Analysis of Cooperative Driving Strategies for Non-Signalized Intersections

Abstract

In this paper, we study the difference between two major strategies of cooperative driving at non-signalized intersections: namely the “ad hoc negotiation based” strategy and the "planning based" strategy. The fundamental divide of these two strategies lies in how to determine the passing order of vehicles at intersections. The "ad hoc negotiation based" strategy makes vehicles roughly follow first-come-first-served order but allows some adjustments. This leads to a local optimal solution in many situations. The "planning based" strategy aims to find a global optimal passing order of vehicles. However, constrained by the planning complexity and time requirement, we often stop at a local optimal solution, too. We carry out a series of simulations to compare the solutions found by two strategies, under different traffic scenarios. Results indicate the performance of a strategy mainly depends on the passing order of vehicles that it finds. Although there exist several trajectory planning algorithms associating with the solving process of passing orders, their differences are negligible. Moreover, if the traffic demand is very low, the performance difference between two strategies is small. When the traffic demand becomes high, the "planning based" strategy yields significantly better performance since it finds better passing orders. These findings are important to cooperative driving study.

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 Abstract—In this paper, we study the difference between two
major strategies of cooperative driving at non-signalized
intersections: namely the “ad hoc negotiation based” strategy and
the "planning based" strategy. The fundamental divide of these
two strategies lies in how to determine the passing order of
vehicles at intersections. The "ad hoc negotiation based" strategy
makes vehicles roughly follow first-come-first-served order but
allows some adjustments. This leads to a local optimal solution in
many situations. The "planning based" strategy aims to find a
global optimal passing order of vehicles. However, constrained by
the planning complexity and time requirement, we often stop at a
local optimal solution, too. We carry out a series of simulations to
compare the solutions found by two strategies, under different
traffic scenarios. Results indicate the performance of a strategy
mainly depends on the passing order of vehicles that it finds.
Although there exist several trajectory planning algorithms
associating with the solving process of passing orders, their
differences are negligible. Moreover, if the traffic demand is very
low, the performance difference between two strategies is small.
When the traffic demand becomes high, the "planning based"
strategy yields significantly better performance since it finds
better passing orders. These findings are important to cooperative
driving study.
Index Terms—Cooperative driving, planning, Ad hoc
negotiation, non-signalized intersection
I. INTRODUCTION
OOPERATIVE driving emerges as a promising method to
improve traffic safety and efficiency. Its key idea is to
apply wireless communication to organize and coordinate the
movements of neighboring vehicles [1-4]. To reach this goal,
Manuscript received March 6, 2016; revised May 30, 2017; October 26,
2017. This work was supported in part by National Natural Science Foundation
of China (Grant No. 91520301) and National Major Research and Development
Project of China 2016YFB0100906. (Corresponding author: Li Li)
Y. Meng is with Department of Automation, Tsinghua University, Beijing,
China 100084.
L. Li is with Department of Automation, NTList, Tsinghua University,
Beijing, China 100084. (Tel: +86(10)62782071, email: li-li@tsinghua.edu.cn).
F.-Y. Wang is with State Key Laboratory of Management and Control for
Complex Systems, Institute of Automation, Chinese Academy of Sciences,
Beijing, China 100080.
K. Li is with the State Key Lab of Automotive Safety and Energy,
Department of Automotive Engineering, Tsinghua University, Beijing, China
100084.
Z. Li is with Department of Automation, Tsinghua National Laboratory for
Information Science and Technology, Tsinghua University, Beijing 100084,
China and also with the Graduate School at Shenzhen, Tsinghua University,
Shenzhen, China 518055.
we need to solve a number of problems, including high-speed
and high-reliability vehicle-to-vehicle communication design
[5-6], precise speed control of autonomous vehicles, and
vehicle trajectory planning. Before further discussing, let us
first explain the difference between the concept of cooperative
driving and two related concepts.
Advanced traffic signal control via vehicle-to-infrastructure
(V2I) communication [7-11] assumes that vehicles' movements
will only be controlled by traffic lights. So, our objective in
such situations is to collect and predict accurate arriving rates
of traffic flows in the next few minutes so that we can set the
best traffic light timing plan to maximize traffic efficiency. The
introduction of V2I communication makes such an objective
feasible and not too hard to reach. However, we only know
which and when vehicles are coming. In contrast, cooperative
driving uses vehicle-to-vehicle (V2V) communication to
collaborate the vehicles' movement so that we also control the
arrival time of every vehicle. This further enriches the
flexibility of traffic control and thus leads to a further boost of
traffic efficiency.
Platoon-based traffic control approaches group vehicles into
several platoons before they arrive into the vicinity of the
intersection [12-15]. A platoon of vehicles can then pass the
intersection without any interruption so as to increase traffic
efficiency. Differently, cooperative driving [16-19], [2] not
only allow vehicles to change their speeds so as to form groups
before they arrive into the vicinity of the intersection, but also
allow some vehicles coming from different branches to pass
through the intersection simultaneously. As a result,
appropriate cooperative driving could make full use of the
capacity of the intersections.
A successful implementation of cooperative driving depends
on solving several difficulties. First, we need to guarantee that
V2V communication is fast and reliable. There are several good
surveys concerning the recent advancements on this issue.
Readers may check [20-21] for a detailed explanation. Second,
we need to design automated connected vehicles to follow the
guidance so as to reach and pass the intersection in a controlled
manner. Third, we need to establish a good strategy to guide
vehicles. There were several good comprehensive surveys in
[4], [6]. In this paper, we will focus on the third issue.
In this paper, we focus on the last difficulty. During the last
decades, different coordination strategies had been proposed
for cooperative driving. As summarized in [4], [6], most of
them can be categorized into two kinds:
Analysis of Cooperative Driving Strategies for
Non-Signalized Intersections
Yue Meng, Li Li, Fellow, IEEE, Fei-Yue Wang, Fellow, IEEE, Keqiang Li, and Zhiheng Li, Member,
IEEE
C

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The first kind of approach can be named "ad hoc negotiation
based" [16-17], [21-23]. It considers the vehicles that are about
to arrive at the intersection and formulates short-term driving
plans for them via bilateral negotiations. Such a strategy indeed
makes vehicles roughly follow first-come-first-served order to
pass the intersection though allowing some adjustments. This
leads to a local optimal solution in many situations [24-25].
The second kind of approach can be named "planning based"
[18], [2]. It considers the vehicles that will arrive within a
certain spatial scope of the intersection and formulates
relatively long-term driving plans for vehicles [8], [26-28].
Generally, "planning based" approaches provide more
flexibility to cooperative driving and thus allow potentially
better traffic efficiency than "ad hoc negotiation based"
approaches. However, the computation cost of "planning
based" approaches grows significantly, as the number of
vehicles increases. Nevertheless, constrained by the planning
complexity and time requirement, we often stop at a local
optimal solution before reaching the global optimal solution.
Our major purposes of this paper are fourfold.
First, we aim to fully compare the performance between two
cooperative driving approaches and to find out what factors
mainly causes the difference. Much literature in this field only
studies one of these two kinds of methods but seems to have no
idea of the other one. Since the above two methods are the roots
of almost all existing work on cooperative driving, a
comprehensive comparison between these two methods helps
to answer many important problems that have been omitted in
recent literature.
Second, we aim to clarify the influence of trajectory planning
in cooperative driving. Most existing studies assume that the
passing order is the major factor, since it determines the time
points of vehicles entering and leaving the potential conflicting
area [4], [8]. The formulated passing order indeed acts as the
traffic signals in the traditional intersection solution. However,
the determination process of passing order tightly interlaces
with vehicle trajectory planning. Few studies have fathomed
the possible difference between various trajectory planning
algorithms.
Third, we also aim to introduce some novel techniques for
cooperative driving studies. Specially, we had noticed that
some papers neglected the influence of congestions and thus
made bias conclusions. Hence we adopt virtual queue method
[33-35] into generation of vehicles to provide fair and accurate
evaluation of system performance.
Fourth, we formulate the communication delay and position
measurement errors that are unavoidable in design cooperative
driving strategy into a lump parameter of position uncertainty.
So, we can then design error-tolerance trajectory planning for
cooperative driving. In addition, we also simplify the trajectory
planning part of the planning-based approach which accelerates
the computation.
Our tests show that
1) The passing order plays the major role of cooperative
driving. The performance of a strategy depends on the passing
order of vehicles that it finds. The difference between two
representative trajectory planning algorithms is small and could
be omitted.
2) If the traffic demand is very low, the performance
difference between two strategies is small; but when the traffic
demand becomes high, the "planning based" strategy yields
significantly better performance, since it finds better passing
orders.
3) The collision probability can be noticeably reduced, if an
appropriate tolerance threshold is set in trajectory planning, so
as to deal with position uncertainty.
All these findings are important to cooperative driving
research. To better explain our findings, the rest of this paper is
arranged as follows. In Section II, we briefly review the
formulation and assumptions of two cooperative driving
strategies. In Section III, we present the simulation platform for
traffic performance evaluation. In Section IV, we design a series
of numerical tests to compare different approaches. In Section
V, we conclude the whole paper.
II. PROBLEM PRESENTATION
A. The Intersection Scenario
In this paper, we study isolated non-signalized intersections,
as was studied in [16-18]. For simplicity, we assume the
intersection contains four branches coming from the north,
south, and east and west; see Fig.1 for an illustration. For
presentation simplicity, we call the area within the outer and
inner circles as annuls, the area within the inner circle as the
crossing area, and the square overlapping area as the junction.
The lane index is denoted clockwise.
Vehicles approaching the intersection are allowed to pass
straight through, turn left or turn right but not U-turn at the
crossing area. The other intersections with different geometric
shapes cannot be handled in a similar way and are thus omitted.
Vehicle flows are assumed to arrive continuously to the
intersection. For a particular time, we only need to consider a
few vehicles moving in the vicinity of the intersection. This
assumption greatly simplifies the problem [16-18]. Moreover,
we assume that all vehicles have relatively low speeds when
approaching the intersection, and they will not change lanes
after entering the outer circle, since it is often too close for
vehicles to safely change lanes without causing collisions.
In this paper, combining the ideas of both "ad hoc
negotiation based" and "planning based" cooperative driving
approaches, we set up two virtual circles centered at the
junction center; see Fig.1. At each time that a new vehicle
enters the outer circle, the trajectories of all vehicles within the
annulus will be rescheduled according to the latest states of the
vehicles. Only the vehicles that are running within the annulus
will be considered for trajectory planning. Once a vehicle
enters the inner circle, its trajectory will not be changed for
safety reasons. It does not mean that a vehicle within the
crossing area will not change its speed. Indeed, it means that the
planned trajectory of a vehicle will not be changed, if it enters
the inner circle.
In addition, we assume that all the information about the
vehicles' driving states (speeds, positions, etc.) and intensions

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are instantly available to every other vehicle within the outer
circle with the aid of vehicle-to-vehicle (V2V) communication.
Any kinds of cooperative driving algorithms should arrange
the velocities of the vehicles to ensure that they will not collide
either in the branches or in the crossing area. No dead-lock
scenario is allowed to happen, either. Besides being
collision-free, cooperative driving algorithms also aim to
smooth traffic.
Inner Cycle
Outer Cycle
Annulus
Crossing
Area
Junction
Outer Cycle
Radius
Fig. 1. An illustration of cooperative driving around a non-signalized
four-way intersection. Each branches has two lanes with opposite
directions.
B. Planning Based Approaches
As pointed out in [18], [8], the key problem of cooperative
driving around intersections, is to determine the passing orders
that vehicles pass the junction area in this paper; see Fig.2 for
an example of the passing order.
A C
B D
Fig. 2. An illustration of the passing order. Suppose vehicles A, B, C
and D are going to drive through the intersection. The passing order A
B | C | D denotes that vehicle A and B passes the intersection
simultaneously; then Vehicle C passes the intersection; finally Vehicle
D passes the intersection. Some passing orders, e.g. C | A B | D, are
apparently invalid, since we do not allow overtaking here.
Unfortunately, the passing order planning problem is heavily
correlated with detailed trajectory planning for vehicles. If the
passing order of all vehicles within the annulus is scheduled, we
need to construct the corresponding trajectories of all vehicles
with respect to the given performance indices (e.g. to find the
set of trajectories consuming the least total delay) to check the
feasibility of this scheduled passing order. The obtained
performance value, in return, characterizes the quality of a
passing order. The ac/deceleration capability of vehicles, the
speed limits around intersections, and the order of vehicles
arriving at the annulus will be taken as the scheduling
constraints for planning.
In "planning based" approaches, we need to enumerate all
the valid passing orders in the solution space to find the global
optimal passing order which is tightly linked with the best set of
trajectories. However, the process of finding the best trajectory
from all the passing orders owns a heavy computational cost,
due to two reasons:
First, the number of all the valid passing orders in the
solution space generally grows exponentially with the number
of vehicles considered.
Second, to construct the time-optimal trajectories of all the
vehicles is also time consuming, if a passing order is selected.
So, different algorithms have been proposed to find a good
passing order instead [8], [26-28]. In this paper, we adopt the
original tree-like solution space representation and pruning
technique that is used to quickly filter invalid passing orders
when searching among the solution space [2]. However, we
generate time-suboptimal trajectories for each valid passing
order to reduce planning time; see Section III.A for detailed
explanations.
C. Ad Hoc Negotiation Based Approaches
As explained in [17], the passing order in "ad hoc negotiation
based" approaches is mainly determined by a first-come-first-
served reservation rule.
At each time to reschedule, all the vehicles estimate the time
used to approach the intersection and then send reservation
requests (the estimated time of each vehicle to pass the crossing
area) to the intersection. The intersection receives all these
reservation requests, sorts and handles them by the ascending
order of the estimated passing times. The intersection then uses
the grid-occupancy test to judge whether to accept the
reservation or delay it a little bit until the previous conflicting
request had been served. In addition, the request of a vehicle
will not be handled until all the vehicles in front of it on this
lane have received an acceptance from the intersection for the
request, which will prevent some deadlock scenario. The core
of "ad hoc negotiation based" approaches can be summarized as
Fig.3.
"Ad hoc negotiation based" approaches do not strictly plan
the trajectories of vehicles but allow vehicles to run in a normal
leading-vehicle-following manner. This also reduces the
computation costs.

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From the viewpoint of optimization, "ad hoc negotiation
based" approaches actually use a greedy search to determine
the passing order of vehicles. This trick leads to not just a
simple decision rule, but local optimal solutions in many
situations. To the best of our knowledge, few studies have
thoroughly discussed the properties of the local optimal
solutions that have been found by using first-come-first-served
rule.
Speed Planning
Time Estimating
Grid-Occupancy Test
Trajectory Planning
For each
vehicle
For each
reservation
request
Fig. 3. The sketch of "ad hoc negotiation based" approaches.
III. THE SIMULATION PLATFORM
In order to compare the performance of different cooperative
driving strategies, we establish a simulation platform in this
paper. Its major function is to determine how vehicles move
through the intersection.
Since no lane change is allowed, any vehicles within the
outer circle may fall into one of three states: 1) car-following at
branches; 2) passing the crossing area; and 3) the switching of
states between state 1) and 2). In non-signal intersections with
leading vehicles possibly turning or going straight, the
following vehicles cannot drive too fast. Also, considering
drivers comfort during the turning process, the turning speed
also should not be high. Therefore, in all these situations, if this
vehicle does not make a left/right turn at the crossing, the
maximum passing speed is set as 9m/s in the following
numerical simulations; if the vehicle needs to steer, the
maximum steering speed is set as 4m/s for safe passing.
In this paper, both "planning based" and "ad hoc negotiation
based" approaches use the same car-following model at
branches but different simulation models to determine how to
pass the crossing areas. We will present the detailed updating
rules respectively in the following sections.
A. Car-Following Model
To fairly compare two kinds of approaches, we use a
simplified trajectory planning algorithm which requires much
less computational costs than the ones used in existing
"planning based" approaches. More precisely, we allow the first
vehicle within the annulus to run at the maximum allowed
speed. The other vehicles will use a set of rules to track their
leading vehicles according to the designed passing order to
determine their trajectories. That is, we turn a complex
trajectory planning problem into a series of car-following
simulation problems that will be sequentially solved.
Our considerations are trifold here:
First, the trajectories generated by a car-following model
may not be the best trajectories for cooperative driving.
However, if planning based approaches still work better than
negotiation based approaches, we are safe to conclude that
planning based approaches (which use even advanced
trajectory planning methods) should be adopted rather than
negotiation based approaches.
Second, to determine the best trajectories is really time
consuming. So, we suggest that we could use a simple
car-following model to determine the trajectories when our
computational resources are limited. In the future, we need to
invent more powerful (faster and performance-superior)
trajectory planning methods to replace the current ones.
Third, we can use a car-following model to generate
suggestive trajectories for both automated vehicles and human
drivers. So, the obtained cooperative driving plan could be
helpful for mixed (manual and automated) traffic control. Since
automated vehicles still need a long period of time to gain a
larger share of the market, a car-following model based
trajectory planning method still has its unique benefit.
The car following model used here is an extension of the
collision avoidance model [29]. We assume that the following
vehicle should keep a reasonable distance from the leading
vehicle. The following vehicle first calculates the final distance
)(tL
since time
t
, if it ac/decelerates to reach the same speed
of the leading vehicle with a fixed ac/deceleration
max
a
(particularly

4m/s2 in the following numerical simulations),
based on the current gap and speeds.
That is, the vehicle will first calculate
max
22
2
)()(
)()()( a
tvtv
txtxtL followlead
followlead


(1)
where the positions and the speeds of both the leading and
following vehicles at time
t
are denoted as
)(txlead
,
)(txfollow
,
)(tvlead
, and
)(tvfollow
respectively.
Then, it judges whether this final distance is big enough, by
comparing
)(tL
with the desired distance
G
. If
)(tL
is
smaller than
G
, the following vehicle will decelerate. If
)(tL
is larger than
G
, then the vehicle will accelerate until it is
running at the maximum speed. Therefore, we can figure out
the speed of the following vehicle as

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 
 





 GtLTatvv
GtLTatv
Ttv follow
follow
follow )(,)(,min
)(,)(,0max
)( maxmax
max
(2)
where
max
v
is the maximum car-following speed limit in this
scenario (particularly 9m/s in the following numerical
simulations).
T
is the simulation time interval (particularly
0.2s in this paper).
The desired distance
G
is introduced to avoid collisions in
some extreme conditions. In almost all the existing work in this
field, researchers assume that V2V communications work in a
perfect way. So, the gap between vehicles can be kept very
small. However, this arrangement has some risks. For example,
suppose one vehicle suddenly stops in front of the crossing area
for certain reasons (e.g. mechanism fault), the following
vehicle may not have enough gap to stop, if the gap is kept very
small. Moreover, this gap is also maintained to tolerate
potential position/speed estimation errors or communication
delays. In the following simulations, we set
G
as 12m so that
the vehicles can have enough gaps to slow down before
entering the junction. We will discuss how to select an
appropriate desired distance
G
in Section IV.C.
B. Crossing Area Passing Model for Planning Based
Approaches
In this paper, we adopt the virtual vehicle mapping
techniques that were used in [30-32].
In general, a vehicle may encounter four kinds of situations
when passing crossing areas. The first kind of situation is free
passing, which means this vehicle neither has any leading
vehicles nor meets any conflicting vehicles. So, it will manage
to pass the crossing area using the least time. In other words,
this vehicle should accelerate as much as possible until it
reaches the maximum crossing speed or enters the inner circle.
The second kind of situation is consistent following, which
means this vehicle continuously follows its leading vehicle
before, within and after passing the crossing. This situation is
similar to car following outside the crossing.
The third kind of situations is first leading vehicle following
and then free driving, when the leading vehicle turns to other
lanes. We will let the following vehicle first track the leading
vehicle, and then let it accelerate to maximum possible speed
after the previous leading vehicle has entered the new lane.
The fourth kind of situation is first free driving and then
following the merging vehicle, which means a conflicting
vehicle will enter the crossing area right before this vehicle and
become its new leading vehicle. We will map a virtual vehicle
into the destination lane of the following vehicle and let the
following vehicle use the car-following model to track this
virtual vehicle so as to avoid collision. For example, as shown
in Fig.4, Vehicle A moves from lane 7 to lane 6 and vehicle B
moves from lane 1 to lane 6. Vehicle B must make enough
headway to avoid collision with vehicle A. So, vehicle B
generates a virtual vehicle A' by mapping vehicle A into its own
lane and using the car-following model to follow virtual vehicle
A'. The detailed explanation of virtual vehicle mapping
technique can be found in [30-32], [2].
The whole flow chart of trajectory planning used by the
planning-based approach is shown in Fig.7. The other details of
the planning-based approach can be found in [2].
A
Headway for Safety
Distance
Headway for Remain
Distance through the
Intersection
12
3
4
6 5
8
7
A' B
Remain Distance through
the Intersection
Fig. 4. An illustration of virtual vehicle mapping technique used by
"planning based" approaches.
C. Crossing Area Passing Model for Ad Hoc Negotiation
Based Approaches
The "ad hoc negotiation based" approach uses another
method to determine the crossing trajectory of vehicles. It first
grids the junction into a set of reservation tiles; see Fig.5. Once
receiving the reservation parameters from an approaching
driver agent, it simulates the try-and-test trajectory of the
vehicle across the intersection. At each time step of this
try-and-test simulation, it determines which reservation tiles
will be occupied by the vehicle so as to detect potential
collisions (if at any time, the requesting vehicle occupies a
reservation tile that is already reserved by another vehicle, it
rejects the request). Otherwise, the policy accepts the
reservation and saves the try-and-test trajectory for future
collision tests.
12
3
4
6 5
8
7
12
3
4
6 5
8
7
(a) (b)
Fig. 5. An illustration of gridding technique used by "ad hoc
negotiation based" approaches. (a) the gridding of the junction area, (b)
a collision detected between two vehicles moving in different
directions.
If the request is rejected, the inquiring vehicle will generate

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another request in which it will occupy the junction area a short
time (e.g. 1 second) later. The above try-and-test simulation
will be executed again to check whether this delayed request is
valid. If the new request is accepted, the system determines a
crossing area passing plan for the inquiring vehicle; otherwise,
the above process will be repeated until we finally find a valid
crossing area passing plan.
The whole flow chart of trajectory planning used by the "ad
hoc negotiation based" approaches is shown in Fig.6. The other
details of the “planning-based” approaches can be found in
[17].
Do grid simulation
test
Make a plan that
pass the junction
as fast as possible
Collide with
grid-occupying
record
Is request for
reservation
Yes
Is request for
new reservation
Yes (New request)
No
Change request:
Delete related grid-
occupying record
No
Accept reservation
request and give
speed instructions
No
Make a plan that
pass the junction in
unchanged speed
Yes
Do grid simulation
test
Collide with
grid-occupying
record No
Reject the request
for reservation
Yes
Cancel request:
Delete related grid-
occupying record
End
Start
Judge request type
Do aggressive plan for junction and test
validity
Do conservative plan for junction and test
validity
Fig. 6. The flow chart of crossing area passing model used by "ad hoc negotiation based" approaches.

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Drive out of
junction
Still on the first
lane
No
Plan speed for
junction
Exist leading
vehicle before
junction
Yes
No
End
Yes
Exist
conflicting
vehicle not
driving out of
junction
No
Need turn
No
Current speed
higher than up-
bound speed
No AccelerateNo
Yes
Decelerate
Yes
Calculate up-
bound speed from
car- following
model
Yes
Calculate up-
bound speed from
mapping-vehicle
model
Yes
Start
Trajectory
planning in
junction
Car-following model
Decelerate for turning
Fig. 7. The flow chart of crossing area passing model used by "planning based" approaches.
IV. SIMULATION RESULTS AND DISCUSSIONS
In the following tests, we consider the four-way intersection
shown in Fig.1. The length of every branch is set as 120m. The
radius of the inner circle is set as 20m, and the radius of the
outer circle is set as 70 m. The initial speed of all the vehicles
are set as 5m/s. We choose 0.2 as the simulation time step.
The vehicles' arrival rate (traffic demand) at each branch is
assumed to be a Poisson Process whose average value is
denoted as

. Varying the values of

, we can check the
system performance under different traffic demands. For each
round of simulation, we randomly generate a consequence of
arriving vehicles that follows the given vehicles' arrival rates
and feed this consequence to both "ad hoc negotiation based"
and "planning based" approaches, so as to guarantee the
fairness of comparison. Due to the randomness embedded in
the simulation, we run the simulation for 10 times and calculate
the mean values of systems performance for comparison.
In this test, we assume that the vehicles come equivalently
from different branches and the vehicles' arriving rate is set as

. For each branch, 1/4 of vehicles will turn left at the junction,
1/4 of vehicles will turn right at the junction, and the rest ½ of
vehicles will pass straight through the junction. We also tested
the traffic scenarios where the vehicles' arriving rates at
different branches are different. Results show that the
conclusions presented in the following subsections still hold.
So, for presentation simplicity, we only present the testing
results under the above traffic assignments.
In the following tests, we just compare the "ad hoc
negotiation based" strategy with the new "planning based"
strategy, which enumerates all the possible passing orders but

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generates time-suboptimal trajectories for each valid passing
order.
A. The Influence of Crossing Area Passing Models
In the first test, we examine the possible influence of
different crossing passing models. To eliminate the influence of
the passing order, we first simulate the "ad hoc negotiation
based" approach and record the passing order that it finds. Then,
we preserve the passing order and use a virtual vehicle mapping
technique to determine the trajectories of vehicles. Finally, we
compare the time of each vehicle to pass the junction area.
We vary

from 0.05veh/(lane•s) to 0.25veh/(lane•s). For
each given

, we run 10 rounds of simulation to suppress the
influence of randomness. In each simulation, we generate 100
vehicles and let them pass through the intersection. Fig.8 shows
the time of each vehicle to pass the junction area in two
approaches, respectively, in one round of simulation with

=0.05veh/(lane•s). It is clear that, in general, the time of each
vehicle to pass the junction area in two approaches is
equivalent.
Furthermore, we run simulations with arrival rate varying
from 0.2 vehicle/(lane•s) to 0.5 vehicle/(lane•s) to check the
mean and standard deviation of the passing through time for a
vehicle during the inner cycle. In each special scenario (with a
certain arrival rate and a certain trajectory planning method),
we simulated 10 times. In each special simulation, we generate
100 vehicles in four directions. The results illustrate that,
although some slight differences exist, the average times for a
vehicle to pass through the inner circle are quite close for both
crossing area passing models (the virtual vehicle mapping
algorithm and the collision try-and-test algorithm), no matter
what traffic demand is studied. This indicates that traffic
performance is mainly decided by the passing order.
Fig. 8. The time of each vehicle to pass the junction area in two
approaches, respectively, in one round of simulation, where

=0.05veh/(lane•s).
Table 1 A traffic performance comparison of two strategies
Arrival
Rate
(veh/(lane·
s))
Mean value
Standard deviation
Planning-b
ase
Negotiate-b
ase
Planning-b
ase
Negotiate-b
ase
0.10
1.0270
1.0974
0.6898
0.7516
0.20
1.0479
1.0923
0.6796
0.7489
0.30
1.0472
1.0919
0.6769
0.7487
0.40
1.0431
1.0902
0.6784
0.7462
0.50
1.0445
1.0905
0.6777
0.7477
B. A Comparison of Various Cooperative Driving Strategies
Before we present the main result of the second test, let us
first discuss how to fairly calculate the system performance for
cooperative driving.
As pointed out in [4], [6], it is better to use the passing-
through time rather than queuing length to measure the
performance of different cooperative driving strategies, since
the vehicles may not fully stop. However, in several previous
studies, the passing-through time was not correctly defined, so
that some not readily noticeable errors were introduced.
These errors are caused by failing to recognize the spatial
evolution of vehicles queues around intersections. Indeed, all
cooperative driving strategies focus on making better use of the
limited road resource by locating within the junction area,
because this is the bottleneck of the whole problem. As a result,
simulations reveal that, if traffic demand is high enough, the
vehicles will queue up outside of the outer circle (but not the
inner circle as intuitively expected), because cooperative
driving strategies implicitly reserve space for vehicles to
accelerate within annuls so as to make the vehicles pass the
junction area as fast as possible. The backs of vehicle queues
will propagate upstream and influence the arrival rates of
vehicles to the intersections.
It is biased to calculate the time for a vehicle to pass through
the inner circle (or the outer circle) with respect to the given
traffic demand, and use it as the performance index to evaluate
cooperative driving strategies, since the outcomes did not
correctly reflect the relationship between traffic demand and
the performance of the whole traffic system studied.
If we want to compare two cooperative driving strategies,
this primary problem must be carefully solved, because we
need to guarantee that each generated vehicle should enter two
traffic simulation systems at the same time. Otherwise, we may
get wrong estimations.
Since the simulation system cannot handle a virtual road with
infinite length, we adopt the point-queue method [33-35] which
was frequently used in network flow studies to solve this
problem in this paper. The point-queue model assumes that
traffic flow travels in free flow state from the other part of a
road network until it gets to the boundary of the intersection

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that we study. Since the vehicles queue outside the intersection,
the vehicles may not be able to enter the intersection
intermediately. So, a queue may form; but this queue does not
consume any physical length. Thus comes the name of
"point-queue". If the leading vehicle moves forward towards
the intersection and leaves enough space, the vehicle in the
front of the point-queue will then dequeue and enter the
intersection.
As shown in Fig.9, we calculate the average time interval
between the time that a vehicle is generated in the traffic
simulation system and the time that it leaves the system. If the
traffic demand is low and the traffic flow is in free flow state,
the newly generated vehicle will immediately enter the
boundary of the intersection and run on the lane. Otherwise, if
the traffic demand is high and the boundary of the intersection
occupied by vehicles, we will store this newly generated
vehicle into the corresponding point-queue that locates right on
the boundary. Using the "point-queue" technique, we obtain a
more accurate evolution of system performance.
Inner Cycle
Outer Cycle
Annulus
Crossing
Area
Junction
Outer Cycle
Radius
A
B
C
Traffic Simulation System
Fig. 9. An illustration of the point-queue technique used in this paper.
Three vehicles (Vehicle A, B, and C) are generated and stored at the
point-queue that locates at the entrance of the west branch of this
intersection.
To test traffic performance under different traffic loads, we
further vary

from 0.05veh/(lane•s) to 0.9veh/(lane•s).
Fig.10 shows the average time for a vehicle to pass through the
whole intersection, with respect to different

. We can see that
the performance of this new "planning based" strategy is
equivalent to that of "ad hoc negotiation based" strategy, when
the traffic demand is low (e.g.

=0.05veh/(lane•s) which
means the total inflow rate of all directions is 720veh/h); but it
becomes notably better than that of "ad hoc negotiation based"
strategy, when the traffic demand is high (e.g.

=0.20veh/(lane•s) which means the total inflow rate of all
directions is 2880veh/h).
Fig. 10. The average time for a vehicle to pass through the whole
intersection, with respect to different

.
Fig.11 further plots the time of each vehicle to pass the whole
system in two approaches, respectively, in one round of
simulation with

=0.05veh/(lane•s) and one round of
simulation with

=0.05veh/(lane•s). We can see that, when
the traffic demand is low, the two approaches behave similarly;
but when the traffic demand is high, the time of a vehicle to
pass the whole system in the "ad hoc negotiation based"
approach increases much faster than that in the "planning
based" approach. So, the small difference between the two
approaches in the passing time of the whole system will
cumulate, when the traffic demand is high enough. This
accumulation finally leads to a significant difference in the
performance between the two kinds of approaches.
Fig. 11. The average time for a vehicle to pass through the whole
intersection, in two approaches, respectively, in (a) one round of
simulation, where

=0.05veh/(lane•s); (b) another round of
simulation, where

=0.25veh/(lane•s).

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Similar conclusions hold when multilane traffic is
considered. Fig.12 shows the average time for a vehicle to pass
through the whole intersection, with respect to different

,
when each branch of the intersection has four lanes (two inflow
lanes and two outflow lanes). Other settings are kept the same.
We can see that planning based approaches still behave
noticeably better than negotiation based approaches. However,
when there are more lanes in the system, conflicts between
left/right-turn vehicles at the crossing area become fiercer, so
the whole through time of each vehicle increases as the number
of lanes increases.
In the rest of this paper, we still only consider the single-lane
traffic scenario.
Fig. 12. The average time for a vehicle to pass through the whole
intersection, with respect to different

.
C. The Influence of Disturbance
Subsections above answer the three problems raised in the
beginning of this paper. In this subsection, we design an
experiment to explain the need for a safety gap.
We assume that the communication and measurement errors
are all reflected by the position errors of the vehicles. The
planning based approaches adopt the biased positions and sets
up speed guidance according to the biased information.
Let us consider the four-leg intersection with a single lane in
each approach. Suppose we fix the inflow rate of vehicles at a
moderate value and vary the safety gap from a small value to a
large value. The gaps between real vehicle position and biased
vehicle position are assumed to follow a zero-mean normal
distribution, which is characterized its standard deviation

.
For each biased level of vehicle positions, we will simulate
25 times to check the times that we encounter collisions. In
each simulation, we generate 100 vehicles in four directions
with measurement errors. Once we detect a collision in the
simulation, we abort the simulation immediately. Fig.13 shows
the probability of collisions vs. the value of desired distance. It
can be seen that larger position errors lead to a higher
probability of collision; while a longer maintained distance
increases the tolerance to position errors hence reduces the
probability of collision.
It should also be pointed out that long maintained distance
will cause low efficiency in the intersection. Therefore, we
need to set an appropriate desired distance to keep a good
balance between the capability of error-tolerance and the
efficiency of traffic. In this paper, we set the desired distance as
12m as a tradeoff.
Fig. 13. The relationship between position error, desired distance, and
collision probability.
D. The Choice of Desired Distance
Since the size of the inner and outer cycles may influence the
conclusion, we further check their influences.
Fig. 14. The average whole through time per vehicle, with respect to
different radius of outer cycle.
We do not vary the size of inner cycle (which is 30m), since

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an even shorter inner cycle may be dangerous in planning based
approaches, if a vehicle reschedules its movements in a place
that is too close to the junction area.
In the tests, we increase the radius of the outer cycle and do
not change other settings. The maximum radius of the outer
cycle is still less than the length of every branch (120m). We
vary the radius of outer cycle from 60m to 95m. The vehicle's
arriving rate

is chosen as 0.20veh/(lane•s). Under each
setting, we run 10 simulations with 400 vehicles for both the
planning-based approach and the negotiation-based approach.
The obtained results, shown in Fig.14, indicate that the average
whole through time per vehicle roughly remains unchanged for
both approaches. Planning-based approaches still outperform
negotiation-based approaches when the arriving rate is high, no
matter what radius of the outer cycle is chosen.
E. The Computation Costs of Planning-Based Approach
Finally, we give some numerical testing results to show that
the current tree-pruning planning based approach needs to be
further improved, since it is still time-consuming.
When the vehicles' arriving rate

increases, we may get
more vehicles in the annulus and we need to examine more
possible passing orders so as to find the best one. We vary

from 0.20veh/(lane•s) to 0.80veh/(lane•s). Under each certain
arrival rate, we run 10 simulations with 400 vehicles each. We
record the total number of possible passing orders and the
associated consuming time for each trajectory planning process.
Finally we present the average number of possible passing
orders and the associated consuming time with respect to
different numbers of vehicles in the annulus area.
Fig.15 (a) shows the increase of the average number of
passing orders that has been examined with respect to the
number of vehicles that we need to schedule. We can see that
the average number of passing orders grows almost
exponentially with respect to the size of the number of vehicles.
(a)
(b)
Fig. 15. (a) The average number of passing orders that has been
examined vs. the number of vehicles that we need to schedule, and (b)
the average computational time vs. the number of vehicles that we
need to schedule.
Correspondingly, Fig.15 (b) shows that the average
computational time grows almost exponentially, too. So,
although the planning based approach yields significantly
better performance than the negotiation based approach, it is
more time consuming. Therefore, although we had made
changes to planning-based approach and significantly reduce
its computation costs, planning-based approach is still not
perfect. It still consumes too much running time, when we
handles large number of vehicles (more than 10). This indicates
the great need for us to further improve planning-based
approach in the near future.
V. CONCLUSIONS
In this paper, we compare two representative cooperative
driving strategies at non-signalized intersections. In essence,
the cooperative driving problem is an optimization problem.
The objective is the performance of the intersection; the arrival
times, and ac/deceleration mechanical limits of the vehicles'
mechanical limits act as constraints implicitly. The decision
variable of the cooperative driving problem is the trajectories of
vehicles around the intersection. However, we can use the
passing order of vehicles to characterize the key property of the
trajectories. So, we can take the passing order of a vehicle as the
intermediate decision variable of the cooperative driving
problems.
The basic difference between "ad hoc negotiation based" and
"planning based" cooperative driving lies mainly in their
different methods to solve this optimization problem. More
precisely, these two kinds of approaches use different
algorithms to determine the passing order of vehicles.
The "ad hoc negotiation-based" method seeks the solution in
a greedy search way, which leads the solution to roughly follow

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purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
a first-come-first-served rule. In contrast, "planning based"
approaches intend to find the best solution by enumerating all
the possible passing orders.
Our tests show that the performance of a strategy depends on
the passing order of vehicles that it finds. The difference
between two representative trajectory planning algorithms is
small and could be omitted. Moreover, when the traffic demand
is low, two cooperative driving strategies behave similarly;
when the traffic demand is high, the performance of this new
"planning based" strategy is still better than that of "ad hoc
negotiation based" strategy. This shows that we find a way to
achieve a better passing order plan than "ad hoc negotiation
based", and meanwhile keep the planning complexity lower
than conventional "planning based" strategy.
We find that the tree-pruning "planning based" strategy is
time-consuming and needs to be further accelerated. Besides,
we also highlight the necessity of considering enough safety
gap in trajectory planning and introducing point-queue
technique in simulations.
In addition, we still do not exactly know how to choose an
appropriate circle radius for "planning based" strategy. Clearly,
communication constraints restrict the upper-bound of the outer
radius. Since the radius of the outer circle also determines the
size of solution space for the cooperative driving problem,
computation resources limits restrict the upper-bound of the
outer radius, too. We will further discuss this problem in a
dedicated paper in the near future.
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IEEE Transactions on Vehicular Technology, 2017
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purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
Yue Meng is with Department of Automation,
Tsinghua University, studying intelligent
vehicles.
Li Li (S'05-M'06-SM'10-F'17) is currently an
Associate Professor with Department of
Automation, Tsinghua University, Beijing,
China, working in the fields of complex and
networked systems, intelligent control and
sensing, intelligent transportation systems and
intelligent vehicles. Dr. Li had published over
60 SCI indexed international journal papers and
over 60 international conference papers as a
first/corresponding author. He serves as an
Associate Editor of IEEE TRANSACTIONS
ON INTELLIGENT TRANSPORTATION
SYSTEMS and AUTOMATICA SINICA.
Fei-Yue Wang (S'87-M'89-SM'94-F'03)
received the Ph.D. degree in computer and
systems engineering from Rensselaer
Polytechnic Institute, Troy, NY, USA, in 1990.
In 1990 he joined University of Arizona,
Tucson, AZ, USA, where he became a
Professor and the Director of the Robotics and
Automation Laboratory and the Program in
Advanced Research for Complex Systems. In
1999 he founded the Intelligent Control and
Systems Engineering Center, Institute of
Automation, Chinese Academy of Sciences
(CAS), Beijing, China, under the support of the
Outstanding Overseas Chinese Talents
Program and, in 2002, he was appointed as the Director of the Key Laboratory
for Complex Systems and Intelligence Science, Institute of Automation, CAS.
From 2006 to 2010 he was the Vice President for research, education, and
academic exchanges with the Institute of Automation, CAS. Since 2005 he has
been the Dean of the School of Software Engineering, Xi’an Jiaotong
University, Xi’an, China. In 2011 he became the State Specially Appointed
Expert and the Founding Director of the State Key Laboratory of Management
and Control for Complex Systems, Institute of Automation, CAS. He is the
author or coauthor of over 10 books and 300 papers published in the past three
decades in his research areas, including social computing and parallel systems.
Dr. Wang has served as the General or Program Chair of more than 20 IEEE,
Institute for Operations Research and the Management Sciences (INFORMS),
Association for Computing Machinery (ACM), and American Society of
Mechanical Engineers (ASME) conferences. He was the President of the IEEE
Intelligent Transportation Systems (ITS) Society from 2005 to 2007, the
Chinese Association for Science and Technology (USA) in 2005, and the
American Zhu Kezhen Education Foundation from 2007 to 2008.
He is a member of Sigma Xi; an Outstanding Scientist of the ACM; and a
fellow of the International Federation of Automatic Control, the International
Council on Systems Engineering (INCOSE), the ASME, and the American
Association for the Advancement of Science.
Keqiang Li received the B.Tech degree from
Tsinghua University, Beijing, China, in 1985
and the M.S. and Ph.D. degrees from
Chongqing University, Chongqing, China, in
1988 and 1995, respectively.
He is a Professor in automotive engineering
at Tsinghua University. He has authored over
90 papers and is a co-inventor of 40 patents in
China and Japan. His main areas of research
interest include vehicle dynamics and control
for driver assistance systems and hybrid
electrical vehicle. Dr. Li has served on the
editorial boards of International Journal of ITS
Research and International Journal of Vehicle
Autonomous Systems. He has received the "Changjiang Scholar Program
Professor" and some awards from public agencies and academic institutions of
China.
Zhiheng Li (M'05) received the Ph.D. degree
in control science and engineering from
Tsinghua University, Beijing, China, in 2009.
He is currently an Associate Professor with
Department of Automation, Tsinghua
University, Beijing, and with the Graduate
School at Shenzhen, Tsinghua University,
Shenzhen, China. His research interests include
traffic operation, advanced traffic management
system, urban traffic planning and intelligent
transportation systems. He serves as an
Associate Editor for IEEE TRANSACTIONS
ON INTELLIGENT TRANSPORTATION
SYSTEMS.