Content uploaded by Meng Wang
Author content
All content in this area was uploaded by Meng Wang on Jan 15, 2018
Content may be subject to copyright.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1
Cooperative Car-Following Control: Distributed
Algorithm and Impact on Moving Jam Features
Meng Wang, Winnie Daamen, Serge P. Hoogendoorn, and Bart van Arem, Member, IEEE
Abstract—We design controllers and derive implementable al-
gorithms for autonomous and cooperative car-following control
(CFC) systems under a receding horizon control framework. An
autonomous CFC system controls vehicle acceleration to optimize
its own situation, whereas a cooperative CFC (C-CFC) system
coordinates accelerations of cooperative vehicles to optimize the
joint situation. To realize simultaneous control of many vehicles in
a traffic system, decentralized and distributed algorithms are im-
plemented in a microscopic traffic simulator for CFC and C-CFC
controllers, respectively. The impacts of the proposed controllers
on dynamic traffic flow features, particularly on formation and
propagation of moving jams, are investigated through a simula-
tion on a two-lane freeway with CFC/C-CFC vehicles randomly
distributed. The simulation shows that the proposed decentralized
CFC and distributed C-CFC algorithms are implementable in
microscopic simulations, and the assessment reveals that CFC and
C-CFC systems change moving jam characteristics substantially.
Index Terms—Car-following, cooperative systems, receding
horizon control, distributed algorithm, moving jam.
I. INTRODUCTION
ONE of the main achievements in transportation science
and technology in the past decades is the emergence
of intelligent vehicles. Intelligent vehicle systems support or
even take over drivers in performing driving tasks such as car-
following or lane-changing and are seen as a promising ap-
proach in improving traffic safety, efficiency and sustainability
[1]. In general, intelligent vehicle systems can be categorized
into two groups, i.e., autonomous systems and cooperative sys-
tems. Autonomous vehicles do not communicate with others.
They rely solely on their on-board sensors and make control de-
cisions for their own sake [2]–[4]. On the contrary, cooperative
or connected vehicles ‘talk’ to each other via Vehicle-to-Vehicle
(V2V) and/or Vehicle-to-Infrastructure (V2I) communications
to enhance the perception of the driving environment and/or
to assist cooperative vehicles in maneuvering together under a
common goal [5]–[9].
The Adaptive Cruise Control (ACC) system is the earliest
car-following control (CFC) system, which specifically aims
Manuscript received March 11, 2015; revised July 1, 2015 and September 29,
2015; accepted November 25, 2015. This work was supported by Shell under
the project Sustainability Perspectives of Cooperative Systems. The Associate
Editor for this paper was L. Vlacic.
The authors are with the Department of Transport and Planning, Delft
University of Technology, Delft 2628, The Netherlands (e-mail: M.Wang@
tudelft.nl).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TITS.2015.2505674
at enhancing driving comfort [2], [6], [7]. The most widely
used ACC controller is a PD controller, where the vehicle
acceleration is proportional to the gap and the derivative of the
gap (relative speed with respect to the preceding vehicle) at
car-following conditions. This type of controller has been ex-
tensively studied [2], [6], [10]–[12]. The control strategy is re-
ferred to as constant time headway (CTH) policy. Extensions of
this ACC controller have been used to design ACC systems with
variable time gap policies [13] and cooperative ACC (CACC)
systems by including the acceleration of the predecessor [2],
[6], [7], [14] and positions and speeds of multiple leaders
[15]. However, there is no safety mechanism in this model.
Under critical conditions, ACC systems have to be overruled by
drivers and hard braking has to be performed to avoid a collision
[16]. The operation of the extended CACC controllers requires
a high penetration rate of CACC systems, i.e., both the leader
and the follower have to be equipped vehicles. The cooperation
embedded in this type of CACC systems is based on improving
the situation awareness by cooperative sensing [9]. There is no
cooperation in the decision-making process.
Car-following models are used as state feedback algorithms
for ACC systems. The Optimal Velocity Model (OVM) is used
to describe the ACC vehicle behavior [17], [18]. The OVM
regulates the speed of the controlled vehicle towards an optimal
speed, which is a function of the following gap. Unfortunately,
the optimal velocity model is not collision free. The Intelligent
Driver Model (IDM) is also used to design ACC controllers,
with a driving strategy that varies parameters according to
traffic situations to mitigate congestion at bottlenecks [19],
[20]. Although benefits on capacity are gained through the
IDM controller, physical limits such as minimum allowed de-
celeration and limited sensor detection range are not explicitly
included in the model.
Artificial intelligence (AI) techniques are also used to design
ACC systems. A rule-based controller is proposed for generic
intelligent driver support systems [21]. The vast number of rules
and scenarios involved makes the controller highly non-linear
and it is not straightforward to gain insights into the properties
of the controller. Other AI technologies are also reported in
ACC controller design, such as fuzzy logic or self-learning
systems [3], [22], [23].
Model predictive control, also called receding horizon con-
trol, is used in the design of ACC and CACC controllers. Com-
pared to other control approaches, model predictive control is a
flexible approach in dealing with multiple design criteria and
constraints on state and control variables. A linear quadratic
regulator (LQR) is used for longitudinal control of automated
1524-9050 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
2IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
vehicles [24], [25]. In this special ACC controller, the reference
acceleration can be calculated with a linear feedback control
law of the state. Model predictive ACC controllers, where the
reference acceleration is assessed in a receding horizon way
have been proposed [26], [27]. The ACC controller aims at
minimizing deviation from desired gap, deviation from prede-
cessor speed, accelerations and jerk, and the deviation from a
human desired acceleration calculated with Helly model [26].
However, the resulting traffic flow stability properties of the
controllers are not examined [26], [27].
In our previous work, we proposed a generic receding hori-
zon control approach based on Pontryagin’s Principle to design
both autonomous CFC and cooperative CFC (C-CFC) systems
[4], [9]. The autonomous and cooperative CFC systems include
a complex cost function of non-quadratic form that gives high
penalty when the subject vehicle approaches the predecessor at
small gaps. This mechanism guarantees that at safety-critical
conditions, the controllers take safety as first priority and hence
can avoid rear-end collision with the predecessor. Safety per-
formance of the controllers has been verified in [4] and [9]. The
approach is flexible in deriving cooperative CFC algorithms
that are based on sharing information to improve situation
awareness, i.e., cooperative sensing, and on maneuvering to-
gether under a common objective, i.e., cooperative control [9].
A centralized communication and optimization scheme is
proposed and tested in a platoon of 10 cooperative vehicles [9].
The computational load of the centralized algorithm increases
with the number of cooperative vehicles in the platoon due
to the expansion of dimensionality of state and control input
space and becomes computationally intractable when the size
of the platoon increases substantially in real traffic systems
with high penetration rates of cooperative vehicles. Therefore,
it is still challenging to implement receding horizon controllers
for autonomous and cooperative vehicle systems in large-scale
traffic simulations. Furthermore, systematic investigation of
the impacts of autonomous and cooperative vehicles with
receding horizon controllers on macroscopic traffic flow and
sustainability have not been reported due to the lack of efficient
algorithms and hence their impacts on traffic flow have not
been understood sufficiently.
In this article, we propose efficient algorithms for au-
tonomous and cooperative CFC systems under a receding hori-
zon control framework. An autonomous CFC vehicle optimizes
its own situation. When two or more C-CFC vehicles form a
platoon, the distributed C-CFC algorithm entails neighboring
cooperative vehicles transmit their most recent state informa-
tion and predicted control information via V2V communication
to facilitate the decision-making of neighbors and minimize
a joint cost function consisting their own situation and the
situation of their follower. Even when one C-CFC vehicle
is followed by an uncontrolled vehicle where V2V commu-
nication is not feasible, the C-CFC vehicle can still exhibit
cooperative behavior by predicting the uncontrolled follower
behavior and minimizing the joint cost. To realize simultaneous
control of many vehicles in a traffic system, decentralized
and distributed algorithms are proposed and implemented in a
microscopic traffic simulator for CFC and C-CFC controllers
respectively. The impact of the proposed controllers on traffic
flow dynamics, particularly on formation and propagation of
moving jams, is investigated through simulation on a two-lane
freeway, with CFC/C-CFC vehicles randomly distributed. The
simulated freeway stretch constitutes a traffic system with more
than 500 vehicles running in the network.
The main contributions of this article are the fast distributed
receding horizon cooperative control algorithm that is scalable
to large-scale platoons and the new insights into the collective
traffic flow characteristics with CFC and C-CFC vehicles.
The rest of the paper is organized as follows. First, the
mathematical formulation of the autonomous CFC controller
and the corresponding decentralized implementation algorithm
is presented in Section II. Following that, the C-CFC con-
troller is formulated and the distributed algorithm is described.
Section IV illustrates the experimental design to test the ap-
plicability of the proposed algorithms and to assess the impact
of the proposed systems. The simulation results are discussed
in Section V.
II. AUTONOMOUS CONTROLLER AND
DECENTRALIZED ALGORITHM
CFC systems operate in two modes, being following mode
and cruising mode [4]. In cruising mode, the CFC system
aims to maximize travel efficiency and comfort, while in fol-
lowing mode the system aims to maximize safety in addition
to efficiency and comfort. The two modes are distinguished
by a critical gap sfdetermined by the controller parameters
of free/desired (cruising) speed and the desired gap td.Note
that CFC vehicles operate autonomously, i.e., neighboring CFC
vehicles do not communicate with each other, nor do they
coordinate their behavior when making their control decisions
[4]. It is assumed that the lane-changing decisions of CFC
vehicles are made by human drivers and vehicle steering is
executed by human drivers.
In the remainder of this section, we describe the autonomous
CFC controller formulation of CFC systems and present the
implementation algorithms in microscopic simulations.
A. Autonomous Controller Formulation
The system state xfrom the perspective of a CFC vehicle
is defined by the gap (or distance) siand relative speed Δvi=
vi−1−viwith respect to the arbitrary leader i−1, x=(si,Δvi)T,
where vi−1and videnote the speed of leader and that of the
CFC vehicle respectively, as shown in Fig. 1(a). When follow-
ing an arbitrary leader, the system state can be estimated with
information from in-vehicle sensors, e.g., forward-looking ra-
dar. For the sake of control approach illustration, we assume the
duality problem of state estimation has been solved elsewhere.
Hence, we do not consider noise in the data from the sensors.
Let u=uidenote the controlled acceleration of vehicle i.At
each sampling time, the receding horizon CFC controller solves
a finite horizon optimal control problem at current time tkwith
initial state x(tk)as follows:
min
u
J(x,u)=min
u
tk+TP
tk
L(x(τ),u(τ)) dτ (1)
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 3
Fig. 1. Definition of state variable xand control variable u.
subject to the system dynamics equation:
d
dt x=d
dt si
Δvi=Δvi
ui−1−ui=f(x,u)(2)
and admissible constraints of control and state [4]:
u(t)∈Uand x(t)∈X,∀t≥0.(3)
In Eq. (1), Jdenotes the cost functional to be minimized. L
denotes the running cost and Tpdenotes the prediction hori-
zon. ui−1denotes the acceleration of the predecessor. For an
arbitrary leader, the constant speed heuristics is used to predict
the behavior of the predecessor in the prediction horizon, i.e.,
ui−1=0. The feedback nature of the receding horizon process
can correct the mismatch between the prediction and the real
dynamic behavior of the predecessor [4].
Note that although the linear system model (2) may not
adequately describe the vehicle dynamics near physical limits,
e.g., tire force saturation due to emergency maneuvers, we are
primarily interested in normal vehicle operations in this work
where the nonlinear vehicle dynamics can be omitted.
The running cost function is specified as:
L=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
c1Δv2
iΘ(−Δvi)
si
safety
+c2(sd−si)2
efficiency
+u2
i
2
comfort
,if si≤sf
c3(v0−vi)2
efficiency
+1
2u2
i
comfort
,if si>s
f.
(4)
sfis the gap threshold distinguishing cruising mode (si>s
f)
from following mode (si≤sf). The gap threshold is deter-
mined by a user-defined desired time gap tdat following mode,
the desired speed v0, and the minimum gap between vehicles at
standstill conditions s0:
sf=v0td+s0.(5)
Θis the Heaviside function [4], ensuing that the safety cost
only occurs when approaching the preceding vehicle. sdis the
desired gap, which is determined by the current speed and a
desired time gap td:
sd=vi(t)td+s0.(6)
The gap policy of (6) follows the constant time gap policy
[2]. The framework allows implementation of variable time gap
policies [4]. The running cost formulation (4) is refined based
on the ACC controller in [4], and allows smoother transition
between cruising mode and following mode.
The running cost function (4) contains multiple criteria of
safety, efficiency and comfort. Applying Pontryagin’s Principle
can express the optimal acceleration as the marginal cost of
the relative speed [4]. An efficient numerical scheme based
on Pontryagin’s Principle is used to solve the optimal control
problem [28]. For details on the performance and tuning of the
controller, we refer to [4], [29].
B. Decentralized Algorithm
When simulating a large scale system with many CFC vehi-
cles as subsystems, the dynamics of neighboring subsystems
are decoupled, but the cost function (4) includes coupling
terms of neighboring vehicles in the form of relative position
and speed with respect to the preceding vehicle. This fea-
ture allows straightforward decentralized implementation of
the CFC control algorithm in microscopic simulation models.
At each time instant tk, each subsystem/vehicle isolves its
local autonomous optimal control problem of Eqs. (1) and (4),
synchronously, subject to system dynamics equation (2), state
and control constraints (3), and initial conditions. The behav-
ior of its predecessor is predicted using the constant speed
heuristics, assuming that the predecessor maintain the current
speed in the prediction horizon, i.e., ui−1,[tk,tk+Tp)=0. The
iterative numerical solution algorithm based on Pontryagin’s
Minimum Principle (iPMP) [28] is used to compute the opti-
mal control/acceleration trajectory ui,[tk,tk+TP). Only the first
sample of the acceleration trajectory ui,[tk,tk+1)is implemented
to update the system state. The optimal accelerations are
re-calculated after each control cycle in a receding horizon
manner, using newest information regarding the system state
available from on-board sensors.
III. COOPERATIVE CONTROLLER AND
DISTRIBUTED ALGORITHM
Cooperative CFC (C-CFC) controllers have been designed
in [9] and a centralized optimization scheme is implemented
for platoon control. Although it shows promising results in
controlling platoons with 10 controlled followers, the central-
ized communication and control is practically unfeasible due to
computation and communication requirements [30], [31]. This
section synthesizes the cooperative controllers in [9] to a more
general formulation and proposes a more efficient distributed
algorithm for cooperative platoon.
A. Cooperative Controller Formulation
The C-CFC controller considered here is assumed to be
equipped with both a forward-looking sensor detecting the
gap and relative speed with respect to its predecessor and a
backward-looking sensor detecting the gap and relative speed
of its follower, as depicted in Fig. 1(b). Furthermore, each
C-CFC vehicle is equipped with a V2V communication unit
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
4IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
Fig. 2. Distributed communication and control scheme in a cooperative platoon.
to receive the state and control information from the down-
stream neighboring C-CFC vehicle (when applicable) and to
transmit its own state and control information to the upstream
neighboring C-CFC vehicle (when applicable), as shown in
Fig. 2. The V2V communication is assumed to be perfect and
the communication delay is negligible compared to the control
cycle of C-CFC controllers. Similar to the design of CFC
systems, lane change decisions of C-CFC vehicles are made and
lane change maneuvers are executed by human drivers through
steering wheels.
To determine the optimal behavior, a C-CFC vehicle predicts
the behavior of its predecessor and its follower, based on the
information from on-board sensors when direct neighbors are
human-driven vehicles and from V2V communication when
one or two of its direct neighbors are C-CFC vehicles. The
cooperative controller determines its acceleration to minimize
its own cost depending on the situation in front as well as the
cost of its follower i+1 depending on the situation behind.
To formulate the cooperative controller, we define the system
state from the C-CFC vehicle as: x=(si,Δvi,s
i+1,Δvi+1 )T.
The system dynamics equation is as follows:
d
dt x=⎛
⎜
⎜
⎝
Δvi
ui−1−ui
Δvi+1
ui−ui+1
⎞
⎟
⎟
⎠=f(x,u)(7)
where u=(ui)Tis the controlled acceleration. ui−1and ui+1
denote the acceleration of the leader and follower of vehicle i
respectively.
To represent the situations in front and behind the controlled
vehicle i, a joint cost function needs to be specified. The most
straightforward formulation of the joint cost function is simply
the sum of the cost of the two vehicles, which gives the running
cost function as:
L=
i+1
n=i
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
c1
sn
Δv2
n·Θ(−Δvn)
safety
+c2(sd,n −sn)2
efficiency
+1
2u2
n
comfort
⎫
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎭
.
(8)
Equation (8) shows that the cooperative controller aims to
minimize the joint safety, efficiency and comfort cost for itself
and its follower. The cooperation only occurs in following
mode. In cruising mode, the C-CFC controller functions as the
CFC controller in the cruising mode.
The derivation of the optimal acceleration for the C-CFC
controller is similar to the CFC controller using Pontryagin’s
Principle. Its optimal acceleration is determined by the mar-
ginal cost of its own relative speed and the marginal cost
of its follower’s relative speed [9]. The numerical scheme
proposed in [28] can solve the cooperative control problem
efficiently.
Note that the cooperative vehicle assumes that its follower
is minimizing some cost function. While this is the case when
vehicle i+1 is a controlled vehicle as vehicle i,itmayde-
viate from the actual behavior of a human-driven vehicle. In
this case, a mismatch between the predicted behavior and the
actual behavior of vehicle i+1 prevails. Due to the feedback
nature of the receding horizon framework and the human-like
behavior of controlled vehicle [32], the controller functions
well irrespective of the actual behavior specification of the
follower i+1 [29]. String stability criterion for C-CFC systems
has been derived analytically in [29, Chapter 5] and simulation
experiments in [9] have demonstrated string stability of the
C-CFC systems.
B. Distributed Algorithm
When controlling a large scale system with many C-CFC
vehicles, it is practically unfeasible to use a centralized im-
plementation of the cooperative algorithm minimizing the per-
formance of the whole system due to the computation and
communication requirements [30], [31]. Therefore, the C-CFC
algorithm is implemented in a distributed fashion, where each
vehicle as a subsystem solves a local cooperative optimal con-
trol problem synchronously, taking into account the predicted
dynamics of its direct predecessor and follower.
C-CFC vehicle iimplements the algorithm as follows:
1) Before optimization starts at each time instant tk,a
C-CFC vehicle ireceives gap and relative speed with
respect to the leader, si(tk)and Δvi(tk), from its
forward-looking sensor. It also receives gap and rela-
tive speed with respect to the follower, si+1(tk)and
Δvi+1(tk), from its backward-looking sensor. If the
predecessor is a cooperative vehicle, vehicle ireceives
predicted control/acceleration trajectory of the prede-
cessor ˆ
ui−1,[tk−1,tk−1+TP)obtained from the last time
instant tk−1via V2V communication. Vehicle iuses the
predicted acceleration trajectory of vehicle i−1start-
ing from the previous time step tk−1as its assumed
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 5
acceleration trajectory starting from current time tkfor
predecessor i−1:
ˆ
ui−1,[tk,tk+TP)=ui−1,[tk−1,tk−1+TP).(9)
Likewise, vehicle itransmits its predicted control trajec-
tory ui,[tk−1,tk−1+TP)obtained from the last time instant
tk−1if its follower i+1 is a cooperative vehicle before
optimization starts to facilitate the decision-making of
vehicle i+1.
2) If vehicle i−1 is a C-CFC vehicle, vehicle ipredicts
the speeds and positions of vehicle i−1 with the as-
sumed acceleration trajectory (9) and initial conditions
of xi−1(tk). If vehicle i−1 is a human-driven vehicle,
vehicle ipredicts the speeds and positions of vehicle i−1
with constant speed heuristics, i.e., ui−1,[tk,tk+Tp)=0.
3) Each C-CFC vehicle isolves its local cooperative optimal
control problem of Eqs. (1), (7), and (8) subject to con-
straints (3) using the efficient solution algorithm in [4],
and determines its own optimal trajectory ui,[tk,tk+TP).
4) The optimal acceleration of each vehicle ui,[tk,tk+1 )is
discretized and the first sample is implemented to update
speeds and positions.
5) The aforementioned procedure repeats at discrete time
instant tk+1, whereas the cooperative vehicles update the
assumed control trajectory with:
ˆ
ui−1,[tk+1,tk+1 +Tp)=ui−1,[tk,tk+Tp)
ˆ
ui,[tk+1,tk+1 +Tp)=ui,[tk,tk+Tp).(10)
Note that in this way, the optimization and communi-
cation are limited to vehicles directly following each
other [30], [31], [33], as depicted in a specific platoon
formation in Fig. 2.
For cooperative vehicles in microscopic simulations, the
accelerations are computed by the iPMP algorithm in a re-
ceding horizon way and a communication channel needs to
be modeled through which the current gap, relative speed and
the predicted acceleration trajectory are transmitted to their
cooperative peers. For the sake of evaluation the feasibility and
performance of the proposed algorithm, we assume the sensors
and V2V communication are perfect.
Here we complete the description on implementation of the
algorithms for CFC and C-CFC controllers in traffic simulator.
In the sequel, we will present the simulation experimental set-
up for assessing the impact of CFC and C-CFC controllers on
traffic flow characteristics near a bottleneck, followed by dis-
cussions on simulation results. Since our focus of the simulation
experiments is on the macroscopic traffic flow impact of au-
tonomous and cooperative vehicles at normal operating condi-
tions, performance verification of the CFC and C-CFC systems
at emergency situations are beyond the scope of this study.
IV. ASSESSMENT METHODS AND EXPERIMENTAL SETUP
To test the workings of the proposed algorithms in a dynamic
environment and investigate their impacts on traffic flow char-
acteristics, the algorithms are implemented in a microscopic
traffic simulator. Extensive traffic simulation experiments are
carried out to evaluate the impact of the proposed algorithms
on collective traffic dynamics under a bottleneck, with a focus
on the formulation and propagation of moving jams.
A. Bottleneck and Necessary Modeling Aspects
In real traffic, jams are caused by bottlenecks [20]. A bottle-
neck is defined as a local reduction of the road capacity [20],
which can be permanent or temporary. Permanent bottlenecks
are usually caused by heterogeneity in road infrastructure, such
as on-ramps and off-ramps, weaving areas, curves, and uphill
and downhill gradients. Temporary bottlenecks are usually
caused by accidents, roadworks or temporary change in traffic
regulations such as speed limits. We choose the second type of
bottleneck induced by temporal changes of speed limits in this
study, since the focus of the study is on longitudinal driving
control and the car-following maneuvers determines the traffic
flow dynamics at this type of bottleneck to a great deal.
When a bottleneck is activated, traffic breaks down at the
bottleneck and congested traffic forms upstream of the bot-
tleneck. Different jam patterns at freeway bottlenecks have
been reported and defined in literature [20], which can be
in general categorized into two types: one with an upstream
moving downstream front (jam head) and upstream front (jam
tail), which is often called stop-and-go wave or moving jam,and
one with a fixed downstream front at the bottleneck location
[20]. The first type of jam is the focus of this study, since it
is highly related to decelerating and accelerating behaviors of
vehicles.
The jam head of a stop-and-go wave propagates against the
driving direction with a characteristic velocity in the order of
−10 to −20 km/h, while the propagation velocity of the jam
tail depends on the traffic states upstream of and in the jam
[20], [34]–[37]. One important feature of traffic flow operations
at bottlenecks is the so-called capacity drop phenomenon. The
capacity drop refers to the phenomenon that the maximum
outflow observed downstream of a jam (referred to as queue
discharge flow) is usually smaller than the maximum flow
observed before traffic breaks down to congestion (referred
to as free flow capacity) [20], [35], [38]. The discrepancy
is reported to be around 10–30% [35], [38]. Although the
discussions on the capacity drop phenomenon have last for
decades [36], [39]–[41], one plausible microscopic explanation
for the capacity drop is that drivers tend to keep a larger gap in
the transition from an equilibrium state with low speeds to an
equilibrium state with high speeds and keep a smaller gap vice
versa, i.e., the microscopic hysteresis [42], [43].
The aforementioned traffic flow properties, in particular the
backward propagating moving jam and capacity drop phenom-
ena, should be resembled by the traffic simulation model. Fur-
thermore, multiple driver-vehicle classes, e.g., human drivers,
CFC and C-CFC systems, should be distinguished in the model.
In the following, we describe the chosen simulation model that
is able to address these modeling issues.
B. Simulation Model and Network Settings
We choose a simulation model called MOTUS for the impact
study. MOTUS is an open-source microscopic traffic simulation
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
6IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
TAB L E I
EXPERIMENTAL SCENARIOS FOR IMPACT
STUDY OF CFC/C-CFC SYSTEMS
package that is developed in Java [44]. Among many other fea-
tures, the MOTUS model uses an improved Intelligent Driver
Model (IDM) as the car-following module and a lane change
model with relaxation and synchronization [44]. It generates
realistic traffic wave patterns and free flow capacity, and resem-
bles better multilane traffic at a macroscopic level regarding the
amount of traffic volumeper lane, the traffic speeds across lanes
and the onset of congestion at bottlenecks. For details of the
models, we refer to [44].
In MOTUS, the traffic system is represented by a set of
interacting objects, including network, vehicle with a driver and
on-board unit, and roadside units. The drivers are represented
by the lane-changing model and the car-following model. In
implementation, we create separate vehicle and driver classes
for CFC vehicles and C-CFC vehicles respectively. The CFC
and C-CFC algorithms are implemented in the driver classes,
replacing the default car-following model and gives acceler-
ations inputs to the vehicles every simulation time step. We
remark that the proposed decentralized CFC and the distributed
C-CFC algorithms are not limited to the coupling with MOTUS.
They can be implemented in any microscopic traffic simulator
with open interfaces.
Simulation is set up in analogy to a long freeway stretch
where stop-and-go wave is the major type of jams in the
Netherlands. The road network is a two-lane freeway of 14 km,
with a demand of 1900 veh/h on both lanes. Loop detectors
are placed every 250 meters on each lane along the freeway,
collecting flow and time mean speed every 30 seconds.
A bottleneck is created by posting low speed limits on
Variable Speed Limits (VSL) gantries on parts of the freeway.
The speed limits are activated for 2 minutes, with speed values
of 80 km/h, 60 km/h and 40 km/h displayed at the location of
11 km, 11.5 km and 12 km respectively.
Parameters for MOTUS are chosen based on the face valida-
tion on the resultant capacity drop and moving jam propagation
characteristics, as we will show in Section V-A.
C. Experimental Scenarios
The variables to be tested for the impact study are the
controller type (CFC or C-CFC) and the penetration rate of con-
trolled vehicles in traffic (5%, 10%, 50%, 100%). Together with
the reference scenario with 100% human drivers, this amounts
to 9 simulation scenarios as shown in Table I. 10 simulation
runs are conducted for each scenario.
As discussed in [29], the desired time gap settings for CFC
and C-CFC systems impact the road capacity and traffic flow
stability. In this study, we choose the same desired time setting
as human drivers in MOTUS with td=1.3s.Thisleadstothe
same equilibrium flow-density relation and theoretical capacity
at the macroscopic level. Hence, the potential changes in dy-
namic traffic operations depend predominantly on differences
of the accelerating and decelerating characteristics of CFC/C-
CFC vehicles compared to human-driven vehicles. This allows
us to investigate the potentials of advanced model predictive
control strategies of CFC/C-CFC vehicles in improving traffic
operations without setting smaller time gaps.
D. Assessment Indicators
For each simulation run, the following indicators are
calculated:
• Total time spent (TTS) in network. TTS is calculated from
the vehicle trajectories of the simulation as:
TTS =
Nveh
n=1
tsn(11)
where tsndenotes the time spent in the network for
vehicle nand Nveh denotes the total number of vehicles
generated in the network during the simulation period.
• Average outflow: Qout. This is measured by the most
downstream detector on the freeway stretch and aver-
aged in the simulation period. For homogeneous freeway
stretch, this gives an indication on the effective capacity
at the bottleneck.
• Jam area: Ajam. Jam area is calculated with
Ajam =
Ksim
i=1
Ljam,i ·dT (12)
where dT is the detector aggregation time, which is 30 s
in this case and Ksim is the number of aggregation time
intervals for the whole simulation period. Ljam,i is the
spatial length of the jam at aggregation interval i,andthe
location of a jam is present is detected by:
Vi,j ≤Vmax (13)
where Vi,j is the detector speed at time interval iand
location j·dX.dX denotes the distance between loop
detectors, which is 250 meters in this case. Vmax is the
speed threshold to distinguish free flow and congested
traffic, which is 50 km/h. Note that when there is no jam
in the network, Ajam =0.
•FlowQjam and speed Vjam of jam area. These are the
average flow and speed of the spatio-temporal jam area
determined by the speed threshold Vmax, which indicate
the traffic state in the jam.
• Downstream jam front velocity Chead. This is measured
with the position of jam head determined by Vmax,which
reflects how fast the resultant travels. To avoid large
estimation errors due to small jam size, we only calculate
Chead for jams that last longer than 5 minutes.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 7
TAB L E I I
INDICATORS FOR DIFFERENT SCENARIOS AVERAGED OVER TEN SIMULATION RUNS FOR EAC H SCENARIO
• Mean absolute speed difference across lanes DVlane for
the network. This gives an indication on the inhomogene-
ity of traffic states across lanes.
For sustainability indicators, we focus on average spatial
fuel consumption rate per vehicle (AFC). To this end, a modal
fuel consumption model is employed, because it captures the
operational characteristics of vehicle engines and uses instan-
taneous vehicle speed and acceleration to calculate (temporal)
fuel consumption rate [45]. All model parameters are available
in [45]. Assuming the specific engine type in [45], this model
estimates instantaneous fuel consumption rate of vehicle n,Ft
n
as a function of vehicle speed vnand acceleration an:
Ftn=3
j=0 bjvj
n+c1vnan+c2vna2
n,if an≥0
3
j=0 bjvj
n+c1vnan,if an<0(14)
where bjand cjare model parameters. For details of the fuel
consumption model, we refer to [45]. The AFC is calculated by
dividing total fuel consumption with the total distance traveled
by all vehicles in the network.
The average values of indicators over all simulation runs are
summarized in Table II.
Apart from the indicators, we also visualize the simulation
results in different scenarios, including the spatial-temporal
contour plots of flow Qand speed V, flow-density scatter plots.
The contour plots depicts the spatio-temporal evolution of ag-
gregate traffic flow and speed, which give insights into the jam
patterns and traffic flow dynamics. In the flow-density plots,
we differentiate the whole freeway into upstream, downstream
and jam regions when a jam prevails, which gives insights
into the differences in the inflow and outflow of a jam area.
Furthermore, to gain insights into the changes at microscopic
level, we plot the average gap and speed relationships in
different scenarios. Particularly, we distinguish the trajectory
data samples into the acceleration state, deceleration state and
equilibrium state. The different states for each vehicle nat time
tare differentiated with an acceleration threshold of 0.01 m/s2
in acceleration:
•ifan>0.01, the vehicle is in acceleration state;
•ifan<−0.01, the vehicle is in deceleration state;
•ifan∈[−0.01,0.01], the vehicle is in equilibrium state.
The trajectory data points are aggregated into the same spatial
and temporal length of the detectors with different states.
Fig. 3. (a) Flow contour and (b) time mean speed contour plots, and (c) flow-
density plots and (d) gap-speed plots in Scenario 1 with 100% human drivers.
V. S IMULATION RESULTS
This section describes the simulation results, with a focus
on the impact of CFC and C-CFC systems on formation and
propagation of moving jam at the bottleneck. First, the traffic
states and jam patterns in the reference case is described, show-
ing the face validity of the simulation model. Then the flow
characteristics with CFC and C-CFC systems are discussed
subsequently.
A. Verification of the Reference Scenario
In this study, a bottleneck is activated by temporarily chang-
ing speed limits on part of the freeway stretch, resulting in a
lower road capacity than the demand. Fig. 3(a) and (b) show the
spatio-temporal evolution of flow and time mean speed per lane
on the simulated freeway collected from loop detectors. As we
can see from the figures, the traffic speed drops from 120 km/h
to about 40 km/h at around 12 km from 15 minutes, due to the
change in speed limits. The speed limits cause vehicles in the
bottleneck area to slow down, increasing the density in the bot-
tleneck area and limiting the outflow from the bottleneck. After
the vehicles move out of the bottleneck, they start to accelerate
back to the free speed, which is around 120 km/h. This leads to a
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
8IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
wave propagating downstream with low flow and high speed in
the flow and speed contour plots. The bottleneck is only active
for two minutes. Directly after the release of the bottleneck,
the desired speeds of vehicles in the bottleneck switch back to
120 km/h. The vehicles in the bottleneck with high density start
to accelerate consequently, leading to a high flow and high speed
state propagate downstream, as shown in Fig. 3(a) and (b).
Traffic flow theorists have shown that the high density state with
high flow is not stable [20], [46]. Indeed, after a while, traffic
breaks down with speeds degrading gradually, which leads to a
persistent moving jam propagating upstream [20], [46].
The average traffic speed and flow in the jam is 11.7 km/h
and 402 veh/h respectively, with the jam head, or the down-
stream jam front, propagating with a characteristic velocity of
−11.8 km/h, as shown in Table II. The traffic state downstream
of the jam area is quite homogeneous, i.e., there are hardly any
variations in the flow and speed, as shown in Fig. 3(a) and (b).
The capacity drop phenomenon is clearly visible in the flow
contour plot of Fig. 3(a) and the flow-density scatter plot of
Fig. 3(c), i.e., outflow from the jam maintain an average value
of 1647 veh/h, which is significantly lower than the average
inflow of 1900 veh/h. The discrepancy between outflow and the
capacity is in accordance with the reported values of around
10–30% [20], [35], [38]. Due to this discrepancy, the size of the
jam increases with the course of time, with the upstream jam
front (jam tail) traveling upstream with a faster speed than that
of the downstream jam front (jam head). This leads to a total
jam size of 41.7 veh·h.
It is commonly accepted that the microscopic explanation of
the capacity drop phenomenon is that drivers keep a larger gap
in accelerating phase compared to decelerating phase, i.e., the
microscopic hysteresis phenomenon [42], [43]. This common
phenomenon is reproduced in our simulation, as depicted by
the average gap and speed scatter plots in the decelerating and
accelerating phase in Fig. 3(d).
B. Impacts of CFC Systems on Flow Characteristics
Compared to the reference case, scenarios 2–5 with differ-
ent penetration rates of CFC systems bear some resemblance
regarding flow characteristics at the bottleneck. The activation
of the bottleneck creates a traffic wave of low flow and high
speed traveling downstream, followed by a wave with high flow
and high speed propagating downstream immediately after the
release of the bottleneck. The bottleneck leads to backward
propagating moving jams in all CFC scenarios, as shown with
one representative simulation run in Fig. 4.
There are several differences that need special attention when
CFC vehicles prevail in the network. We discuss the qualitative
differences with Figs. 4 and 5, and the quantitative differences
with indicators of Table II. We discuss consecutively traffic
efficiency, stability and jam propagation, and sustainability.
1) Traffic Efficiency: CFC systems increase traffic efficiency
and mitigate the capacity drop phenomenon. The average total
time spent (TTS) in the network and jam sizes in scenarios 2–5
are much smaller than in the reference scenario. The TTS and
jam size decrease to 477.4 veh ·h and 24.9 km ·min in scenario 2
from 562.8 veh ·h and 41.7 km ·min in the reference scenario
Fig. 4. Spatio-temporal evolution of flow and speed of CFC with different
penetration rates (Scenarios 2–5) in one simulation run. (a) Flow of scenario 2
with 5% CFC; (b) speed of scenario 2 with 5% CFC; (c) flow of scenario 3 with
10% CFC; (d) speed of scenario 3 with 10% CFC; (e) flow of scenario 4
with 50% CFC; (f) speed of scenario 4 with 50% CFC; (g) flow of scenario 5
with 100% CFC; (h) speed of scenario 5 with 100% CFC.
respectively. The TTS and jam size decrease further to similar
values in scenarios 3 and 4. The TTS and jam size are reduced
to only 443.8 veh ·h and 5.3 km ·min when all vehicles are
controlled by the CFC system.
The outflow from jams in scenarios 2 is higher than that of
the reference scenario, but still lower than the inflow. Hence the
capacity drop and microscopic hysteresis phenomenon remains
in scenario 2, as we can see from Fig. 5(a) and (b). As a result,
the spatial size of the jam increases with the course of time
in scenario 2, as shown in Fig. 4(a) and (b). When the pene-
tration rate increases to 10% and higher, the outflow increases
more or less to the value of the inflow, resulting in moving
jams with more or less constant sizes, as we can see from
Fig. 4(d), (f), and (h). Hence capacity drop is not pronounced in
scenarios 3–5, which is also evidenced by the flow-density plots
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 9
Fig. 5. Flow-density plots for CFC impact study with different penetration
rates (Scenarios 2–5) in one simulation run. (a) Scenario 2 with 5% CFC;
(b) scenario 2 with 5% CFC; (c) scenario 3 with 10% CFC; (d) scenario 3
with 10% CFC; (e) scenario 4 with 50% CFC; (f) scenario 4 with 50% CFC;
(g) scenario 5 with 100% CFC; (h) scenario 5 with 100% CFC.
of Fig. 5(c), (e), and (g) and gap-speed plots of Fig. 5(d), (f),
and (h). The reason for this is that the formulation and pa-
rameter settings for CFC controllers result in a more agile
driving style, i.e., the CFC vehicles accelerate faster towards
the high speed state than human drivers under same conditions
of gaps (s), relative speeds Δvand speeds v, which leads
to smaller headway and hence higher flow in the acceleration
transition. Furthermore, the human-driven vehicles following
CFC vehicles are convicted to the follow-the-leader rule in
mixed traffic scenarios, and hence are dragged by the CFC
vehicles to keep smaller headways than in scenario 1, which
consequently increases the outflow from the jam area.
2) Stability and Jam Propagation: As we can see from
Fig. 4 and Table II, the traffic speed and flow in the jam of
scenario 2 are higher than those in scenario 1. This implies
that the CFC vehicles improve the traffic flow stability of the
jam area, i.e., the traffic does not break down to a speed as low
as the reference case. When the penetration rate increases to
10% or higher, the stabilization effects are more pronounced,
as the average speed in the jam area stays around the bottleneck
speed of 40 km/h. The stability effects can be explained by the
controller design of CFC systems. As we have explained in the
previous work [4], in decelerating transitions, the safety cost
due to approaching the preceding vehicle dominates the CFC
vehicular behavior. Hence CFC vehicles are more sensitive
to the relative speed in the decelerating phase, exhibiting a
more anticipative driving style which stabilizes traffic flow
approaching the jam tail.
Regarding the propagation of the jam head, although the
size and period of the jams are different, they all propagate
in the upstream direction after the start of the bottleneck.
However, unlike the reference case where the jam head prop-
agates upstream with a constant characteristic velocity, the jam
propagation velocity differs with different penetration rates of
equipped vehicles across scenarios, as shown in Fig. 4 and
Table II. In scenario 2, the jam head propagates faster than that
of scenario 1 while in scenario 3–5, the jam heads propagate
slower than in scenario 1. In scenario 5 as shown in Fig. 5(h),
the jam wave first propagates upstream from 17 minutes to
about 25 minutes, then it gradually changes its velocity and
stays at around 9.75 km for 10 minutes and finally propagates
in the reversed direction. After a few minutes the jam dissolves
when propagating in the downstream direction.
It is noteworthy that several waves propagating in the down-
stream direction from the jam head are observed in speed
contour plots in CFC scenarios, e.g., from around 40 minutes
in Fig. 4(b), from around 42 minutes onwards in Fig. 4(d), and
from around 34 minutes in Fig. 4(f). This is quite different
compared to the homogeneous traffic speeds downstream of
the jam area in the reference scenario 1, as shown in Fig. 3(b).
These waves are not sustained and vanish in the free flow region
after propagating downstream for a few minutes. Although
these disturbances do not result in persistent waves, it does raise
some concerns on the stability property at the downstream area
of the jam. Since the CFC vehicles accelerate faster and keep a
smaller gap from the jam area to the downstream free flow area
compared to human-driven vehicles, the human-driven vehicles
in scenario 2 that follow CFC vehicles also accelerate faster
and maintain a smaller gap compared to the normal situations
in the reference case. Although this increases the outflow from
the jam area, it may destabilize traffic flow downstream of the
jam area.
The existence of CFC vehicles in the mixed traffic scenarios
of 2–4 increase the inhomogeneity of traffic states across lanes.
As we can see from Table II, the average speed differences
across lanes in the network are higher in scenarios 2–4 than
those in scenarios 1 and 5. The inhomogeneity of traffic states
across lanes are caused by the intrinsic differences in the car-
following rules between human drivers and CFC vehicles.
3) Sustainability: From sustainability perspectives, the re-
duction of the stop-and-go waves has clear benefits in reduc-
ing fuel consumption, since the accelerating and decelerating
maneuvers and their durations are substantially reduced with
the decreasing size of jams. As we can see from Table II, the
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
10 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
Fig. 6. Spatio-temporal evolution of flow and speed of CCFC with different
penetration rates (Scenarios 6–9) in one simulation run. (a) Flow of scenario 6
with 5% CCFC; (b) speed of scenario 6 with 5% CCFC; (c) flow of scenario 7
with 10% CCFC; (d) speed of scenario 7 with 10% CCFC; (e) flow of
scenario 8 with 50% CCFC; (f) speed of scenario 8 with 50% CCFC; (g) flow of
scenario 9 with 100% CCFC; (h) speed of scenario 9 with 100% CCFC.
average spatial fuel consumption rates are reduced when CFC
vehicles are present in the network, and the benefits increase
with the increase of penetration rate in general.
C. Impacts of C-CFC Systems on Flow Characteristics
Compared to human drivers and CFC systems, C-CFC sys-
tems have clear benefits in improving traffic flow operations and
sustainability at the bottleneck type in this study.
1) Traffic Efficiency: In scenario 6 with 5% C-CFC vehicles,
the average outflow from the jam is 1824 veh/h, which is much
higher than 1647 veh/h in the reference case, but still lower than
the inflow of 1900 veh/h. Hence the capacity drop phenomenon
prevails and spatial jam size increases with the course of time,
as shown in Fig. 6(a) and (b). The jam size is in the same order
as in scenario 2.
Fig. 7. Flow-density plots for CCFC impact study with different penetration
rates (Scenarios 6–8) in one simulation run. (a) Scenario 6 with 5% CFC;
(b) scenario 7 with 10% CFC; (c) scenario 8 with 50% CFC; (d) scenario 9
with 100% CFC.
When the penetration rate of C-CFC systems increases to
10% and 50%, the differences between the C-CFC scenarios
and their CFC counterparts become apparent. The average
outflow is much higher and the TTS and jam size in scenario 7
are much smaller than those in scenarios 6 and 3. The indi-
cators in scenario 7 with 10% C-CFC systems are even better
compared scenario 5 with 100% CFC vehicles. As we have
shown in previous work [9], C-CFC systems generate more
anticipative and responsive accelerating behavior compared to
CFC systems, which account for the substantial improvement
in traffic efficiency.
In scenarios 8 and 9, after the release of bottleneck, the
outflow downstream of the jam area remains at very high
values, and the resultant TTS and jam size decrease with the
increase of penetration rate of C-CFC vehicles.
The improvement in traffic efficiency with CFC systems are
clearly seen in the flow-density plots. As we can see in Fig. 7,
the number of data points in the jam area decreases with the
increase of C-CFC penetration rate, and the data points are less
scattered with the increase of C-CFC penetrate rate.
2) Stability and Propagation of Jams: The cooperative con-
trol strategy of C-CFC systems leads to smoother decelerating
behavior and improves stability of flow approaching the jam.
As we can see from Table II, the traffic speed and flow in
the jam areas are higher than those in the reference scenario 1
and those with their CFC counterparts. In scenarios 7–9, aver-
age traffic speeds in the jam are even higher than the bottle-
neck speed of 40 km/h. This is explained by the controller
characteristics, i.e., the smoother behavior of C-CFC controllers
decreases the overshooting effects in the decelerating transition
[9] and vehicles in scenarios 7–9 do not decelerate further to
speeds lower than 40 km/h.
Although the bottleneck results in a persistent stop-and-
to wave in scenario 6, with only 10% of C-CFC vehicles
in the network in scenario 7, the stop-and-go wave dissolves
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 11
itself after propagating upstream a few minutes, as we can see
from Fig. 6(c) and (d). The stop-and-go waves also dissolve
themselves in scenarios 8 and 9, as shown in Fig. 6(e)–(h).
Although the jam head speed still varies across different
scenarios with different C-CFC vehicle penetration rates, it is
clear that for all scenarios where jams longer than 5 minutes are
observed, the jam head in C-CFC scenarios propagates faster
compared to the reference case and to their CFC counterparts.
The propagation speed also increases with the penetration rate
of C-CFC systems. This can be explained by the distributed
cooperative algorithm that V2V communication enables, i.e.,
the current state and the predicted acceleration trajectory of
C-CFC vehicles are transmitted to their C-CFC follower when
applicable and are taken into account by the C-CFC follower in
determining cooperative optimal accelerations. This allows the
C-CFC vehicles to react earlier to the downstream disturbances
compared to uncontrolled vehicles and CFC vehicles.
Similar to scenarios with CFC systems, we observe several
forward propagating waves originating from the jam head char-
acterized with relatively high speeds (between 60 and 80 km/h)
and very high flow (around 2000 veh/h), e.g., at about
18 minutes, 24 minutes and 37 minutes in Fig. 6(c) and (d).
Similar to the CFC scenarios, the mixtures of C-CFC and
human-driven vehicles in the network increase the inhomo-
geneity in the traffic states across lanes compared to scenario 1.
The average speed difference across lanes is much larger in
scenarios 6 and 7 than in scenarios 1, 8, and 9.
3) Sustainability: The improvement in sustainability with
C-CFC systems is obvious compared to human drivers, as
shown in Table II. In all scenarios with C-CFC systems, the
average spatial fuel consumption rates are lower compared to
the reference scenario 1. Even compared to CFC system, the
benefits are still clear. While the average fuel consumption rate
in scenario 6 remains at a similar level compared to scenario 2,
the average spatial fuel consumption rates with C-CFC systems
in scenarios 7–9 are considerably lower than their CFC coun-
terparts in scenarios 3–5, as a result of the reduced jam size.
This suggests improvement in sustainability of when C-CFC
vehicles travel in networks.
D. Discussion on Changed Flow Characteristics
The impact study reveals some new insights into traffic flow
characteristics with CFC and C-CFC systems. In this subsec-
tion, we summarize and discuss the changes in flow dynamics
at the bottleneck.
1) Traffic Downstream of Jam Area: Downstream of the jam
area, vehicles are in acceleration transition from low speed
state to high speed state. Our simulation shows that under
the designed parameter setting, CFC systems lead to more
efficient flow moving out of jam and reduce the capacity drop.
The microscopic explanation of this change is the responsive
behavior of CFC systems, i.e., CFC vehicles recovers the high
speed faster than human drivers, and thus they follow with a
smaller gap in the accelerating phase. However, this is achieved
at the expenses of compromising stability, since decentralized
CFC vehicles have limited knowledge of their predecessor
behavior and make simple assumptions in the state prediction,
i.e., constant speed heuristics for predecessors. This has a
potential risk for triggering new jams in the downstream area
of the jam with CFC systems.
When employing the cooperative control strategy, C-CFC
vehicles have better knowledge of the predecessor behavior
when they are following their C-CFC peer, and hence can
predict the dynamics of the predecessor more accurately. As
a result, they are able to react earlier to the accelerating stimuli
while at the same time preventing the overshooting in the
transition from low speed state to high speed state [29]. This
leads to smaller headways in the accelerating phase, but also
improves traffic stability in the downstream area of a jam.
2) Traffic Upstream of Jam Area: Stability/instability of flow
approaching the jam tail is an important feature in the formation
of jams. The stability is determined by two counteracting
processes: the retarded adaptation to the low speed and the
ability to anticipate downstream traffic [38]. For the human-
driven vehicular flow, the retarded adaptation outweighs the
anticipation, and hence the temporary speed drop leads to
formation of jam.
The stability of traffic flow approaching the jam tail is
improved with CFC vehicles in the network. This is explained
by the controller formulation: when CFC vehicles predict costs
under decelerating disturbances, the weight on safety cost
increases with a decreasing gap in Eq. (4). Hence the CFC
vehicles react more to the relative speed with respect to the
preceding vehicle. As the relative speed is a simple form of
anticipation for the future gap [20], [32], this implies that CFC
vehicles exhibits an anticipative drivingstyle in the decelerating
phase. Compared to CFC systems, C-CFC systems based on
the cooperative control strategy lead to more anticipative and
smoother decelerating behavior by maneuvering together as a
platoon [9], and hence further improve the stability of traffic
approaching the jam tail compared to CFC systems.
3) Propagation of Jam: For stop-and-go waves in human-
driven vehicular flow, the jam head has a characteristics velocity
[20]. The jam head velocity changes in scenarios with different
penetration rates of CFC systems in traffic. At a low penetration
rate of 5%, the jam heads travels faster, while at scenarios with
10% or more CFC vehicles in the network, the jam heads travel
slower compared to the reference case. According to kinematic
wave theory [34], the jam head velocity is determined by the
traffic state in the jam and traffic state downstream of the jam,
both influenced by the specific compositions of traffic (pene-
tration rates and locations of CFC vehicles) in the respective
areas. This makes the jam head velocity less characteristic with
CFC/C-CFC systems.
Although the jam head velocity also varies with different
penetration rates of C-CFC systems, it is quite clear that the
jam head travels much faster when C-CFC systems exist in the
network due to V2V communication.
4) Implications for Dynamic Traffic Management: The
changes in flow characteristics have implications for dynamic
traffic management. Under the same strength of a bottleneck,
the CFC and C-CFC systems may stabilize the upstream traffic
approaching the bottleneck that reduces the probability of traf-
fic break down, which consequently lowers the necessity for the
traffic controller to intervene. Even if the jam prevails, the more
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
12 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
efficient outflow due to the presence of CFC/C-CFC systems
reduces the size of the jam, which is also favorable for traffic
controllers since this implies less control efforts.
However, possible difficulties are expected when controlling
traffic flow with CFC/C-CFC systems. Firstly, the resultant
jam state is difficult to predict due to the inhomogeneous
distribution of controlled vehicles in the network. Furthermore,
CFC systems may destabilize traffic flow in the accelerating
transition, and hence increase the risk of triggering new jams
downstream of the considered jam.
VI. CONCLUSION
In this study, we tested the CFC and C-CFC algorithms in
multilane traffic scenarios and examined the impact of CFC
and C-CFC systems on traffic flow operations. Decentralized
algorithms and distributed algorithms are proposed and im-
plemented for CFC and C-CFC controllers in the microscopic
simulator respectively. The CFC and C-CFC algorithms have
been successfully implemented on a large scale system with
more than 500 controlled vehicles as subsystems. The proposed
algorithms work well under discontinuities in state variables
(i.e., gap and relative speed with respect to the preceding
vehicle) caused by lane-changing maneuvers and dynamically
changing parameters, e.g., free/desired speeds due to variable
speed limits. In principle, the decentralized CFC and distributed
C-CFC algorithms can be implemented in any microscopic
simulation model.
Simulation results provide insights into impacts of CFC and
C-CFC systems on traffic flow characteristics. CFC systems
mitigate the capacity drop phenomenon and improve the stabil-
ity of traffic flow upstream of the jam area. The jam propagation
speed changes with different penetration rates of CFC vehicles
in the network, and the jam propagation direction is even
reversed in scenarios with high penetration rates, resulting in
a new phenomenon which is not observed in human-driven
vehicular flow. CFC systems may destabilize traffic down-
stream of the jam area due to the closer following distance in
the transition from low speed state to high speed state. Fuel
consumption is reduced with CFC systems in traffic compared
to the reference scenario with all human-driven vehicles.
The C-CFC systems employing the cooperative control strat-
egy are more predictive and anticipative, since the predicted
acceleration trajectory of the cooperative predecessor is taken
into account in the state prediction of the cooperative follower.
These characteristics improve the stability at both jam tail and
jam head, while at the same time increasing the outflow in the
accelerating phase. Under the bottleneck created in this study,
the disturbance caused by temporarily reduced speed limits is
damped out and hence does not evolve into persistent waves
with only 10% C-CFC vehicles in traffic. The fact that C-CFC
vehicles predict the future of the predecessor behavior and take
into account the expected behavior of the follower has clear
benefits in the bottleneck. C-CFC systems stabilize traffic flow
and increase the effective capacity of the bottleneck compared
to human drivers and CFC systems. One noteworthy flow
property is that C-CFC systems result in faster stop-and-go
waves propagating upstream due to V2V communications.
At very low penetration rates of CFC and C-CFC vehicles in
traffic, e.g., less than 5%, human drivers still dominate the traf-
fic flow characteristics. Hence the flow characteristics remain
qualitatively the same, i.e. capacity drop and jam propagation,
as the reference case with 100% human drivers.
Note that different types and strengths of bottlenecks may
result in jam types and flow patterns other than the stop-and-go
waves discussed in this study. Hence, it remains an interesting
research question how the proposed decentralized CFC and
distributed C-CFC systems influence the characteristics of other
jam patterns.
Based on the impact study results, it can be concluded
that the CFC and C-CFC system changes flow characteristics
substantially, and a roadside controller is likely to be necessary
to resolve stop-and-go waves at low penetration rates when
human-driven vehicles dominate the flow operations.
Future research is directed to the robust design of the au-
tonomous and cooperative intelligent vehicle controllers in
more practical situations where noises and delays prevail in the
control loop. Another future research direction is to examine the
impact of the proposed systems in active bottlenecks with road
geometric inhomogeneities, such as on- and off-ramps. The
proposed control algorithms only regulate longitudinal motion
of controlled vehicles. Extension of the control algorithms by
regulating vehicle steering and orientations in the lateral motion
remains an interesting topic in the future [47].
REFERENCES
[1] P. Varaiya and S. E. Shladover, “Sketch of an IVHS systems architecture,”
in Proc. IEEE Veh. Navig. Inf. Syst. Conf., 1991, vol. 2, pp. 909–922.
[2] J. VanderWerf, S. E. Shladover, N. Kourjanskaia, M. Miller, and
H. Krishnan, “Modeling effects of driver control assistance systems on
traffic,” Transp. Res. Rec., vol. 1748, pp. 167–174, 2001.
[3] G. N. Bifulco, L. Pariota, F. Simonelli, and R. D. Pace, “Development
and testing of a fully adaptive cruise control system,” Transp. Res. C,
Emerging Technol., vol. 29, pp. 156–170, Apr. 2013.
[4] M. Wang, W. Daamen, S. P. Hoogendoorn, and B. van Arem, “Rolling
horizon control framework for driver assistance systems. Part I: Math-
ematical formulation and non-cooperative systems,” Transp. Res. C,
Emerging Technol., vol. 40, pp. 271–289, Mar. 2014.
[5] S. Tsugawa, S. Kato, T. Matsui, H. Naganawa, and H. Fujii, “An architec-
ture for cooperative driving of automated vehicles,” in Proc. IEEE Conf.
Intell. Transp. Syst., 2000, pp. 422–427.
[6] B. van Arem, C. J. G. van Driel, and R. Visser, “The impact of cooperative
adaptive cruise control on traffic-flow characteristics,” IEEE Trans. Intell.
Transp. Syst., vol. 7, no. 4, pp. 429–436, Dec. 2006.
[7] S. E. Shladover, D. Su, and X.-Y. Lu, “Impacts of cooperative adaptive
cruise control on freeway traffic flow,” Transp. Res. Rec., vol. 2324,
pp. 63–70, 2012.
[8] J. Monteil, R. Billot, J. Sau, and N.-E. El Faouzi, “Linear and weakly
nonlinear stability analyses of cooperative car-following models,” IEEE
Trans. Intell. Transp. Syst., vol. 15, no. 5, pp. 2001–2013, Oct. 2014.
[9] M. Wang, W. Daamen, S. P. Hoogendoorn, and B. van Arem, “Rolling
horizon control framework for driver assistance systems. Part II: Coopera-
tive sensing and cooperative control,” Transp. Res. C, Emerging Technol.,
vol. 40, pp. 290–311, Mar. 2014.
[10] P. A. Ioannou and C. C. Chien, “Autonomous intelligent cruise control,”
IEEE Trans. Veh. Technol., vol. 42, no. 4, pp. 657–672, Nov. 1993.
[11] S. Darbha and K. R. Rajagopal, “Intelligent cruise control systems and
traffic flow stability,” Transp. Res. C, Emerging Technol., vol. 7, no. 6,
pp. 329–352, Dec. 1999.
[12] R. Rajamani and S. E. Shladover, “An experimental comparative study of
autonomous and co-operative vehicle-follower control systems,” Transp.
Res. C, Emerging Technol., vol. 9, no. 1, pp. 15–31, Feb. 2001.
[13] J. Wang and R. Rajamani, “Should adaptive cruise-control systems be
designed to maintain a constant time gap between vehicles?” IEEE Trans.
Veh. Technol., vol. 53, no. 5, pp. 1480–1490, Sep. 2004.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
WANG et al.: COOPERATIVE CFC: DISTRIBUTED ALGORITHM AND IMPACT ON MOVING JAM FEATURES 13
[14] J. Ploeg, N. van de Wouw, and H. Nijmeijer, “Lpstring stability of cas-
caded systems: Application to vehicle platooning,” IEEE Trans. Control
Syst. Technol., vol. 22, no. 2, pp. 786–793, Mar. 2014.
[15] I. R. Wilmink, G. A. Klunder, and B. van Arem, “Traffic flow effects of
Integrated Full-Range Speed Assistance (IRSA),” in Proc. IEEE Intell.
Veh. Symp., 2007, pp. 1204–1210.
[16] D. Godbole, K. N. , R. Sengupta, and M. Zandonadi, “Breaking the
highway capacity barrier: Adaptive cruise control-based concept,” Transp.
Res. Rec., vol. 1679, pp. 148–157, 1999.
[17] K. Hasebe, A. Nakayama, and Y. Sugiyama, “Dynamical model of a co-
operative driving system for freeway traffic,” Phys. Rev. E, vol. 68, no. 2,
2003, Art. ID 026102.
[18] J. I. Ge and G. Orosz. “Dynamics of connected vehicle systems with
delayed acceleration feedback,” Transp. Res. C, Emerging Technol.,
vol. 46, pp. 46–64, Sep. 2014.
[19] A. Kesting, M. Treiber, M. Schonhof, and D. Helbing, “Adaptive cruise
control design for active congestion avoidance,” Transp. Res. C, Emerging
Technol., vol. 16, no. 6, pp. 668–683, Dec. 2008.
[20] M. Treiber and A. Kesting, Traffic Flow Dynamics—Data, Models and
Simulation. New York, NY, USA: Springer-Verlag, 2013.
[21] J. A. Michon, Generic Intelligent Driver Support. New York, NY, USA:
Taylor & Francis, 1993.
[22] R. Mller and G. Nöcker, “Intelligent cruise control with fuzzy logic,” in
Proc. IEEE Intell. Veh. Symp., Detroit, MI, USA, 1992, pp. 173–178.
[23] A. Shaout and M. Jarrah, “Cruise control technology review,” Comput.
Electr. Eng., vol. 23, no. 4, pp. 259–271, Jul. 1997.
[24] K. Chu, “Decentralized control of high-speed vehicular strings,” Transp.
Sci., vol. 8, no. 4, pp. 361–384, Nov. 1974.
[25] J. Mårtensson et al., “The development of a cooperative heavy-duty vehi-
cle for the GCDC 2011: Team scoop,” IEEE Trans. Intell. Transp. Syst.,
vol. 13, no. 3, pp. 1033–1049, Sep. 2012.
[26] S. Li, Z. Jia, K. Li, and B. Cheng, “Fast online computation of a model
predictive controller and its application to fuel economy-oriented adap-
tive cruise control,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 3,
pp. 1199–1209, Jun. 2014.
[27] M. Kamal, J. I. Imura, T. Hayakawa, A. Ohata, and K. Aihara. “Smart
driving of a vehicle using model predictive control for improving traffic
flow,” IEEE Trans. Intell. Transp. Syst., vol. 15, no. 2, pp. 878–888,
Apr. 2014.
[28] S. P. Hoogendoorn, R. G. Hoogendoorn, M. Wang, and W. Daamen,
“Modeling driver, driver support, and cooperative systems with dynamic
optimal control,” Transp. Res. Rec., vol. 2316, pp. 20–30, 2012.
[29] M. Wang, “Generic model predictive control framework for advanced
driver assistance systems,” Ph.D. dissertation, Dept. Transp. Plan., Delft
Univ. Technol., Delft, The Netherlands, 2014.
[30] W. B. Dunbar and R. M. Murray, “Distributed receding horizon control
for multi-vehicle formation stabilization,” Automatica, vol. 42, no. 4,
pp. 549–558, Apr. 2006.
[31] R. Scattolini, “Architectures for distributed and hierarchical model predic-
tive control—A review,” J. Process Control, vol. 19, no. 5, pp. 723–731,
May 2009.
[32] M. Wang, M. Treiber, W. Daamen, S. P. Hoogendoorn, and B. van Arem,
“Modelling supported driving as an optimal control cycle: Framework
and model characteristics,” Transp. Res. C, Emerging Technol., vol. 36,
pp. 547–563, 2013.
[33] M. A. Muller, M. Reble, and F. Allgöwer, “Cooperative control of dynam-
ically decoupled systems via distributed model predictive control,” Int. J.
Robust Nonlinear Control, vol. 22, no. 12, pp. 1376–1397, Aug. 2012.
[34] M. J. Lighthill and G. B. Whitham, “On kinematic waves II: A theory of
traffic flow on long crowded roads,” Proc. R. Soc. A, vol. 229, no. 1178,
pp. 317–345, May 1955.
[35] M. J. Cassidy and R. L. Bertini, “Some traffic features at freeway bottle-
necks,” Transp. Res. B, Methodol., vol. 33, no. 1, pp. 25–42, Feb. 1999.
[36] L. Leclercq, J. A. Laval, and N. Chiabaut, “Capacity drops at merges:
An endogenous model,” Transp. Res. B, Methodol., vol. 45, no. 9,
pp. 1302–1313, 2011.
[37] M. Treiber and A. Kesting, “Evidence of convective instability in con-
gested traffic flow: A systematic empirical and theoretical investigation,”
Transp. Res. B, Methodol., vol. 45, no. 9, pp. 1362–1377, Nov. 2011.
[38] C. M. J. Tampère, “Human-kinetic multiclass traffic flow theory and
modelling—With application to advanced driver assistance systems
in congestion,” Ph.D. dissertation, Dept. Technol. Eng., Delft Univ.
Technol., Delft, The Netherlands, 2004.
[39] J. A. Laval and C. F. Daganzo, “Lane-changing in traffic streams,” Transp.
Res. B, Methodol., vol. 40, no. 3, pp. 251–264, Mar. 2006.
[40] M. Treiber, A. Kesting, and D. Helbing, “Understanding widely scattered
traffic flows, the capacity drop, and platoons as effects of variance-driven
time gaps,” Phys. Rev. E, vol. 74, pp. 10–16, 2006.
[41] B. Coifman and S. Kim, “Extended bottlenecks, the fundamental rela-
tionship, and capacity drop on freeways,” Transp. Res. A, Policy Pract.,
vol. 45, no. 9, pp. 980–991, Nov. 2011.
[42] J. Treiterer and J. A. Myers, “The hysteresis phenomenon in traffic flow,”
in Proc. 6th Int. Symp. Transp. Traffic Theory, 1974, pp. 13–38.
[43] D. Chen, J. A. Laval, S. Ahn, and Z. Zheng, “Microscopic traffic hys-
teresis in traffic oscillations: A behavioral perspective,” Transp. Res. B,
Methodol., vol. 46, no. 10, pp. 1440–1453, Dec. 2012.
[44] W. J. Schakel, V. Knoop, and B. van Arem, “Integrated lane change
model with relaxation and synchronization,” Transp. Res. Rec., vol. 2316,
pp. 47–57, 2012.
[45] R. Akcelik, “Efficiency and drag in the power-based model of fuel
consumption,” Transp. Res. B, Methodol., vol. 23, no. 5, pp. 376–385,
Oct. 1989.
[46] R. E. Wilson, “Mechanisms for spatio-temporal pattern formation in high-
way traffic models,” Philosoph. Trans. R. Soc. A, vol. 366, no. 1872,
pp. 2017–2032, 2008.
[47] M. Wang, S. P. Hoogendoorn, W. Daamen, B. van Arem and R. Happee,
“Game theoretic approach for predictive lane-changing and car-following
control,” Transp. Res. C, Emerging Technol., vol. 58, pp. 73–92, Sep. 2015.
Meng Wang received the M.Sc. degree in transporta-
tion engineering from Research Institute of Highway,
Beijing, China, in 2006 and the Ph.D. degree in
transport and planning from Delft University of
Technology, Delft, The Netherlands, in 2014. From
2014 to 2015, he was a Postdoctoral Researcher
with the Department of BioMechanical Engineering,
Delft University of Technology. Currently, he is an
Assistant Professor with the Department of Transport
and Planning, Delft University of Technology. His
main research interests are driver behavior modeling
and control approaches for intelligent vehicle systems.
Winnie Daamen received the M.Sc. and Ph.D. de-
grees in transport and planning from Delft University
of Technology, Delft, The Netherlands, in 1998 and
2004, respectively. Currently, she is an Associate
Professor with Delft University of Technology. She
developed the pedestrian simulation model SimPed.
Her current research involves modeling of drivers,
ships, and pedestrians, as well as crowd manage-
ment. To develop pedestrian models, she pioneered
in pedestrian laboratory experiments and empirical
observations on pedestrians. Her research interests
also include empirical analysis of merging behavior on on-ramps.
Serge P. Hoogendoorn received the M.Sc. degree in
applied mathematics and the Ph.D. degree in trans-
port and planning from Delft University of Tech-
nology, Delft, The Netherlands, in 1995 and 1999,
respectively. Currently, he is the Chair Professor
of Traffic Flow Theory and Management with the
Department of Transport and Planning, Delft Uni-
versity of Technology. His research involves theory,
modeling, and simulation of traffic and transporta-
tion networks, focusing on innovative approaches to
collect detailed microscopic traffic data and the use
of these data to underpin the models and theories.
Bart van Arem (M’04) received the M.Sc. and
Ph.D. degrees in applied mathematics from the Uni-
versity of Twente, Enschede, The Netherlands, in
1986 and 1990, respectively. From 1992 and 2009,
he was a Researcher and a Program Manager with
TNO, working on intelligent transport systems, in
which he has been active in various national and
international projects. Since 2009, he has been the
Chair Professor of Transport Modeling with the De-
partment of Transport and Planning, Delft University
of Technology, Delft, The Netherlands, focusing on
the impact of intelligent transport systems on mobility. His research interests
include transport modelling and intelligent vehicle systems.
