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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1
Cooperative Platoon Formation of Connected and
Autonomous Vehicles: Toward Efficient Merging
Coordination at Unsignalized Intersections
Zhiyun Deng ,Graduate Student Member, IEEE, Kaidi Yang ,WeimingShen ,Fellow, IEEE, and Yanjun Shi
Abstract— This paper p resents a Vehicle-Platoon-Aware
Bi-Level Optimization Algorithm for Autonomous Intersection
Management (VPA-AIM) to coordinate the merging of Con-
nected and Automated Vehicles at unsignalized intersections.
The constraint-coupled bi-level optimization is operated within a
rolling horizon to balance traffic performance and computational
efficiency. In each decision step, the platoon formation scheme
is incorporated into an upper-level traffic scheduling model as
decision variables to pursue an optimal schedule from a systemic
view. Meanwhile, the passing sequence and timeslots of vehicles
are jointly optimized with the platoon configuration scheme by
virtue of real-time traffic states to improve operational efficiency
and fairness. After that, a lower-level trajectory planning model
will generate dynamically-feasible and energy-efficient trajecto-
ries according to the given schedule and coupling constraints with
the objective of improving space utilization to prevent spillbacks.
Moreover, the quantifiable connection between the makespan of
traffic scheduling schemes and the occurrence of spillbacks is
established, demonstrating that the cooperative platoon forma-
tion strategy is effective in avoiding and mitigating spillbacks in
normal and saturated traffic states. Additionally, the proposed
algorithm can be extended to mixed traffic scenarios. Numerical
experiments are conducted on extensive scenarios with different
arrival flows, where the Constraint Programming technique is
employed to produce the optimal schedule. Experimental results
indicate the superiority of the proposed approach in optimality
and stability with reasonable sub-second computation time for
real-life applications.
Index Terms—Cooperative driving, vehicle platooning, traffi c
scheduling, queue spillback, unsignalized intersections.
I. INTRODUCTION
TRAFFIC intersections are the physical area where differ-
ent transport flows meet and cross, resulting in natural
Manuscript received 15 September 2022; revised 31 December 2022;
accepted 6 January 2023. This work was supported in part by the National Key
Research and Development Program of China under Grant 2018YFE0197700
and in part by the Fundamental Research Funds for the Central Universities of
China under Grant 2021yjsCXCY048 and Grant 2021GCRC058. The work of
Kaidi Yang was supported by the Singapore Ministry of Education under its
Academic Research Fund Tier 1 under Grant A-8000404-01-00. The Associate
Editor for this article was G. Guo. (Corresponding author: Weiming Shen.)
Zhiyun Deng and Weiming Shen are with the School of Mechanical
Science and Engineering, Huazhong University of Science and Technology,
Wuhan 430074, China (e-mail: dengzy@hust.edu.cn; shenwm@hust.edu.cn).
Kaidi Yang is with the Department of Civil and Environmental Engi-
neering, National University of Singapore, Singapore 119077 (e-mail:
kaidi.yang@nus.edu.sg).
Yanjun Shi is with the School of Mechanical Engineering, Dalian University
of Technology, Dalian 116024, China (e-mail: syj@dlut.edu.cn).
Digital Object Identifier 10.1109/TITS.2023.3235774
bottlenecks in urban road networks. However, the present
signalized intersection is far from perfect for the burgeoning
number of vehicles [1]. It is observed that the switching of
traffic signals constantly interrupts the traffic flow and gives
rise to a frequently observed phenomenon called stop-and-
go traffic [2]. Consequently, drivers may be tired, agitated,
and even angry, leading to undesirable driving behaviors
called road rage [3], which may further aggravate congestion.
In addition, the signal-switching process is not instantaneous
but requires a setup phase (i.e., the yellow light) lasting
about five seconds [4], which reduces intersection throughput
considerably. Furthermore, when adverse weather occurs (e.g.,
heavy rain, fog, snowstorms, and dust storms), it can be
challenging for drivers or onboard infrared cameras to capture
the signal light accurately [5].
Fortunately, Connected and Automated Vehicles (CAVs)
that combine wireless communication and autonomous driving
hold the potential to revolutionize intelligent transportation
systems [6], [7], [8], offering advantages for accident avoid-
ance [9], mobility improvement [10], and emission reduc-
tion [11]. The benefits of CAVs on intersection control are
mainly two-fold. On the one hand, CAVs enable the joint opti-
mization between passing sequences and motion trajectories at
autonomous traffic intersections [12], [13], [14], [15]. In other
words, vehicles will run with the pre-determined trajectories
within assigned timeslots to improve traffic efficiency by
avoiding unnecessary speed up/down operations and stops.
Therefore, it is expected that physical traffic signals will no
longer be necessary for future traffic management [16], since
the Vehicle-to-Everything (V2X) technique enables virtual
traffic lights [17] that reside at each vehicle to reduce the
difficulty of signal detection. On the other hand, CAVs enable
the application of vehicle platooning [18], [19], [20], [21],
[22], which can further increase road storage by reducing
inter-vehicular headway considerably [23], [24], [25], [26] and
improve energy efficiency by mitigating aerodynamic drag and
unnecessary speed fluctuations [27]. Hence, researchers try
to facilitate the advantages of vehicle platooning to enhance
traffic mobility at autonomous intersections, which raises a
critical research question of how to determine the optimal
platoon formation scheme for vehicles to optimize important
objective indicators subject to relevant constraints.
Despite extensive existing works on jointly optimizing vehi-
cle trajectories and passing sequence [12], [13], [14], [15],
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2IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
the problem of platoon configuration has not been adequately
addressed due to the complexity of the requirement for a global
decision-maker. For example, most of the existing research
assumes that platoons have been formed before vehicles enter
the control zone [14], [28], [29], whereas other works group
vehicles into platoons by virtue of empirical rules from the
individual point of view [13], [30], [31], without cooperation
with vehicles on other lanes. Hence, this paper aims to address
these gaps in cooperative platoon formation to explore the
potential of platoon-aware traffic management.
Compared to existing studies, the contributions of this
paper are threefold. First, this work incorporates the platoon
formation scheme as decision variables into the joint opti-
mization of vehicle trajectories and intersection controllers,
intending to pursue the global-optimal schedule, significantly
improving operational efficiency and fairness compared with
the state-of-the-art algorithms. In other words, the decision
to merge vehicles into platoons is based on real-time traf-
fic states to achieve one-dimensional cooperation on the
same lane and two-dimensional cooperation with vehicles
on another lane. Second, this work presents an effective
traffic coordination algorithm to avoid/mitigate spillbacks in
normal/saturated traffic states, where the quantifiable con-
nection between the makespan of traffic scheduling schemes
and the occurrence of spillbacks is established. Additionally,
the proposed algorithm can be extended to mixed traffic
scenarios with various penetration rates of CAVs based on
the assumptions that Human Driven Vehicles (HDVs) have
bounded tracking errors and CAVs serve as platoon leaders.
Third, it is able to produce provable optimal traffic scheduling
schemes with high computational efficiency and stability for
real-life applications using the Constraint Programming (CP)
technique, whose computation time remains at a sub-second
level even for high-flow traffic states in most scenarios
tested.
The remainder of this paper is organized as follows:
Section II discusses related works on Autonomous Inter-
section Management (AIM). Section III presents definitions
of the cooperative merging problem, followed by a detailed
description of the proposed bi-level optimization method in
Section IV. Numerical simulation experiments are conducted
in Section V along with performance comparison with other
existing methods. Section VI concludes this paper and dis-
cusses some open issues and future work.
II. RELATED WORK
Since Dresner and Stone presented the concept of AIM [32],
numerous strategies have been proposed to improve traffic
efficiency at autonomous intersections without signal con-
trollers. It is clear that the overall performance of the sys-
tem is susceptible to the underlying control strategy [33],
[34], which can be categorized into three groups, i.e.,
the Priority-based AIM (PR-AIM), Optimization-based AIM
(OP-AIM), and Heuristic-based AIM (HR-AIM). The First-
In-First-Out (FIFO) policy [35] is a classical priority-based
method, while the FIFO-based reservation system has been
proved to outperform the signal controller in terms of delay
under certain circumstances [36], [37]. In that case, the priority
of nvehicles will be determined by a centralized controller
according to their arrival times, which effectively reduces
the computational complexity from O(n!)to O(n). Hence,
feasible solutions can be generated in real-time, while the
performance of solutions cannot be guaranteed since it sets
fairness as the fixed goal [38].
In order to obtain the optimal solution, a variety of
OP-AIM methods are proposed by researchers, who translate
the traffic scheduling problem into a mathematical program-
ming problem and employ optimization-based methods to
generate high-performance solutions in terms of delay [39],
throughput [40], energy consumption [41], quality of experi-
ence [42], and communication overhead [28]. Besides, con-
straints regarding first-order dynamics limits and inter-vehicle
separation distance are well-designed in [40] to ensure safety.
Among OP-AIM methods, Mixed-Integer Linear Programming
(MILP) models are widely adopted by existing literature to
describe the discrete and continuous aspects of the system. For
example, passing sequences of vehicles can be formulated by
discrete variables, while their states (e.g., location, velocity,
and acceleration) must be continuous. Besides, to generate
dynamically feasible trajectories, Lu et al. [43] directly set
instantaneous speeds of vehicles as time-varying decision
variables, considering n×Nvariables in total, where n
and Mrepresent the number of vehicles and time steps,
respectively. By contrast, several hierarchical frameworks are
developed in [13], [14], [15], [44], [45], [46]. For example,
Guo et al. [13] propose a framework of dynamic programming
with shooting heuristic as a subroutine (DP-SH) to find the
near-optimal solution for the integrated trajectory optimization
and intersection control problem. Note that such two-step
approaches have smaller search space than the former since
they decoupled the optimization of vehicles’ crossing timeslots
and trajectories. Although these programming models can be
solved with off-the-shelf software packages, obtaining solu-
tions for large-scale problems is still time-consuming [29],
which limits its application to dynamic traffic conditions.
Besides, HR-AIM methods use some heuristic rules to
group vehicles into platoons, which accelerates the process
of finding a satisfactory solution [23], [25]. Such a strategy
can reduce model complexity since the centralized controller
only needs to deal with platoon leaders, while the computation
and communication load can be released [47]. For example,
Miculescu et al. [48] proposed a polling-based method to
schedule passing sequences of vehicles, where natural platoon-
ing behaviors emerge and help to save switching time. Besides,
the authors compared different polling policies (i.e., exhaus-
tive, gated, and k-limited policies) in the MATLAB-based
simulations. Tallapragada et al. [49] adopted the k-means
algorithm to form clusters based on vehicle positions, while
the maximum number of clusters is pre-defined to reduce the
computational burden. Ge et al. [50] developed a centralized
coordination scheme based on MILP and used graph theory
to decompose the original vehicle swarm into small batches
after determining the relative priority and speed of vehi-
cles. However, these platoon formation strategies are derived
from previous experiences without being optimal, perfect,
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 3
or rational since they make decisions from the local point of
view without considering the global traffic information.
Although different studies use different control strategies,
most incorporate the rolling horizon procedure into their
method. Therefore, the long-term optimization can be decom-
posed into a series of subproblems with a shorter planning
horizon, which helps to reduce computational complexity.
Admittedly, a longer horizon can enable these subproblems to
better approximate the long-term optimization problem, thus
improving the optimization performance. However, the predic-
tion of dynamic traffic flow is only reliable over a limited hori-
zon. Moreover, a long horizon may increase the scale of the
subproblems, making it computationally challenging to solve
them. Hence, the horizon length should be carefully selected
to balance optimality and computation efficiency. Accordingly,
Levin et al. [51] presented a rolling-horizon algorithm to
extend the MILP model to larger numbers of vehicles, which
takes 5-10 seconds to schedule up to 40 vehicles within a
15-second planning horizon. Mirheli et al. [52] established
a mixed-integer non-linear programming model to determine
optimal conflict-free reservations in an isolated intersection,
which takes more than 10 seconds to schedule 70 vehicles
within a 15-second planning horizon. Yao et al. [45] proposed
a 0-1 MILP model for vehicles entering scheduling, which
takes less than one second to find the optimal scheduling
scheme for up to 12 vehicles within a 10-second planning
horizon. Ge et al. [50] take about three seconds to schedule
40 vehicles within a 15-second planning horizon. To the best of
our knowledge, most existing research cannot solve large-scale
AIM problems in real-time (e.g., at the sub-second resolution,
which is crucial to reduce tracking errors and ensure vehicles
follow the planned trajectories [53]). Hence, it motivates us
to develop an efficient traffic scheduling method to pursue the
optimal solution in a short time even for high-flow traffic states
by integrating the advantages of OP-AIM and HR-AIM.
III. PROBLEM DEFINITION
In this paper, we focus on the cooperative merging problem
through a fully autonomous traffic intersection without signal
controllers as shown in Fig. 1. It is assumed that all the
vehicles are CAVs equipped with wireless communicators
(e.g., Dedicated Short Range Communication (DSRC) and
cellular devices) to support vehicular communications [54],
[55], [56], while their kinematic states (e.g., position, speed,
and acceleration) can be precisely estimated by Kalman filters
through fusing GPS, camera, and IMU as illustrated in [57],
[58], and [59]. This simple scenario consisting of two one-way
traffic streams is defined as a standard test scenario by [12],
[44], [45], [48], [60], and [61]. It is chosen to gain insights into
the benefits of platoon-aware traffic scheduling for automated
traffic operations, which serves as a building block for sub-
sequent studies. Besides, we assume that Base Stations (BSs)
and Road Side Units (RSUs) are responsible for providing
cellular- and DSRC-based V2X networks outside and within
the control region, respectively. Thus, the kinematic states of
vehicles can be captured by the decision-maker via the cellular
network before they enter the control zone [62], such that their
Fig. 1. Illustration of the cooperative merging problem at a fully autonomous
traffic intersection without signal controllers.
Fig. 2. Illustration of time parameters within the intersection area.
arrival time can be predicted ahead of time. After that, the
RSU, which serves as a centralized controller, can control the
motion of vehicles via wireless communication.
Given the planning horizon t∈[T0,T0+T], we assume
that there are nkvehicles existing on the road k∈K={0,1},
which can be denoted by Vk,iand indexed by i∈I=
{1,2,··· ,nk}according to their sequence of arrival. Besides,
the overlapped region of two roads is called the merging zone
and has a width of W, while the portion of the road segment
within a distance of Lto the merging zone is called the control
zone. It is assumed that vehicles are required to form mk
platoons within the control zone (mk≤nk), which can be
denoted by Pk,iand indexed by j∈J={1,2,··· ,mk}.
Without loss of generality, each vehicle is represented by
a two-dimensional and rectangular rigid body with length l
and width w. Besides, suppose each vehicle is subject to
second-order dynamics of the following form:
¨st
k,i=at
k,i,∀k,i,(1)
where st
k,idenotes the displacement of the vehicle’s front
bumper between the entrance of the control zone and current
position, ˙st
k,ithe velocity, and at
k,ithe acceleration.
During the time when each vehicle passes through the con-
trol zone and merging zone, there are three special moments
as shown in Fig. 2. In detail, (1) the arrival time t+
k,iis
the moment when its front bumper enters the control zone
where st
k,i=0; (2) the start time t∗
k,iis the moment when
its front bumper enters the merging zone (i.e., crosses the
stop line) where st
k,i=L; and (3) the departure time t−
k,i
is the moment when its rear bumper leaves the merging zone
where st
k,i=L+W+l. It is obvious that t−
k,i>t+
k,ifor
all vehicles. After that, we define the interval of these three
moments as the (1) waiting time t+,∗
k,i=t∗
k,i−t+
k,i, (2) operation
time t∗,−
k,i=t−
k,i−t∗
k,i, and (3) travel time t+,−
k,i=t−
k,i−t+
k,i,
respectively. With these notations in hand, we define safety as
follows.
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4IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
Fig. 3. Illustration of the sequence-dependent switching time.
Definition 1 (Safety): The control zone is said to be safe
at time t, if each vehicle maintains a sufficient separation
with its preceding vehicle, i.e., st
k,i−1−st
k,i>lfor all
k∈K={0,1}when i>1. Besides, the merging
zone is said to be safe, if there are no pairwise collisions
among vehicles, i.e., [t∗
k,i,t−
k,i]∩[t∗
k,i−1,t−
k,i−1]=∅and
[t∗
k,i,t−
k,i]∩[t∗
1−k,i,t−
1−k,i]=∅for all k∈Kand i,i∈
I={1,2,··· ,nk}.
From a practical point of view, there should be an extra
separation between vehicles when they enter the merging zone
in case of communication latency and control error. Hence,
we define the switching time on the occupation timeline of
the merging zone as shown in Fig. 3, which should be greater
than a minimum threshold value for security.
Definition 2 (Switching Time): In the merging zone, the
switching time between vehicles coming from the same road
is defined as t∗
k,i−t∗
k,i−1for all k∈{0,1}and i>1. The
calculation of switching time is the same as the time-headway
of vehicle iand i−1 at the stop line when st
k,i=st
k,i−1=L.
In addition, the switching time between vehicles coming from
different directions can be calculated by |t∗
k,i−t∗
1−k,i|for all
k∈{0,1}and i,i∈{1,2,··· ,nk}.
In this paper, we formulate the assumption of
sequence-dependent switching time tk,i
k,ias follows since the
vehicle platooning technique helps to reduce inter-vehicular
distances considerably [25].
Assumption 1 (Sequence-Dependent Minimum Switching
Tim e): We assume that the minimum switching time tk,i
k,i
of vehicles in the merging zone is varied with each pair of
individuals, which can be calculated by
tk,i
k,i=
τ, ,if k=kand same platoon,
σ1τ, k=k,
σ2τ, else if k= k
∀k,k,i,i.
(2)
where τdenotes the minimum time-headway of vehicles in the
same platoon on the same road, σ1the factor of safety when
vehicles are assigned into different platoons on the same road,
and σ2the factor of safety when vehicles come from different
roads (σ2>σ
1>1).
Given the departure velocity v−, the delay of an individual
vehicle can be calculated by the difference between its actual
departure time t−
k,iand virtual departure time, i.e., (t+
k,i+
L+W+l
v−). In detail, the latter one is the time in ideal driving
scenarios where the vehicle travels through the control and
merging zone under free-flow1conditions.
1Note that the free-flow condition is only used to estimate the virtual
departure time of vehicles, not the necessary condition of the proposed
algorithm.
Fig. 4. Illustration of the occurrence of spillbacks.
Definition 3 (Delay): The delay of vehicle is defined as
tD
i,k=max{0,t−
k,i−(t+
k,i+L+W+l
v−)}.
Note that the maximum delay among vehicles reflects the
fairness of the traffic scheduling scheme. In other words, the
smaller the maximum delay, the smaller the variance of travel
times, and the better the traffic scheduling scheme in terms of
fairness.
Next, we define the makespan of a given traffic scheduling
scheme as the departure time of the last vehicle within the
current horizon. It is the period of time that the scheduling
scheme took to let all the vehicles pass through the intersection
area, reflecting the operational efficiency of the underlying
control policy.
Definition 4 (Makespan): Given a set of vehicles denoted
by Vk,iwhere k∈K={0,1}and i∈{1,2,··· ,nk},the
makespan of a traffic scheduling scheme is defined as
Cmax =max
k∈Kt−
k,nk=max
k∈K{t∗
k,nk+W+l
v−}.
As illustrated in Fig. 4, the traffic spillback refers to the
situation when the back of the queue propagates to the
previous intersection, leading to extended blockages and queue
overflowing buffers. It is evident that spillbacks occur because
vehicles cannot pass through the merging zone on schedule,
e.g., due to the sudden increase in traffic volume or inefficient
traffic management methods.
In this paper, we show that the makespan is a helpful indica-
tor to predict the time when spillbacks occur. To demonstrate
this, we first establish a condition in Lemma 1 such that
the violation of this condition will cause queue to constantly
grow, and hence spillback will eventually happen. Based on
this condition, we then calculate in Property 1 the estimated
number of rolling horizon cycles without the occurrence of
spillbacks.
Lemma 1: For a given planning horizon t∈[T0,T0+T],
let us assume that Tmin is the minimum time interval between
a vehicle’s arrival and start time in each horizon, the value
of which is affected by the trajectory planning algorithm. Let
Cmax be the makespan of the current traffic scheduling scheme.
Then, the queue will not be carried over from the current
horizon to the next one if
Cmax ≤T+Tmin.(3)
Proof: Let us consider two adjacent planning horizons,
i.e., [T0,T0+T]and [T0+T,T0+2T]. The ideal
earliest moment when the front bumper of the first vehicle
in the next horizon enters the merging zone can be denoted
by T0+T+Tmin, the value of which is determined by the
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 5
Fig. 5. Schematic diagram for calculating the number of rolling horizon
cycles without the occurrence of spillbacks.
trajectory planning algorithm without considering the collision
avoidance constraint. In addition, the moment when the rear
bumper of the last vehicle in the previous horizon leaves the
merging zone can be denoted by T0+Cmax. This is the actual
earliest available time for vehicles in the next horizon to enter
the merging zone that ensures safety.
It is obvious that if the actual earliest available moment
(which is affected by vehicles in the previous horizon) is less
than the ideal one, the queue will not be carried over from the
previous horizon to the current one. Therefore, we have
T0+Cmax ≤T0+T+Tmin.
This completes the proof.
In this paper, we try to avoid spillbacks in normal traffic
states where traffic can be effectively managed by minimizing
the makespan of optimized traffic scheduling schemes and
preventing delay propagation. Moreover, we try to mitigate
spillbacks (i.e., postpone the occurrence of spillbacks) in
saturated traffic states. To this end, we provide an upper
bound for the number of rolling horizon cycles without the
occurrence of spillbacks to calculate the maximum duration
for which it can disperse traffic without causing a spillback.
Property 1 (Number of Rolling Horizon Cycles Without the
Occurrence of Spillbacks): Suppose L∗denotes the remaining
road storage space, which is determined by the number of
vehicles that arrived in advance but still exist on the road,
i.e., L∗=L−L,whereLdenotes the length of queue. Let
dbe the minimum inter-vehicle distance and hbe vehicles’
arrival intensity in seconds per vehicle (s/veh), which denotes
the average headway. Then, in scenarios where the arrival flow
is slowly changing, a spillback is expected to occur after N
cycles of rolling horizons, where
N=[
L∗
l+d·h−Tmin
Cmax −T−Tmin
].(4)
Recall that Land ldenote the length of the road and
vehicles, Tthe length of the planning horizon, Tmin the
minimum travel time of vehicles, Cmax the makespan of the
traffic scheduling scheme in the current horizon. According to
Lemma 1, it is clear that the queue will not be carried over
from the current horizon to the next one if Cmax ≤T+Tmin.
On the contrary, the queue will be carried over to the next
horizon if Cmax >T+Tmin asshowninFig.5,which
may cause delays propagating backward and accumulating,
eventually leading to congestion and spillbacks. Note that
spillbacks are expected to occur when the number of queued
vehicles exceeds the maximum road storage (i.e., L
l+d). Then,
the time when the road storage reaches its limit can be
Fig. 6. Framework of the proposed bi-bevel optimization model.
estimated by Lh
l+d. Note that the derivation of Eq.(4) relies
on a point queue model to calculate an upper bound for the
duration for which it can disperse traffic without causing a
spillback.
IV. VEHICLE-PLATOON-AWA R E BI-LEVEL OPTIMIZATION
FOR AUTONOMOUS INTERSECTION MANAGEMENT
A. Method Framework
In this section, we propose a bilevel optimization algorithm,
named VPA-AIM, which assigns vehicles to platoons to get
through the unsignalized intersection cooperatively. Efficient
coordination is achieved by solving two coupled optimiza-
tion models. In detail, the upper-level task is referred to as
platoon-aware traffic scheduling, which determines the optimal
platoon formation scheme of vehicles during the control zone
and allocates the sequence and timeslots of platoons passing
through the merging zone. The lower-level task is referred to
as multi-vehicle trajectory optimization, which designs refer-
enced trajectories for multiple vehicles during the process of
vehicles merging into platoons and passing through the control
and merging zones. The two models are connected to each
other via several coupling constraints, which ensures that the
decisions generated by the upper-level traffic scheduling model
are feasible for the lower-level trajectory planning model. The
workflow of the VPA-AIM algorithm is presented in Fig. 6.
This paper proposes a rolling horizon procedure to deal
with this online optimization problem since the prediction of
dynamic traffic flows is reliable only over a limited horizon.
This procedure decomposes the long-term optimization into a
series of subproblems with a shorter time horizon, such that the
computation time can be reduced. According to this method,
a vehicle scheduling scheme is first determined up to a given
point in time, ignoring everything that could happen afterward.
After that, the planning interval is iteratively moved forward
in time to generate the following schedule and so on.
In each decision step, the traffic scheduling scheme of
vehicles (i.e., their departure time, which includes informa-
tion about the platoon formation scheme) is optimized in
the upper-level model to minimize the makespan and the
maximum delay. Besides, referenced trajectories of vehicles
are designed and optimized in the lower-level model according
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6IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
to the pre-determined arrival and departure time to reduce the
overall energy consumption of vehicles and improve space
utilization to prevent spillbacks within the intersection area.
B. Upper-Level Traffic Scheduling Model
1) Decision Variables: Recall that there are nkvehicles
existing on the road k∈K={0,1}, which are indexed by i∈
I={1,2,··· ,nk}. These vehicles are required to be assigned
into mkplatoons indexed by j∈{1,2,··· ,mk}(mk≤nk).
Therefore, we define the decision variables as the start time
of vehicles, i.e., t∗={t∗
k,i}k∈K,i∈I.
Besides, we characterize platoon formation using a dummy
binary variable xk
ithat represents whether vehicle Vk,iis the
leading vehicle of a platoon. In other words, we have
xk
i=1,if Vk,iis a platoon leader,
0,if Vk,iis a platoon follower.∀k,i,(5)
which can be expressed as a nk-dimensional vector xkfor all
i∈I. For example, suppose there are five vehicles indexed
by {1,2,3,4,5}on the road kand they are assigned into three
groups, i.e., {1,2},{3},{4,5}. In this case, Vk,1,Vk,3,andVk,4
serve as platoon leaders, while Vk,2and Vk,5serve as platoon
followers. Therefore, we have xk=[1,0,1,1,0].
To describe the formation scheme directly, we take ykas
an intermediate variable to denote the number of vehicles that
have been assigned to each platoon on the road k, i.e.,
yk={yk
j|j=1,2,··· ,mk},(6)
mk
j=1
yk
j=nk,∀k,(7)
which can be inferred according to the value of xk
i.For
example, suppose there are five vehicles (nk=5) on the road
kindexed by {1,2,3,4,5}and they are assigned into three
groups (mk=3), i.e., {1,2},{3},{4,5}. In this case, Vk,1and
Vk,2are assigned into the first platoon, Vk,3the second, Vk,4
and Vk,5the third. In other words, there are two, one, and
two vehicles in each platoon, respectively. Therefore, we have
yk={2,1,2}.
In addition, we take zi,ias another intermediate variable to
denote the passing sequence of vehicles through the merging
zone, i.e.,
zi,i=0,t∗
k,i≤t∗
1−k,i
1,t∗
k,i>t∗
1−k,i,∀k,i,i.(8)
For example, suppose the passing sequence of vehicles is
{V1
1,V0
1,V1
2}and t∗
1,1<t∗
0,1<t∗
1,2, then it can be inferred
that z1,1=1andz1,2=0sincet∗
0,1>t∗
1,1and t∗
0,1<t∗
1,2,
respectively.
2) Constraints: Similar to [15], [33], [61], and [63],
we assume overtaking is not allowed in the control zone.
Hence, the passing sequence of vehicles through the merging
zone on the same road should correspond to the order of
arrival at the control zone. In addition, there should be an
extra separation between vehicles when they enter the merging
zone to avoid rear-end collisions, which is referred to as
the switching time tk,i
k,ias described in Definition 2 and
Assumption 1. Therefore, we have the following precedence
constraints in the form of chains for vehicles on the same road:
t∗
k,i−t∗
k,i+1−tk,i+1
k,i≥0,∀k,i<nk.(9)
To avoid side-impact collisions in the merging zone, the
start time of two vehicles coming from different roads should
also maintain a separation. Therefore, we have
zi,i×(t∗
k,i−t∗
1−k,i−t1−k,i
k,i)≥0,∀k=0,i,i,
(10)
(1−zi,i)×(t∗
1−k,i−t∗
k,i−t1−k,i
k,i)≥0,∀k=0,i,i.
(11)
where zi,idescribes the sequence of vehicles passing through
the merging zone as stated in Eq. (8). It takes only the value
of 1 or 0 to choose one of these two equations to activate. For
example, suppose t∗
0,1>t∗
1,1which suggests that V0,1pass
through the intersection after V1,1,thenwehavez1,1=1.
In that case, Eq. (10) will be activated and Eq. (11) will be
disabled.
In addition, the ranges of decision variables and inter-
mediate variables are restricted by the following coupling
constraints explicitly dependent on the lower-level model:
t+
k,i+Tmin ≤t∗
k,i≤t+
k,i+Tmax,∀k,i,(12)
1≤yk
j≤Mmax,∀k,j,(13)
where Tmin and Tmax denote the minimum and maximum
time interval between arrival time t+
k,iand start time t∗
k,i;
Mmax denotes the maximum number of vehicles in a platoon.
Note that Tmax is used to prevent vehicles from stopping (i.e.,
to avoid the undesirable phenomenon of stop-and-go traffic),
whose value is affected by the motion pattern defined in the
lower-level trajectory planning model. Besides, the value of
Tmin is also determined by the lower-level model since the
maximum speed and acceleration of vehicles are bounded
by traffic regulations and mechanical limitations, respectively.
As suggested by [64], a larger maximum allowable platoon
size helps to increase roadway capacity, but may introduce
greater difficulties in maintaining string stability. Therefore,
the maximum platoon size Mmax should be limited to a
moderate value to trade off capacity and maneuverability.
3) Objective Functions: In the upper-level model, the pass-
ing sequence and timeslots of vehicles are jointly opti-
mized with the platoon configuration scheme by virtue of
real-time traffic states to improve operational efficiency (i.e.,
the makespan) and fairness (i.e., the maximum delay). Hence,
we formulate a bi-criteria optimization problem that simul-
taneously considers the makespan of the traffic scheduling
scheme and the maximum delay of all the vehicles under
constraints (7) and (9-13). Moreover, we conduct the lexico-
graphic optimization on these objectives, the preferences of
which are imposed by ordering objective functions according
to their importance, rather than by assigning weights. In other
words, the makespan is considered the chief objective while
the maximum delay is subordinated, since the former has a
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 7
direct influence on the occurrence of spillbacks, according to
Eq. (3). Specifically, we have
min
t∗f1(t∗)=max
k∈K,i∈I{t∗
k,i+W+l
v−},(14)
min
t∗f2(t∗)=max
k∈K,i∈I{t∗
k,i−t+
k,i−L+W+l
v−},(15)
where t∗={t∗
k,i}k∈K,i∈Irepresents the decision variables, i.e.,
the start times of vehicles. Additionally, f1(t∗)and f2(t∗)
denote the makespan and the maximum delay, respectively.
4) Solution Algorithm: It is challenging to solve the traffic
scheduling model in real-time through classical mathematical
programming methods (e.g., MILP) due to the complexity of
the merging coordination problem.
Fortunately, the latest released commercial Constraint Pro-
gramming (CP) solvers (e.g., IBM ILOG CPLEX CP Opti-
mizer [65] and Google’s OR-Tools) offer us an opportunity to
employ out-of-the-box algorithms to solve combinatorial opti-
mization problems. The main advantage of CP is it can deal
with complex problems with much more decision variables
within limited runtime budgets while ensuring optimality.
Especially, the standard CP solver provided by IBM ILOG
CPLEX has shown to provide excellent performance in various
scheduling problems (e.g., vehicle routing [66], train schedul-
ing [67], drone scheduling [68], and airline management [69]
problems). However, to the best of our knowledge, CP has
not been used to solve the intersection management problem
yet. Hence, this paper wants to leverage the advantages of this
technique and ventures to pursue the global-optimal solution
within the tight runtime budget, contributing a novel applica-
tion of CP to traffic scheduling problems.
The CP solver works by iteratively trying different combi-
nations of values for variables in the problem, checking to see
if they satisfy all the constraints, and backtracking if they do
not. Additionally, the CP solver uses a search strategy that is
designed to explore all the space of solutions in an efficient
way, and to prune branches of the search tree that are not
likely to contain solutions. This process continues until the
optimal solution is found or it is determined that no solution
exists. We refer readers to [65] for a detailed explanation of
the underlying optimization principle.
C. Revisit of the Lower-Level Trajectory Planning Model
In this section, we first revisit the trajectory planning
method developed in our previous studies [70], [71], where a
Hybrid Evolutionary Algorithm with Cooperative Coevolution
(HEA-CC) is proposed and proved to be efficient to deal
with the multi-vehicle trajectory optimization. Furthermore,
we formulate a new objective function to fit the setting of
this problem, which not only reduces the overall energy
consumption of vehicles but also improves the usage of road
space to avoid/mitigate spillbacks. This task is non-trivial
since vehicles with non-uniform initial separation distance are
required to merge into platoons while complex dynamics and
safety-critical constraints must be satisfied all the time.
It is noteworthy that the arrival time t+
k,iand departure time
t−
k,iof vehicles can be known if the optimal traffic scheduling
Fig. 7. Illustration of the lower-level multi-vehicle trajectory planning task.
Fig. 8. Illustration of the encoding scheme for vehicle trajectories.
scheme has been generated by the upper-level model. Hence,
these two kinds of parameters are defined as the input of
the lower-level trajectory planning algorithm. As shown in
Fig. 7, we are required to design referenced trajectories for
vehicles according to the given platoon formation scheme
and the allocated passing sequence and timeslots. In this
paper, we adopt the HEA-CC algorithm as a building block
in the proposed bi-level optimization approach to solve the
trajectory planning problem. Besides, it is assumed that all
the vehicles have to adjust their speeds to an identical value
before entering the control zone such that their separation
distances are stable. This setting can be achieved by a speed
harmonization operation in advance [72], [73]. In addition,
we assume that the motions of vehicles can be controlled
by the platoon leader who serves as a centralized decision-
maker, where the predecessor-leader-following communication
topology [74] and model predictive control approach [75], [76]
are used to maintain the desired inter-vehicle distance and
velocity according to the referenced trajectories.
Unlike the well-known and widely-used shooting heuristic
algorithm in the literature [77], [78], [79], our trajectory
planning method requires less predetermined rules about the
motion patterns while having a higher degree of freedom
since the speed profiles of trajectories are configured by the
optimization algorithm appropriately. To be specific, each
trajectory is encoded by a set of via-points named knots
as shown in Fig. 8, whose number varies automatically to
balance the computational efficiency and sufficient degrees of
freedom. Hence, the original trajectory planning problem can
be converted to a constrained numerical optimization problem.
The complete shape of trajectories can be easily constructed
for performance evaluation by cubic spline interpolation.
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8IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
After that, we formulate a new objective function for
trajectory optimization, which not only reduces the energy
consumption of vehicles but also improves the usage of road
space to avoid/mitigate spillbacks with the consideration of
dynamics and safety constraints. For a given planning horizon
t∈[T0,T0+T], we can discretize it into evenly-distributed
time points by twhich denotes the interval of time for
decision-making. Therefore, we have tξ=T0+ξt,where
t0=T0,tM=T0+T,andξ={0,1,··· ,M}.
min
stξ
i
=fi[tξ]
nk
i=1
M
ξ=0
Pi(tξ)t+
4
c=1
[σc
nk
i=1
M
ξ=0
g2
c(stξ
i)]
+α
nk
i=1
(L−stξ
i)t.(16)
Here, stξ
idenotes the displacement of the front bumper of
vehicle i∈[1,nk]at time tξ,Pi(tξ)denotes the instantaneous
power, For the second term, gc(stξ
i)denotes the penalty
function with the corresponding weight coefficient σc,where
g1(·)measures the violation of traffic regulations, g2(·)the
mechanical limitation, g3(·)the comfort criteria, and g4(·)
the separation distance. We refer readers to read [70] for the
calculation of these energy and penalty functions.
Additionally, the last term in Eq. (16) denotes the sum of
the area above trajectory curves, where Lis the length of
road and αis the coefficient used to trade-off between the
objectives of eco-driving and spillback avoidance. It is clear
that for given start times t∗
k,i, increasing the sum of the area
under trajectory curves (i.e., the dark area shown in Fig. 8)
can reserve more space for subsequent vehicles, leading to a
smaller length of queue (i.e., L), which helps to mitigate the
occurrence of spillbacks according to Property 1.
In the next step, the set of trajectories within the same
platoon are calculated in parallel using a divide-and-conquer
strategy until a near-optimal solution has been found, or a
terminal condition is met. Note that the HEA-CC algorithm
is able to generate feasible referenced trajectories with high
energy efficiency in a sub-second computation time, which
is at least two orders of magnitude lower than the planning
period even for large-scale instances.
D. Discussion of the Extension to Mixed Traffic
It is noteworthy that the proposed intersection coordination
algorithm can be readily extended to mixed traffic scenarios
with various penetration rates of CAVs. Next, we will briefly
explain how to address two major challenges associated with
the mixed traffic condition.
On the one hand, without the help of traffic signals, the
centralized controller located on the roadside cannot force
Human-Driven Vehicles (HDVs) to comply with the advised
passing sequence, especially if the leading vehicles of both
approaches are HDVs. Therefore, one solution is to mod-
ify the proposed algorithm to preclude such scenarios by
requiring all platoon leaders to be CAVs, which, however,
may not be feasible if the penetration rates of CAVs are
not sufficiently high. Nevertheless, we notice that in current
Fig. 9. Illustration of vehicle trajectories within the mixed traffic.
practice, unsignalized intersections with pure HDV traffic are
coordinated using the FIFO policy to provide right-of-way
to the HDV that arrives earlier. Inspired by this, we can
integrate the proposed algorithm with the classical FIFO policy
to coordinate mixed traffic and deal with specific scenarios
where HDVs are platooned.
On the other hand, it is difficult to predict and con-
trol the behaviors and motions of HDVs. To address this
challenge, many previous works used the classic Optimal
Velocity Model [80] and Intelligent Driver Model [81] to
estimate the behaviors of HDVs. However, such deterministic
car-following models impose many assumptions on vehicles’
desired velocity and spacing time, which require elaborate
tuning of parameters and may not be favorable under uncertain
conditions. Some other researchers try to perform evaluations
against HDVs uncertainties with the least-assumption-based
approach [63] that fixes the velocity of HDVs as constants,
which is however not the setting of this problem.
Fortunately, Advanced Driver-Assistance System (ADAS)
enables the centralized controller to issue proper minimum and
maximum speed recommendations to HDV drivers via Human
Machine Interface (HMI) [82]. In that case, HDVs will be
able to track the desired speed and trajectory such that they
can pass through the merging zone in their pre-determined
timeslots to avoid collisions. Hence, the proposed bi-level
intersection coordination algorithm can be extended to mixed
traffic conditions with the Assumption 2.
Assumption 2 (Tracking errors of HDV trajectories): This
paper assumes that HDVs are able to track the speed profile
provided by the proposed algorithm with bounded tracking
errors, i.e.,
|t∗−treal|≤t
max,
where t∗denotes the expected time-headway of a HDV with its
preceding or succeeding vehicle, treal the actual time-headway,
and t
max the maximum tracking errors of HDVs. In that case,
other vehicles should keep a sufficient inter-vehicle distance
with the maximum tracking error boundaries of HDVs to
ensure safety. Accordingly, the upper-level traffic scheduling
model should also take tracking errors into consideration by
reserving more space for HDVs to ensure safety when it
assigns timeslots for vehicles.
An example of the generated trajectory planning scheme
in the mixed traffic condition is presented in Fig. 9, where
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 9
TAB L E I
PARAMETERS SETTING FOR SIMULATIONS
the vehicle platoon consists of six CAVs marked in blue and
one HDV marked in red. It can be seen that the trajectories
of CAVs are deterministic, while the trajectory of HDV is
uncertain since the driver behavior cannot be precisely con-
trolled. However, the tracking errors of the HDV are bounded
within certain limits (i.e., the area in red), which have been
considered in advance in the trajectory planning phase to
ensure safety. In other words, the other CAVs would leave
enough space to prevent confusion due to the control errors of
HDVs.
V. N UMERICAL SIMULATION EXPERIMENTS
In this section, we formulate a micro-simulation platform
in MATLAB 2021b to evaluate the proposed VPA-AIM algo-
rithm. The simulation parameters are set as shown in Table I.
The basic setting in simulations includes the platooning will-
ingness of vehicles and their ability to communicate with
others. The appropriate length of the control region depends
on the practical needs of applications, but it cannot exceed
the reliable communication range of the intersection manager
located nearby the merging zone. In this paper, we set the
length of the control zone as 150 meters, similar to existing
studies [41], [48], [78]. Note that the minimum time-headway
can be reduced if the latency of vehicular communication is
stably maintained at a low level. Hence, we determine the two
values according to [45], [83], [84], and [85]. The value of the
maximum tracking errors of HDVs depends on a wide range
of factors, including the skill of drivers, the type of vehicles,
and the traffic conditions. In this paper, we set this value as
one-quarter of a second according to the benchmark average
human response time [86]. In addition, we set the arrival and
departure speeds to 60 km/h according to the free flow speed
used in [12] and limit the maximum speed to about 80 km/h
to ensure platooning safety as suggested by [84]. The range
of acceleration and jerk are limited within the comfort criteria
recommended by [87]. The maximum platoon size Mmax is
set to 25 that conforms with the platoon size configuration in
previous studies [77], [88].
A. Design of Test Scenarios
The vehicle arrival time t+
k,iis modeled as a Matérn hard-
core stochastic point process [48] on the non-negative real line.
Additionally, the distance between points is lower bounded by
a certain number (i.e., t+
k+1,i−t+
k,i≥tk,i
k,i), which denotes the
sequence-dependent minimum switching time of vehicles in
the same platoon. This setting guarantees that no two vehicles
are in collision at the time of arrival. Define Matérn process
with parameter λas the Matérn process obtained by thinning
a Poisson process [89] in the line that has intensity λ. Suppose
t=l/Vmax, then the intensity of Matérn Type I point process
can be defined as
λI(λ) =1−exp(−2λt)
2t.(17)
In order to generate multiple scenarios with different arrival
flows within a reasonable range, we define the road capacity
as the maximum flow of vehicles on a road segment. Given
the minimum headway τ, the road capacity can be calculated
by 1/τ .
Next, we generate nine groups of test instances whose
arrival flows vary from 720 to 3600 vph/lane using the Matérn
hard-core stochastic point process in the scenario of balanced
and uniform traffic flow. Meanwhile, each group of traffic
scenarios is simulated five times with different random seeds
to replicate stochasticity in transportation systems, where the
arrival time of vehicles is different, but the arrival flow keeps
the same. In other words, there are 9×5=45 scenarios tested
in total.
B. Computational Results
In this section, the proposed VPA-AIM method is tested in
multiple scenarios with different arrival flows and compared
with the FIFO-, polling-, and scheduling-based methods for
AIM. The FIFO-based method is modified from [83], which
determines the passing sequence of vehicles according to
their arrival orders. The polling-based method is modified
from [48], which switches the priority of vehicles coming from
different directions using an exhaustive policy. The traditional
scheduling-based method is modified from [45], which solves
a linear programming model to determine the passing sequence
of individual vehicles without considering grouping vehicles
into platoons.
The computational results for different scenarios are
reported in Table II. Note that the data shown in this table
denotes the average value of five scenarios, while the average
computation time for the upper-level traffic scheduling model
is presented in the last column. To quantify the optimization
performance of different algorithms, we define the Relative
Percent Deviation (RPD) as below. Suppose fiand fidenote
the indicator obtained by the proposed and comparison algo-
rithms, then we have
RPDi→j=fj−fi
fi
×100%.(18)
It can be seen from Table II that the proposed method
outperforms the other benchmark methods for minimizing both
the makespan and maximum delay in all scenarios tested.
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10 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
Fig. 10. Comparison of performance indicators in different traffic scenarios. The left, middle, and right plots are representative of makespan, maximum
delay, and the number of rolling horizon cycles without the occurrence of spillbacks, respectively.
TAB L E I I
COMPUTATIONAL RESULTS OF DIFFERENT METHODS
The makespan and maximum delay can be reduced by up
to 24.2% and 34.6%, respectively. Besides, the proposed
method maintains the maximum delay among vehicles below
8 seconds for all scenarios, ensuring fairness in passing the
intersection.
Furthermore, the performances of all these methods are
affected by the arrival flow, as shown in Fig. 10. First, it can
be seen that all these methods perform similarly when the
arrival flow is low (e.g., from 720 to 1080 vph/lane) since
vehicles are able to pass the intersection without additional
intervention. In other words, there is little room for opti-
mization in these cases. However, the makespan and the
maximum delay of solutions obtained by the FIFO-, polling-
, and scheduling-based methods increase dramatically with
the arrival flow (i.e., from 1440 to 1800 vph/lane). Second,
it is observed that either the FIFO- or polling-based meth-
ods cannot trade off multiple objectives. For example, the
FIFO-based method is inferior to the polling policy in terms
of efficiency (i.e., makespan) but outperforms the latter in
terms of fairness (i.e., maximum delay). Third, it can be
seen that the scheduling-based method overmatches FIFO-
and polling-based methods in both objectives within low-flow
traffic states. However, its performance has weakened to a level
similar to the polling-based method in medium and high-flow
traffic states, which suggests that the traditional scheduling
method has limitations and cannot work stably in all traffic
scenarios.
By contrast, the proposed VPA-AIM algorithm performs
better than all the benchmark methods. Moreover, the proposed
algorithm keeps the makespan of the traffic scheduling scheme
below the threshold value when the arrival flow is not greater
than 1800 vph/lane. As shown in Table II, when the arrival
flow over 1440 vph/lane, the makespans of FIFO-, polling-,
and scheduling-based methods exceed T+Tmin =20 +9=
29 s, which is the threshold value for ensuring that spillbacks
will not occur as stated in Eq. (3). If the makespan of the
current traffic scheduling scheme exceeds this threshold value,
the queue will be carried over from the current horizon to the
next one, which may cause delays to propagate backward and
accumulate, eventually leading to congestion and spillbacks.
Although the resulting makespan of our method may exceed
the threshold value in over-saturated scenarios, it does not
exceed that value too much and can remain stable for a longer
period of time than those of benchmark methods, and thus our
method is more efficient in avoiding spillbacks and mitigating
congestion.
According to Property 1, the number of rolling horizon
cycles without the occurrence of spillbacks is shown in Fig. 10.
It can be seen that the proposed VPA-AIM algorithm can avoid
spillbacks in normal traffic states (when the arrival flow is not
greater than 2520 vph/lane). Moreover, the proposed method
provides a mitigation mechanism to regulate spillbacks caused
by extreme arrival flows (i.e, 2880-3600 vph/lane). Although
the propagation of delay cannot be avoided in these situations,
the number of rolling horizon cycles without the occurrence of
spillbacks resulting from the proposed method is larger than
the benchmark methods, which suggests that it can disperse
traffic for a longer time.
C. Traffic Scheduling and Trajectory Design Schemes
The differences in traffic scheduling schemes obtained by
different methods in different arrival flows are demonstrated
in Fig. 11 using the conflict-duration-graph developed in our
previous study [37]. In short, the conflict-duration graph is
used to denote the occupation state of the merging zone,
where each block denotes the periods occupied by a vehicle.
Besides, the left and right endpoints of each block correspond
with the start time t∗
k,iand departure time t+
k,iof vehicles,
respectively. Additionally, the interval between two blocks
denotes the separation in time of two vehicles to ensure safety,
whose minimum value is decided by the sequence-dependent
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 11
Fig. 11. Comparison of traffic scheduling scheme in different traffic
scenarios. The top, middle, and bottom plots are representative of light,
medium, and heavy load traffic.
Fig. 12. Optimized vehicle trajectories under different arrival flows. The
top, middle, and bottom plots are representative of light, medium, and heavy
load traffic. The upper half of each plot depicts vehicle trajectories of lane 1,
while the lower half depicts those of lane 0.
minimum switching time. Note that it is non-trivial and
challenging to calculate the optimal platoon formation scheme
and passing sequence and time, which cannot be obtained by
heuristic rules since multiple constraints need to be satisfied
simultaneously.
The optimized trajectories for vehicles obtained by the
proposed method are shown in Fig. 12. The upper and lower
half of each plot depicts the trajectories of lane 1 and lane 0,
respectively, while the vertical axis describes the distance of
vehicles from the merging zone. First, it can be seen that the
platoon configuration is not always consistent, but vary in dif-
ferent situations. This happens because the platoon formation
scheme is designed by the optimization model appropriately
according to real-time traffic states. Hence, more vehicles
are assigned to a platoon when the arrival flow increases.
Second, the generated trajectories are smooth enough without
illegal speed jumps, while there is enough space between
trajectories to prevent collisions. Hence, vehicles can pass the
intersection collaboratively without stopping with the support
of well-designed traffic scheduling and trajectory planning
schemes. Third, it can be observed that the number of vehicles
assigned to a platoon increases with the arrival flow. In high-
flow traffic states, the right-of-way will be given to groups of
vehicles in two lanes alternately with different lengths of time.
This is similar to the phenomenon at signalized intersections
with an adaptive signal controller [90], [91], [92]. Hence, when
it comes to signalized intersections, the proposed algorithm
can be extended and used to design signal timing plans that
determine the optimal green time of each lane. Moreover,
the proposed algorithm can generate smooth trajectories for
vehicles and cluster them into platoons that can properly use
the green light windows and pass the intersection at high speed
to avoid stop-and-go movements.
It can be seen from Fig. 13 that the CP solver can find the
optimal traffic scheduling scheme for up to 32 vehicles with a
sub-second computation time using a 20-second time horizon.
However, the complexity and difficulty of problem-solving
grow with the number of vehicles, leading to an exponentially
increased computation time. For those scenarios with more
than 36 vehicles to be controlled, a smaller planning horizon
is suggested to reduce the number of decision variables such
that the computation time can be maintained within the sub-
second level. Otherwise, the CP solver may not be able to find
the optimal solution within the limited runtime budget. From
the practical point of view, the classical FIFO policy can be
employed as an alternative for those scenarios without suffi-
cient time to optimize or cannot find any feasible solutions.
Additionally, recall that we incorporate a coupled constraint
i,e, Eq.(12), derived from the lower-level trajectory planning
algorithm into the upper-level scheduling model, which is
used to prevent vehicles from stopping. This constraint can be
relaxed (i.e., increase the value of Tmax) if the solver cannot
find a feasible solution since it is possible that vehicles have to
stop and wait before the stop line of intersections at extremely
high-flow traffic states.
D. Mixed Traffic Scenarios With Diverse Autonomy Levels
In order to analyze the impact of different CAV penetration
rates on the performance of the proposed method, we generate
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12 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
Fig. 13. Computation time of the upper-level traffic scheduling model.
9×9 groups of test scenarios whose arrival flows vary
from 720 to 3600 vph/lane and penetration rates vary from
100% to 20%. Meanwhile, each group of traffic scenarios is
simulated five times with different random seeds. To quantify
the robustness of the proposed method in different arrival flows
and penetration rates, we define the Average Performance
Degradation (APD) as below. Let iindex the penetration
rate of CAVs and jindex the arrival flow, we can denote
the performance indicator (i.e., the makespan and maximum
delay) under arbitrary conditions and a specific condition with
100% penetration rate by fi,jand f∗
j, respectively. Then,
we have
APDi,j=fi,j−f∗
j
f∗
j
×100%.(19)
It can be seen from Fig. 14 that, compared with the pure
autonomy scenarios, both performance indicators (i.e., the
makespan and the maximum delay) experience degradation
when the penetration rate decreases in all kinds of arrival
flow. This happens because HDVs require much more space
than CAVs to ensure safety, leading to heavier burdens for
the limited road resource. Additionally, the requirement that
platoon leaders be CAVs imposes additional constraints on
the optimization problem, leading to performance degradation
of the optimal solution. Apart from this, it is also observed
that the performance degradation in terms of the makespan
becomes more significant when the arrival flow increases,
the maximum value of which reaches 60% when the arrival
flow and penetration rate becomes 3600 vph/lane and 20%,
respectively. By contrast, the performance degradation in terms
of the maximum delay reaches 80% when the arrival flow and
penetration rate becomes 2160 vph/lane and 20%, respectively.
An example of the traffic scheduling and trajectory planning
scheme in the mixed traffic scenario with dynamic traffic
demands is illustrated in Fig. 15. Recall that HDVs are
able to track the desired speed profile with limited track-
ing errors according to the Assumption 2. It can be seen
that the upper-level scheduling model tends to assign more
space for HDVs than CAVs to pass through the merging
zone while avoiding collisions. Meanwhile, the lower-level
trajectory planner is able to estimate the maximum tracking
error boundaries of HDVs. Further, the planner will adjust
the trajectories of CAVs such that they can maintain a safe
separation distance from those HDVs nearby to ensure safety.
Simulation results indicate that the proposed algorithm is
Fig. 14. Average performance degradation of the proposed method under
different penetration rates of CAVs. The value of performance degradation
denotes the average percentage of increase in performance indicators com-
pared with that in the 100% CAV penetration rate condition.
Fig. 15. Mixed autonomy scenario with dynamic traffic demands.
sufficiently robust to handle mixed autonomy conditions
involving CAVs and HDVs with dynamic traffic demands.
VI. CONCLUSION
This paper proposes a bilevel optimization algorithm, named
VPA-AIM, to coordinate the merging of CAVs at unsignalized
intersections. In this work, the upper-level task is referred
to as platoon-aware traffic scheduling, which determines the
platoon formation scheme of vehicles during the control zone
and allocates the passing sequence and timeslots of platoons
through the merging zone, with the goal of reducing the
makespan and maximum delay to enhance operational effi-
ciency and fairness. The lower-level task is referred to as
multi-vehicle trajectory planning, which is about designing
referenced trajectories for vehicles during the process of pass-
ing through the control and merging zones, with the goal of
reducing overall energy consumption and avoiding/mitigating
spillbacks. The two levels are coupled by dynamics constraints
and the arrival and departure times of vehicles. The bi-level
optimization framework optimizes traffic operation within a
rolling horizon to balance traffic performance and computa-
tional efficiency. At each decision step, the optimal scheduling
scheme at the upper level can be solved by the CPLEX
Constraint Programming solver with sub-second computation
time, while the near-optimal trajectories in the lower level can
be generated by the coevolutionary algorithm modified from
our previous work [70], [71]. In addition, this paper establishes
the quantifiable connection between the makespan of the
traffic scheduling scheme and the occurrence of spillbacks,
demonstrating that the optimization of the makespan helps to
avoid/mitigate spillbacks in normal/saturated traffic states. It is
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DENG et al.: COOPERATIVE PLATOON FORMATION OF CAVs 13
also noteworthy that the proposed algorithm can be extended to
mixed traffic scenarios with various penetration rates of CAVs
based on the assumptions that HDVs have bounded tracking
errors and CAVs serve as platoon leaders.
The proposed VPA-AIM algorithm is tested in multiple
scenarios with various arrival flows (i.e., 720-3600 vph/lane)
and compared with FIFO-, polling-, and scheduling-based
methods in MATLAB. Extensive numerical examples suggest
that the proposed algorithm outperforms benchmark methods
in terms of efficiency and fairness. For example, the makespan
and maximum delay of traffic scheduling schemes can be
reduced by up to 24.2% and 34.6%, respectively. Besides, the
proposed algorithm remains stable in all scenarios tested, while
the performance of benchmark methods degrades dramatically
with the increase in the arrival flow. Moreover, it has the largest
number of rolling horizon cycles without the occurrence of
spillbacks among benchmark methods, which suggests that it
can mitigate spillbacks even in saturated traffic states.
This study opens several directions for future work. First,
we would like to further generalize the proposed algorithm to
a complex intersection with multiple approaches, and conduct
comprehensive experimental validation using laboratory-scale
Arduino cars. Second, we will extend the algorithm to urban
arterial intersections or networks and devise signal coordina-
tion strategies to enable green waves with consideration of
spillbacks. Third, we will consider intersection control with
multiple types of road users such as transit vehicles that
require priority and pedestrians that could impose additional
randomness on the system dynamics. Finally, we would like to
leverage the interactive protocol proposed by [93] to establish
a verifiable communication scheme between authorized inter-
section controllers and vehicles, which helps to ensure the
authenticity, integrity, and confidentiality of the mobility data
and control commands being transmitted, and thus reduces the
risk of data privacy and cybersecurity issues.
ACKNOWLEDGMENT
The authors would like to thank Prof. Xiangrui Zeng
(Huazhong University of Science and Technology) for discus-
sions on Section III.
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Zhiyun Deng (Graduate Student Member, IEEE)
received the B.E. degree from the School of Auto-
motive Engineering, Wuhan University of Technol-
ogy, Wuhan, China, in 2020, and the M.S. degree
from the School of Mechanical Science and Engi-
neering, Huazhong University of Science and Tech-
nology (HUST), Wuhan, in 2022. He is currently a
Research Assistant with HUST. His current research
interests include planning and scheduling algorithms
for emerging mobility, and the automatic control of
vehicular systems with deep reinforcement learning.
Kaidi Yang received the B.Eng. and M.Sc. degrees
from Tsinghua University and the Ph.D. degree from
ETH Zurich. He is currently an Assistant Professor
with the Department of Civil and Environmental
Engineering, National University of Singapore. Prior
to this, he was a Post-Doctoral Researcher with the
Autonomous Systems Laboratory, Stanford Univer-
sity. His main research interests include the opera-
tion of future mobility systems enabled by connected
and automated vehicles (CAVs) and shared mobility.
Weiming Shen (Fellow, IEEE) received the bach-
elor’s and master’s degrees from Northern Jiao-
tong University, Beijing, China, in 1983 and 1986,
respectively, and the Ph.D. degree from the Uni-
versity of Technology of Compiegne, Compiègne,
France, in 1996. He is currently a Professor with
the Huazhong University of Science and Technol-
ogy, Wuhan, China, and an Adjunct Professor with
the University of Western Ontario, London, ON,
Canada. His research interests include intelligent
software agents, wireless-sensor networks, the IoT,
big data, and their applications in industry. He is a fellow of the Canadian
Academy of Engineering and the Engineering Institute of Canada.
Yanjun Shi received the B.S. degree in mechanical
engineering from Dalian Ocean University, China,
in 1996, the M.S. degree in mechatronic engineering
from Beihang University, China, in 1999, and the
Ph.D. degree in computer engineering from the
Dalian University of Technology, China, in 2005.
He is currently an Associate Professor with the
School of Mechanical Engineering, Dalian Univer-
sity of Technology. He has authored or coauthored
over 80 papers in scientific journals and international
conferences. His research interests include collabo-
rative planning and scheduling, multi-access edge computing, 5G applications,
and autonomous vehicles. He is the Vice Chair of the IEEE SMC Dalian
Chapter. He is an Associate Editor of the IET Collaborative Intelligent
Manufacturing.
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