and driver
override prevent collisions.
If more than one collision warning is given, ACC vehicles at the
front of the string generally receive the warning and switch to human
driver control earlier than the vehicles at the string tail, reflecting
a phenomenon by which the severe disturbance propagates from
downstream to upstream within an ACC string. In addition, no criti-
cal situation was detected by CACC vehicles in either scenario. The
V2V communication reduced the speed difference within the vehicle
string, and the disturbances did not amplify upstream.
No collision or warning was observed in any cut-out simulation
with various operational speeds, opening gaps, and leaving-vehicle
sequence. Particularly in CACC model tests, high collision prob-
ability was expected because of long-lasting decelerations during
gap openings. Because of the fast and smoothing response of CACC
controllers, the disturbances by gap opening were damped out and
no collision occurred. In general, simulation results suggested that
opening gaps by a comfortable deceleration does not cause a colli-
sion, regardless of operational speeds and settings of time gaps. The
number of leaving vehicles and vehicle sequences also do not affect
the collision results.
Vehicle String Performance
Illustrating the vehicle-following performance, nine plots of time-
varied speeds, accelerations, and preceding gaps for ACC and CACC
models, respectively, are presented. Results come from the full-
stop test with decelerations of −0.5 m/s2 in Scenario A, approach-
ing a 20-m/s leader with a 10-m/s relative speed in Scenario E, and
the second vehicle cut-out at a 1.8-s gap in Scenario D.
Figure 2 shows the dynamic response plots of the ACC vehicle
string in the three scenarios. In Figure 2a, the string leader and the
following vehicles decelerate to a full stop with a substantially
amplified deceleration rate, shown in Figure 2d. A deceleration of
0.5 m/s2 leads to driver takeovers for all the following vehicles, and
the fourth vehicle reaches a deceleration up to 1 m/s2. This result
is in accordance with the earlier work (9), and it is explained as
accumulated vehicle response delay when relying solely on onboard
sensors. During the period of 50 to 75 s in the subplot in Figure 2d,
the deceleration variation is observed by the extra spacing margin
setups. ACC vehicles decelerate slightly harder than the string leader
to create extra spacing.
Figure 2, b, e, and h, shows a continuous deceleration and smooth
approaching trajectories with the proposed model parameters for
approaching. The third and fourth vehicles respond to the decelera-
tion of the second vehicle and lead to a speed variation, which may
cause discomfort to drivers.
For the cut-out scenario, the second vehicle changed lane after it
had opened a 1.8-s gap at 18 s. The results point out that following
vehicles behind the cut-out vehicle reacted properly to the comfort-
able deceleration during the gap opening, and they smoothly caught
up to the new leader and returned to car-following status soon after
the cut-out vehicle left.
Compared with ACC, the string operation of CACC vehicles is
smoother and more efficient. Figure 3 shows the vehicle dynamic
response in selected scenarios. CACC vehicles do not lead to ampli-
fied disturbance thanks to the V2V communication. Vehicles at the
tails experienced accelerations similar to the leader even with a
10-vehicle string. The smooth speeds and accelerations in the
approaching scenario suggest a reasonable vehicle trajectory toward
a low-speed vehicle and the 300-m gap was effectively reduced
TABLE 2 Override Timing for Each ACC Vehicle Driver
in Scenario A
Acceleration Second ACC Third ACC Fourth ACC
±1/80 g — — —
±1/40 g — — —
±1/20 g 74.50 75.00 76.30
±1/10 g 40.65 41.75 35.20
Note: — = data are not available, indicating that drivers do not override
the system.
TABLE 3 Override Timing for Each ACC Vehicle Driver
in Scenario E
String Speed (m/s)/
Relative Speed (m/s) Second ACC Third ACC Fourth ACC
15/Δv = 10 — 13.55 14.90
10/Δv = 10 — 12.90 14.45
10/Δv = 0 — — 25.35
30/Δv = 30 10.05 12.75 14.40
30/Δv = 25 10.05 13.70 15.20
30/Δv = 20 10.05 — 17.90
30/Δv = 15 10.05 — —
25/Δv = 25 10.05 14.50 15.90
25/Δv = 20 10.05 18.60 18.40
25/Δv = 15 10.05 — —
20/Δv = 20 10.05 17.00 18.25
20/Δv = 15 10.05 20.40 21.35
15/Δv = 15 10.05 18.75 20.10
Note: Δv ≥ 15 m/s. Initial range for first three lines = 120 m; initial range for
remaining lines = 150 m. — = data are not available, indicating that drivers do
not override the system.
Xiao, Wang, and van Arem 7
within 100 s. These performance plots show that the conceptual
CACC model functions properly in generating plausible vehicle
behavior.
Model Capability in Hard Brake and Vehicle Cut-In
Table 4 summarizes the maximum deceleration time (MDT) of an
ACC-CACC string leader to achieve a collision-free string operation.
The number in each cell is the MDT corresponding to the leader’s
deceleration in the second row and the initial string speed in the first
column. A strong correlation was found between MDT and leader
decelerations. The smaller the decelerations, the larger the acceptable
deceleration time, suggesting the proposed car-following models can
accept either a long-lasting but soft brake or a short but strong decel-
eration as a disturbance that does not cause collisions. In addition, the
effect of an initial ACC vehicle speed on MDT is substantial, whereas
the effect of a CACC vehicle speed is insignificant. At decelerations
of −4 and −6 m/s2, the MDTs of ACC leaders in the high-speed range
doubled the MDTs at low speeds.
Results of the cut-in scenario showed that the maximum safety
speed difference for a low-speed cut-in vehicle is 6, 6, 8, and 10 m/s
for string speed at 20, 24, 28, and 32 m/s, respectively. The results are
the same for the ACC and CACC models, suggesting that impacts
of a cut-in vehicle on ACC-CACC vehicles with equal time gaps are
similar. All maximum speed differences are larger than zero, implying
that a vehicle cut-in with the same speed does not lead to collisions.
Large cut-in speed differences rarely occur in a simulation. An
assumption is often made in a simulation that if the speed difference
between cut-in vehicle and target leader is considerable, the cor-
responding lane-change gap is strongly rejected and the lane-change
maneuver is canceled. For this reason, cut-in vehicles normally do
not evoke extreme collision situations in a simulation.
CONCLUSION AND FUTURE WORK
This study built a bridge between ACC-CACC empirical car-following
models and their applications in microscopic traffic simulations.
The empirical ACC-CACC car-following models presented by
FIGURE 2 Scenarios A, E, and D: (a) through (c) simulated ACC vehicle speeds, (d) through (f) accelerations, and (g) through (i) distance gaps.
v = 30 m/s, open gap = 1.8 s,
second cut-out
Detection range = 120 m,
leader cruising at 10 m/s
Leader deceleration = 0.5 m/s2
Speed (m/s)
Time (s)
(a)
Speed (m/s)
Time (s)
(b)
Speed (m/s)
Time (s)
(c)
Time (s)
Acceleration (m/s2)
(d)
Time (s)
Acceleration (m/s2)
(e)
Acceleration (m/s2)
Time (s)
(f)
Gap with Predecessor (m)
Time (s)
(g)
Gap with Predecessor (m)
Time (s)
(h)
Gap with Predecessor (m)
Time (s)
(i)
8 Transportation Research Record 2623
Milanés and Shladover are ideal for a traffic simulation because
of the well-calibrated vehicle response (9). However, these models
cannot achieve collision-free operation in the full speed range, which
is an essential requirement for effective and efficient simulation.
Multiregime car-following models for ACC and CACC systems were
proposed here, extending the empirical ACC-CACC models with
human intervention. The simulation results suggest that no collisions
occur in representative traffic situations.
Systematic simulation experiments were conducted to test model
collision avoidance properties. The study verified the capability of
the proposed multiregime model with human interventions to avoid
collisions. It was concluded that the proposed models are collision-
free under typical traffic situations and most safety-critical scenarios
in simulations. The proposed model was verified in simulation only.
An analytical proof of the collision-free property needs to be inves-
tigated further. Another research limitation comes from the same
model parameter setting within a vehicle string in the simulation
experiments. The impacts of different vehicle lengths, acceleration
capabilities, and desired time gaps within a string can be found by a
TABLE 4 MDT for Collision-Free ACC-CACC Strings
in Hard Brake Scenario
Initial
String
Speed
(m/s)
Leader Deceleration MDT (s)
At −2 m/s2At −4 m/s2At −6 m/s2
ACC CACC ACC CACC ACC CACC
30 5.0 5.0 3.5 2.5 2.0 1.5
25 5.0 5.0 3.0 2.5 2.0 1.0
20 5.0 5.0 2.5 2.0 1.5 1.0
15 4.0 5.0 1.5 2.0 1.0 1.0
10 4.0 5.0 1.5 2.0 1.0 1.0
Note: At initial string speed of 5 m/s, leader decelerates until full stop.
FIGURE 3 Scenarios A, E, and D: (a) through (c) simulated CACC vehicle speeds, (d) through (f) accelerations, and
(g) through (i) distance gaps.
v = 30 m/s, open gap = 1.8 s,
second cut-out
Detection range = 300 m,
leader cruising at 10 m/sLeader deceleration = 0.5 m/s2
Speed (m/s)
Time (s)
(a)
Speed (m/s)
Time (s)
(b)
Speed (m/s)
Time (s)
(c)
Time (s)
Acceleration (m/s2)
(d)
Time (s)
Acceleration (m/s2)
(e)
Acceleration (m/s2)
Time (s)
(f)
Gap with Predecessor (m)
Time (s)
(g)
Gap with Predecessor (m)
Time (s)
(h)
Gap with Predecessor (m)
Time (s)
(i)
Xiao, Wang, and van Arem 9
sensitive analysis in subsequent simulations. Future research efforts
will implement this model in an advanced and sophisticated traf-
fic simulation model to discover the traffic impacts of ACC-CACC
vehicles.
ACKNOWLEDGMENTS
This research was conducted in cooperation with California PATH at
the University of California, Berkeley, and sponsored by an FHWA
exploratory advanced research program grant. The authors thank
Steven Shladover for his comments on the manuscript.
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The Standing Committee on Traffic Flow Theory and Characteristics peer-reviewed
this paper.
