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Title

Intersection Control Systems with Dynamic Wait
Time Applying Vehicle to Vehicle Communication

Author(s)Tamaru, Rei; Ishibashi, Keisuke; Kotani, Kazunori

Citation

Research report (School of Transdisciplinary
Sciences, Graduate School of Advanced Science andTechnology, Japan Advanced Institute of Scienceand Technology), TS‑RR‑2020‑001: 1‑11

Issue Date

2020‑09‑02

TypeTechnical Report

Text version

publisher

URL

http://hdl.handle.net/10119/16775

RightsDescription

リサーチレポート（北陸先端科学技術大学院大学先端科学技術研究科融合科学系）

Japan Advanced Institute of Science and Technology

Intersection Control Systems with Dynamic Wait Time
Applying Vehicle to Vehicle Communication
Rei Tamaru

Keisuke Ishibashi

Kazunori Kotani

School of Transdisciplinary Sciences, Japan Advanced Institute of Science and Technology
September 2nd, 2020
TS-RR-2020-001

1Intersection Control Systems with Dynamic
Wait Time Applying Vehicle to Vehicle
Communication
Rei Tamaru ∗ Keisuke Ishibashi ∗∗ Kazunori Kotani ∗∗Japan Advanced Institute of Science and Technology, Nomi, Ishikawa
923-1211, Japan∗∗
International Christian University, Mitaka, Tokyo 181-0015 Japan

Abstract: Although automated vehicles are becoming more popular due to the developmentof technology, semi-automated vehicles with auxiliary devices such as automatic braking and
Adaptive Cruise Control(ACC) are now the mainstream. On the other hand, fully automatedvehicles are expected to improve safety and fuel economy by providing optimal driving by amachine compared to semi-automated vehicles. This paper (1) compares previous traffic method,
Autonomous Intersection Management(AIM) and Virtual Traffic Light(VTL), and (2) proposesa new traffic control scheme Dynamic Virtual Traffic Light (D-VTL), which could be replaced
to VTL and improve 29% traffic efficiency in AIM4 simulation.
Keywords:
Transportation control, Computer communication networks, Vehicle simulator,
Interconnection technology
1. INTRODUCTIONa centralized system based on traffic light. Decentralized
control uses V2V communication where communication iscontrolled by individual vehicles or devices. Autonomousvehicles usually travel through the intersection by adopting
either of control type or a combination of both. Types ofcentralized control systems include: an agent-based online
adaptive signal control (ASC) strategy based on realtime traffic information available from connected vehicle
technology Kari et al. (2014), an arterial traffic light(ATL) controlling algorithm which has adopted the ITLC
algorithm to design a traffic scheduling algorithm foran arterial street scenario Younes and Boukerche (2016),
and the AIM method which we use in this paper andexplain it later Dresner and Stone (2005). Types ofdecentralized control systems include: there are Intelligent
Traffic Light Controlling (ITLC) algorithm Younes andBoukerche (2014) which considers the real-time trafficcharacteristics of each traffic flow that intends to crossthe road intersection of interest, whilst scheduling thetime phases of each traffic light, improved adaptive Traffic
Signal Controlling Systems (TSCSs) Shaghaghi et al.
(2017) which decreases vehicle waiting time by using
Webster’s methodWebster (1958), while reducing theirpollutant emissions at the intersection, and Virtual Traffic
Light (VTL) which we use in this paper and explain later
Ferreira et al. (2010).

Recently, interest in self-driving vehicles has gradually
spread around the world, but at present, only semi selfdriving vehicles are available, the main components areautomated braking, automated steering, and adaptive
cruise control. Thus, the self-driving vehicle finds a way forsolutions of safety and efficiency by using communicationequipment. The advantage to introducing a self-driving
vehicle is that it could be an efficient, safe, and economicalmeans of travel. According to the research, self-driving
vehicles consume less gasoline, are safer to ride, andexperience fewer transportation delays in intersections
than do manual driving vehicles Li and Sun (2016).
With regard to efficiency on the road, the greatest
contribution of a self-driving vehicle is its capability for
managing traffic jams. Through Vehicle to Infrastructure(V2I) or Vehicle to Vehicle (V2V) communication, traffic
can be controlled more efficiently and precisely than usinga typical intersection control system such as a stop sign ora traffic light. Intersection jams are caused by difficulties
adjusting to traffic light duration for different traffic
volumes depending on the day, or traffic light needing along time for all lanes due to the high traffic volume. If
a self-driving vehicle has introduced on the real life, it
decreases the delay of intersection trip without the traffic
light and it does not need to wait before intersection due
to a traffic light or a stop sign thanks to its frequent
communication.

According to previous research presented in Section
2, the two control systems have been independently
evaluated in terms on their efficiency and compared withtypical intersection control such as stop sign or traffic
Intersection control systems for self-driving vehicles with light, but very few attempts have been made a directcommunication capability fall into two categories; centralized comparison of these systems within the same environment.
and decentralized control. Centralized control uses V2I Intuitively, centralized control could potentially havecommunication and is controlled by communicating with better performance at the intersection, but has the2disadvantage of needing an intelligent infrastructure. To
judge the requirements for infrastructure, it is necessary
to compare quantitatively.
Hence, we compared these two control systems using a
traffic simulator Dresner and Stone (2005) and observed
the differences in effectiveness between decentralized andcentralized control and determined that the most effective
traffic control system was centralized control.
(a) Vehicle demand and IMIntelligent equipped with communications devices, may
response
not exist until the future due to the high cost of
construction. However, though it was found that adecentralized system is less efficient than a centralized
system, we identified a possibility to improve the efficiency
of decentralized systems. i.e. change the wait time dynamicallyat the intersection depending on the number of vehicles.
We implemented the dynamic control system called
Dynamic Virtual Traffic Light (D-VTL) and demonstrated
the gain of efficiency.
(c) Change content and demandagain

In summary, we will first explain decentralized control andcentralized control with those representative examples.
Next, we will study a decentralized control system in order
to compare its efficiency to that of typical intersection
control systems and centralized control systems. Finally,
based on the results of the comparison, we will argue thatthe improved decentralized control is more efficient thanoriginal, compare it with the original decentralized andcentralized control systems and present the results of thatcomparison.

(b) Accept/Reject(d) Finish transportation

Fig. 1. AIM Logic
2.1 Autonomous Intersection Management
This protocol is based on a multi-agent intersection travel
method involving a driver agent and the intersection
manager to the extent that it is a reasonable approximationof reliable wireless communication. In this method, anintersection manager is equipped for each intersection. It
decides which vehicle to let cross the intersection. Vehicles
communicate with an intersection manager to request
to cross the intersection and receive an acceptance orrejection for the request. Under this control method, we
accept for policy a commonly used algorithm ”first come,first served” (FCFS), which divides the intersection into
an n × n grid of reservation tiles, where the parameter n
represents the granularity of the policy Dresner and Stone(2005). Generally, this policy is aimed at the vehicle which
arrives first, can send messages and be managed by theintersection manager.

The remainder of this paper is organized as follows. In thenext section, we present examples of various centralized
and decentralized control systems. Also, we will introduce
related papers about the design of both types of control
systems. Section 3 describes the results of the comparisonof centralized and decentralized controls. In section 4,
using the results described in Section 3, we will present
some disadvantages of the typical method and suggest DVTL that is more efficient than original. Section 5 provides
the design of a D-VTL that its efficiency. In Section 6, we
introduce D-VTL with some formulae, then we consider
whether D-VTL solves the problems that are mentioned in
Section 3, and show the result. Finally, Section 7 concludes
the paper.

Message Type In Vehicle-to-Intersection (V2I) messages
have 5 types, Request, Change-Request, Cancel, Done,and Away. Intersection-to-Vehicle (I2V) messages have 3
types, Confirm, Reject, and Acknowledgement. At first, we
describe the V2I message.

2. CENTRALIZED AND DECENTRALIZEDINTERSECTION CONTROL METHODS• Vehicle to Intersection(1) REQUEST – If the vehicle does not have a
Generally speaking, there are mostly two ways that canreservation yet, the vehicle would send thismanage the intersection travel with a manual driving
message. This message includes the parameters
vehicle on a road with infrastructure, traffic light and stopof the vehicle and the proposed reservation.
sign. Meanwhile, with a self-driving vehicle, there are two(2) CHANGE-REQUEST – This is the message usedcommon control methods, centralized and decentralized
by a vehicle that has a reservation but it needs
control. In this paper, as representative methods of
to change other parameters.
centralized and decentralized control methods, we evaluated(3) CANCEL – The message used by a vehicle
Autonomous Intersection Management (AIM) Dresnercanceling its reservation.
and Stone (2005), which uses Vehicle-to-Infrastructure(4) DONE – The message a vehicle will send after
communication (V2I) via intersection manager containing
crossing the intersection.
intelligent infrastructure and Virtual Traffic Light (VTL)(5) AWAY – The vehicle will send this message after
Ferreira et al. (2010) which uses Vehicle-to-Vehicle communication
sending DONE, to notify that it is moving away
(V2V) respectively. In the following subsections, wefrom the intersection.
describe each method.
• Intersection to Vehicle32.2 Virtual Traffic Light(1) CONFIRM – This message is sent in response to
a REQUEST or CHANGE-REQUEST message
from a vehicle. The reservation parameter in thismessage is admitted.
(2) REJECT – This message is sent to notify thata REQUEST message has not been approved,
and it does not accept counter-offer. There is afield in this message which indicates whether therejected vehicle does not enter the intersection.
This forces the driver agent to have to request
another entering the intersection.
(3) ACKNOWLEDGMENT – The message is used
to confirm receipt of a CANCEL or DONE
message.

Protocol Actions
vehicle actions.

In this method, there is no intelligent infrastructure that
decides which vehicle crosses the intersection. Vehicles
or devices on a vehicle communicate with each otherand decide which vehicle to cross the intersection in adecentralized manner. Hereafter, we explain the decentralized
decision mechanism Ferreira et al. (2010); Zhang et al.
(2018).
System Design
VTL has the following assumptions
Ferreira et al. (2010).
• All vehicles are equipped with a Dedicated Short
Range Communications (DSRC) device which cancommunicate with vehicles in short range• All vehicles have the same digital map• All vehicles have a Global Positioning System device
which accuracy enough• Under VTL protocol, there is no deficit of security or
network delay beyond the problems that are defined
hereThis section describes the sequence of(1) The vehicle cannot enter the intersection without
reservation.
(2) If the vehicle tries to enter the intersection, it
travels optimally in accordance with the parameter
included in CONFIRM messages received from theintersection.
(3) If the vehicle sends additional new messages toIntersection Manager before intersection manager
responds, intersection manager can ignore them.
Thus, the vehicle sends a new message only after it
has received the response to its last message.
(4) If the vehicle has not entered the intersection and does
not have a reservation, it sends REQUEST message.
If the vehicle has not entered the intersection but
has the reservation, it has the option to sending a
CHANGE-REQUEST or a CANCEL message. If thevehicle sends these messages when it is not allowedby the intersection manager, these messages can beignored.
(5) If the vehicle has a reservation and successfully
crosses the intersection, it sends DONE message.
(6) If the vehicle receives a CONFIRM message, this isconfirmation that the vehicle has a reservation.

In VTL method, we assume there is a virtual traffic lightat each intersection. Each vehicle in the intersection cancommunicate with each other, and they share the statusof virtual traffic light.

(a) Check the crash possibility(b) Decide a leader(c) Decide Wait Time and tell (d) Transfer/Discard the leader’sauthority
othersIntersection Actions This section describes the sequenceof intersection actions.

Fig. 2. VTL Logic(1) When the intersection receives a REQUEST message,
it needs to respond with a CONFIRM or a REJECT
message. If it sends a CONFIRM message, it is VTL Logic
guaranteed there will be no collisions in the intersection (1) Sensing: While the vehicle approaches the intersection,
provided the vehicle travels in accordance with theit starts detecting the vehicles approaching the same
parameter in the message.
intersection using a digital map.
(2) When the intersection receives a CHANGE-REQUEST (2) Leader Election: If other vehicles use the samemessage, it responds with a CONFIRM or a REJECT
intersection and there is a possibility another vehicle
message. If it sends a CONFIRM message, it ismight collide with it, they choose the cluster leader
guaranteed there are will be no collisions in thewhich is the nearest of the intersection on eachintersection provided the vehicle travels in accordanceroad and choose the intersection leader which iswith the parameter in the message. The previous
nearest the cluster leaders, and the intersection leader
guarantees are now invalid.
temporarily has control of the virtual traffic light.
(3) When the intersection receives a CANCEL message,(3) Broadcast: The leader broadcasts information about
it sends an ACKNOWLEDGEMENT message. The
the virtual traffic light. The leader sends a red
previous guarantees are now invalid.
signal, that is a wait time which denies entering the4intersection for a vehicle, to the opposite line to itself
and sends a blue signal to the orthogonal line.
(4) Handover: The leader decides how long red signal
lasts after being chosen. The time is a fixed value
such as 10 and 30 seconds. After the time completes,
the leader hands over its leadership right to theclosest vehicle on the orthogonal lane. If there areany vehicles approaching the intersection on theorthogonal lanes, the leader hands over the leadershipright.
(5) Release: When the leader’s time expires, the leader
releases its leadership right to the intersection functionality
if there are no more vehicles at risk of colliding. When
there is no leader in the intersection and it is foundthat there may be a collision soon, vehicles choose
next leader again and the process repeats from step 1.
It should be noted that it does not occur only except
for either Handover or Release.
It is shown that the AIM method is better as anintersection control system than traffic lights and stop
signs VanMiddlesworth et al. (2008). Several recent papers
have demonstrated that V2I communication is more
efficient than the original traffic control systems and as is
V2V VanMiddlesworth et al. (2008); Zhang et al. (2018).
On the contrary, this report provides the result of acomparison of AIM and VTL methods and presents theincrease of performance of D-VTL in regard to efficiency.

Fig. 3. A screenshot of our simulator in action
AIM4 originally only supported travel straight acrossthe intersection, we added support for random directions
including left and right.

3. PERFORMANCE COMPARISON

To evaluate the VTL system instead of AIM, we updated
the simulator to support the VTL regulations mentioned
3.1 Method
in Section 2. At first, to simulate V2V communication,
we updated the infrastructure transparently transfer
We evaluated the performance through agent-based simulations.
messages to other vehicles. The vehicle should travel
As an agent-based simulator for vehicle transportation, we based on the specification. We updated the intersection
adopted AIM4 Dresner and Stone (2005). Because AIM4 is manager to send a REJECT message whenever there isa simulator for AIM method, we modified AIM to simulate a chance a vehicle might collide with other vehicles while
VTL, TL, and stop sign as follows.
crossing the intersection. If the vehicle receives a REJECT
Originally, AIM4 was designed for the AIM protocol. message and it is the closest vehicle in the intersection,
It is based on Vehicle to Infrastructure communication. that vehicle becomes a leader. After becoming a leader,
To show the result of intersection travel, we applied the the leader vehicle waits for a certain period of time
vehicle identification number (VIN), the lane number the defined by ”WAIT TIME”. According to the protocol for avehicle occupies, and the travel time by measuring the REJECT message, the leader does not resend REQUEST
time between entering and exiting the intersection. Then, or any other message while waiting before the intersection.
we used this information to calculate the variance of Additionally, the vehicle traveling on the opposite lane
completed time and the average traveling time for the from the leader waits for the same time as the leader, whilethe vehicle on the orthogonal lanes crosses the intersection.
vehicles.
Finally, after the leader’s wait time finishes, the leadership
For each experiment, the simulator simulates one lane in right will be handed to any vehicle on the orthogonal lanes
each of the 4 cardinal directions. The total area modeled if there is any vehicle which receives a REJECT message
is a square with sides of 250 meters. The speed limit for all from the intersection manager.
lanes is 25 meters per second. Figure 3 shows a screenshotof the graphical display. Each time step in the simulator
represents .02 seconds of real time. Additionally, thesimulator has 4 types of vehicles coupe, sedan, SUV, and 3.3 AIM Resultvan, and they have different length and other parameterssuch as acceleration or velocity.
We evaluated the performance of intersection control
systems in terms of travel time, which is the time between
3.2 Main Points of Modificationentering and exiting the intersection. We changed thetraffic volume, which is the rate of the number of vehicles
To set up the environment for the experiment, we modified entering the lane per unit of time and calculated thethe configuration of the simulator. Assuming the one-lane average and variance of travel times. Then, we compared
scenario as a condition, the simulator makes it simple to the respective performances of AIM, the traffic light, andachieve the purpose of this paper. Additionally, because the stop sign.

5Fig. 4. Average Traveling Time of AIM

Fig. 6. Average Traveling Time of VTL, TL and SS

Fig. 5. Variance of AIM with Various Wait Time

Fig. 7. Variance of VTL, TL and SS

Considering evaluation conditions, a good result if average
traveling time is shorter, and variance of completed timeof the vehicles is less.

The travel time does not vary at high traffic volume. On
the other hand, VTL in 30 seconds and traffic light in
10 seconds have higher variance than others in terms ofdispersion at traffic volume 800.

According to Figure 4 and 5, AIM is the most efficient
way of the intersection travel, and traffic light and stop
sign follow in this order. In other words, if the road iscongested, it would be inefficient travel in all methods,
and AIM will be the most efficient method.

3.5 VTL with Different Wait TimeWe also evaluated VTL method’s varying wait time, otherthan 10 and 30 seconds, to confirm the optimal wait time.

It should be noted that traffic light with 30 seconds longis more efficient than traffic light with 10 seconds long.
This is for the same reason that the stop sign is the least
efficient method. As a wait time decreases, traffic lightchanges more frequently, and vehicles tend to stop at theintersection. It leads to a lot of delays. Thus, we thoughtvehicle cluster can travel faster than the individual vehicle.

Figure 8 and 9 describe that shorter wait time such as
5 or 10 seconds is more efficient when traffic volume islittle because there is no traffic jam in the intersection.
Meanwhile, there is a small difference when traffic volume
is large among all wait time because the capacity of theintersection is almost full when traffic volume is large andthroughput of traveling would be fixed in this wait time.
On the contrary, when wait time is larger than 50 seconds,
the average time of the intersection travel gets shorter
when traffic volumes are 1200 and 1600. This is because
the throughput of the intersection travel gets improved dueto the change of the rotation of traveling vehicles. Figure
10 shows that the throughput of VTL with the different
wait time. Throughput gets larger until traffic volume gets
1200. After 1200, it does not increase because of the limitof the intersection capacity. Also, throughput gets higher
in accordance with the length of wait time, that is theshortest wait time results in the most efficient intersection
travel.

3.4 VTL Result
The result between the average travel time of vehicles
completed the intersection travel, and traffic volume
and the variance of completed vehicles’ travel time. We
evaluate among VTL, the traffic light, and the stop sign.
According to Figure 6, VTL is an efficient method of theintersection travel, and the performance of VTL equals tothat of traffic light in 30 seconds and follows by traffic
light in 10 seconds, and the least efficient method is thestop sign.

6Fig. 8. Average Traveling Time of VTL

Fig. 11. Average Traveling Time of AIM and VTL

Fig. 9. Variance of VTL with Various Wait Time

Fig. 12. Variance of AIM and VTL with Various Wait Time

3.6 Comparison of AIM and VTL
In this section, we compare AIM and VTL in terms of theaverage time and variance of completed vehicles’ travelingvarious different traffic volumes. In VTL, we experimented
with different wait times before the intersection, 10
seconds, and 30 seconds.
According to Figure 11 and 12, AIM is the most efficient
way to manage intersection travel at any level of traffic
volumes. VTL has almost same efficiency with the traffic
light set to 30 seconds because once the vehicle in VTL
system receives a REJECT message, the leader sets thevirtual traffic light and it continues until the end of thesimulation, that is substantially the same as with a traffic
light. By comparison, a traffic light set to 10 seconds anda stop sign is less efficient. Thus, AIM is the most efficientmethod for intersection travel. As we describe in the next
chapter, however, VTL could be a better method if the
wait time is adjusted depending on traffic volumes.

Fig. 10. Throughput of Travel with VTL
Moreover, the variance of completed vehicles’ travel timeover 50 seconds gets increasingly large depending on wait
time. According to Figure 10, due to the improvementof throughput, one vehicle does not have to wait before
the intersection, but one vehicle should wait for ”WAIT
TIME” which gets longer depending on the VTL wait
time. Until the number of vehicles traveling is beneaththe intersection capacity, the variance would be almost
the same as at high traffic volumes. On the other hand,variance varies greatly at low traffic volume depending onwhether there is a traffic jam.

The results of intersection travel with a traffic light anda stop sign used in a manual vehicle environment, AIM
and VTL used by the self-driving vehicle demonstrate thesuperiority of using a communication system. In addition,
we can see differences in efficiency with different traffic
volumes in each approach to intersection management.

7

3.7 Restrictions

vehicles can cross the intersection more efficiently rather
than individual vehicles.

Here, we mention some differences between the simulator
and real traffic, and their effect on our results.

According to the results comparing AIM and VTL, theperformance of AIM is obviously better than that of VTL.
However, AIM can exist only where there is infrastructuresuch as traffic signals or signboards that can containcommunication device, and not all locales have such an
infrastructure. Also, it takes time and is expensive to
install new devices across all the infrastructure. Moreover,AIM focuses on a self-driving vehicle society, in which
all vehicles on the road are completely autonomous, so
this method is not available given the current market
penetration of self-driving vehicles. Thus, it is important
to improve the performance of VTL.

• Because the simulator is based on FCFS policy,
it sometimes happens that vehicles turning at theintersection have priority over vehicles continuing
straight while vehicles continuing straight has priority
in real life.
• VTL is targeted at manual vehicles but our simulator
is based on self-driving vehicles and does not consider
the lag introduced from the human decision making
in perceiving the environment around the vehicle. It
affects the length of wait time and its result.
• As we only experimented with restricted traffic
volumes because of time constraints, there might beother optimal settings.
• The vehicle in this simulator communicates with theintersection manager while we expect vehicles with
VTL to communicate with other vehicles.

4.2 Proposed Method
Key Idea
To solve the problems, we propose D-VTL
which is more efficient than original VTL by introducing
a dynamic wait time.

Addressing these differences may lead to different results.

In the original VTL, a wait time is configured with a fixedvalue. However, if there is no vehicle on orthogonal lanes
while VTL still shows red to the driver, waiting introduces
needless delays to intersection travel. On the other hand, if
the wait time is too short even when the number of vehicles
waiting in the orthogonal lanes is large, then it causes
excessively frequent signal changes leading to inefficient
travel through the intersection.

4. IMPROVEMENT OF VTL METHODThis chapter first begins with a description of the problemsof original VTL and their causes. Then, we propose amethod to improve the original VTL called Dynamic-VTL(D-VTL).

Thus, we introduced a dynamic wait time to replace
the fixed wait time. When no vehicles approach theintersection while the leader vehicle waiting, a wait time
will be zero seconds. Conversely, when traffic jam happens
on each lane, a wait time will be set longer because thereis optimal time delay depending on the traffic volume andnumber of the waiting vehicles. As a result, improved VTL
uses dynamic wait time for efficient travel in any situations
including redundant waiting. In the next section, we will
mathematically derive the optimal wait time according to
the number of queued vehicles.

4.1 Problems and Their Reasons
This section describes the problems of original VTL fromthe standpoint of efficiency. As we saw in the last chapter,original VTL is inferior to the AIM method. In fact, theperformance of original VTL equals of a traffic light set to
30 seconds even though we expected VTL should be better
than traffic light with any time.
Indeed, VTL is the new method to replace traditionaltraffic control systems such as traffic lights and stop signs
which means VTL needs to be more efficient than others.
According to the results, the vehicle with VTL travels
faster depending on the length of wait time. Longer wait
time introduces a greater variance of travel time; that is,once a vehicle gets caught by traffic light, the vehicle will
have to wait a longer time than that typical for a traffic
light.

4.3 Mathematical Formulation
D-VTL adopts a dynamic wait time depending on thenumber of vehicles on each lane. Specifically, each vehicle
shares the information on the number of vehicles andlane numbers in the intersection, and the leader vehicle
calculates the wait time according to the traffic volume oforthogonal lanes based on the formulae derived in Mingzhe(2015).

The biggest problem is the wait time duration. From thecomparison between VTL set to 30 seconds and AIM, theaverage time for AIM is faster than VTL at any traffic
volumes, especially low traffic volumes. In spite of the
low number of vehicles on orthogonal lanes, vehicles will
wait for a certain time due to the period of virtual traffic
light. Otherwise, the vehicles with AIM can cross theintersection without delay. This dead time results in the
delay of intersection travel at certain traffic volumes.

We introduce mathematical formulae to solve an optimal
wait time. In Mingzhe (2015), the traffic light is assumed
as intersection management and it has yellow signal timeand red signal time on all lanes. Comparing with Mingzhe(2015), there is no yellow signal time all red phases under
our method. Thus, we set parameters with little change.

Moreover, comparing VTL at various different wait times,
it can be seen that the vehicle transits faster when thewait time is short and traffic volume is low and takes
more time to transit the intersection when the wait time islong and traffic volume is high. This is because clustered(1) T : Cycle time(2) a : The red light duration(3) b : The green light duration(4) λ : Average arrival rate from each lane8

is solved. In Figure 14, S is total wait time which thevehicles have to wait while at a red light or the time
which all queued vehicles would need to finish travelingthe intersection.
Cumulative inflow is increased in accordance with theratio of the average number of arrival vehicles. On theother hand, cumulative runoff is increased differently as afunction of time. When the traffic signal is red (variablea), there are no vehicles going into the intersection. While
the period from a to t0 , the vehicle finishes the intersection
travel depending on the ratio of cumulative runoff. Afterall queued vehicles finish the transit, the rest of the vehicles
are arriving at the intersection while the intersection
processes queued vehicles.

Fig. 13. Relation between each parameter in Traffic Cycle

5. EXPERIMENT RESULTS
In this section, we describe empirical evaluations of our
D-VTL method using a modified AIM4.
5.1 Program Setting
We added new code for this method. First, we put the
information on the number of vehicles and lane number.
Note that this number can be collected by the leader ina distributed manner. Second, we implemented a different
wait time depending on the traffic volume of orthogonallanes. The capacity on each lane is 22 or 23 vehicles.
Fig. 14. Vehicles Flow

5.2 Empirical Results(5) µ : Average service rate of the vehicle (the number ofvehicle which can travel through the intersection perunit time)

We applied model Mingzhe (2015) to D-VTL. To solve
the optimal wait time, we found variable µ using manual
inspection. In particular, we counted the time for completing
travel of the queued vehicles and found an intersection
transit of one vehicle per one second. Then we calculateda wait time depending on queued vehicles in the orthogonallanes. As a result, we found optimal µ as 0.412. For
example, if the number of queued vehicles is 10, the mostefficient wait time becomes 24.2 seconds. Additionally, we
multiply a 5 % error rate because we could count the
number of vehicles traveling in each lane, but not the
number of queued vehicles.

In Mingzhe (2015), T , standing for traffic cycle time, isa fixed value, but in our method, T is a dynamic value
depending on the length of wait time which is the sameas with a red signal. Figure 13 shows the relation between
each parameter.
Also, we have limiting conditions.

a=b


T =a+b
 λT ≤ µb
a, b, T ≥ 0(1)

According to these conditions, we ran the simulator andcompared the improved VTL with AIM and original VTL.
From both of the figures for D-VTL, shown in Figures
15 and 16, we observed D-VTL is more efficient thanoriginal VTL. When traffic volume is large such as 1200 or
1600, D-VTL is better than VTL in 5 second wait time.
However, the variance of completed vehicles with D-VTL
is larger than original VTL because vehicles on any lane
travel smoothly, on the other hand, others were stuck in
a traffic jam due to the ratio of driving direction. The
vehicles should wait in accordance with FCFS policy, so it
sometimes happens that turning left has prior over goingstraight.

Let cumulative inflow and cumulative runoff as A(t) andD(t) until time t in one cycle, the formulae are
A(t) = λt(2)(0(0 ≤ t < a)D(t) = µ1 t − µa (a ≤ t < t0 )(3)
λt
(t0 ≤ t ≤ T )Figure 14 demonstrates this formula. Here, t on thehorizontal axis expresses time and on the vertical axis,
n expresses the total number of queued vehicles with zeroacceleration.

5.3 Discussion

If we regard the time for solving the full traffic congestionµa. Thus, it is found that the mostas t0 , t0 is t0 = µ−λefficient wait time is the time until traffic congestion

Thus, D-VTL enhances the efficiency of intersection travel.
It increases efficiency by about 29% as compared with

9

Therefore, fixed wait time using in original VTL proves tolead to the deficit of the system.
Next, we created D-VTL and figured out that it is usefulin the real world. Although we could not exceed theperformance of AIM method, we showed that D-VTL is
more efficient than original VTL when it comes to heavy
traffic in the intersection though a wait time of D-VTL islonger than the original, that is contrary to the fact thatthe shorter wait time could bring better results. D-VTL
results from a way of selection of wait time depending on
the queued vehicles with zero acceleration. By introducing
a dynamic wait time, we achieved a better performancewith 29% comparing to the original. In this way, we believe
we have accomplished a portion of the research of theintersection travel.
As for the future works, first is in larger simulation
applying Vehicle to Vehicle communication, and ultimately
with real physical vehicles. In addition, the vehicles could
send messages safely, or detect failure of sending messages
in the intersection.

Fig. 15. Average Traveling Time of D-VTL

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6. CONCLUSION
In this paper, we made two contributions as follows.
First, we compared typical traffic control systems suchas stop signs and traffic lights, and control systems witha communication-based method such as AIM, and VTL.
Second, we found drawbacks in original VTL in termsof efficiency of the intersection transit and introduced adynamic wait time depending on the number of queued
vehicles on each lane, and we compared that with AIM
and original VTL.
Firstly, we showed the results of the comparison of atypical control system such as stop signs and traffic lights,
and the communication-based methods, AIM and VTL,
respectively. As previous researches explained and ourexperiment has reproduced, AIM is more efficient than
the stop signs and the traffic lights. However, it is observedthat VTL is not a very efficient intersection travel method.
When it comes to the various wait time of VTL, theshortest wait time applies the fastest intersection travel
and the longest results in the slowest intersection travel.

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