=Paper=
{{Paper
|id=Vol-3742/short4
|storemode=property
|title=Optimal Control Scheme for Signalized Intersection Based on Phase Stream Combination in Autonomous Driving Environment
|pdfUrl=https://ceur-ws.org/Vol-3742/short4.pdf
|volume=Vol-3742
|authors=Zhihua Yu,Can Zhou,Wenbin Xiao
|dblpUrl=https://dblp.org/rec/conf/citi2/YuZX24
}}
==Optimal Control Scheme for Signalized Intersection Based on Phase Stream Combination in Autonomous Driving Environment==
https://ceur-ws.org/Vol-3742/short4.pdf
Optimal Control Scheme for Signalized Intersection
Based on Phase Stream Combination in Autonomous
Driving Environment
Zhihua Yu 1,∗,†, Can Zhou 1,† and Wenbin Xiao 2,†
1 CCCC Second HighwayConsultants Co.Ltd.Wuhan 430056, China
2 Fuzhou Municipal State owned Assets Investment Holding Group Co.,Ltd. Fuzhou 344000, China.
Abstract
The form of phase stream combination directly affects the control effectiveness of signalized
intersections. With the introduction and improvement of autonomous driving technology, the
current phase combinations at signalized intersections cannot meet the requirements of phase
stream combination in the autonomous driving environment. Based on the existing optimal
signal control algorithm for streamline overlap and the existing timing models, this study
calculates signal phase timing and average vehicle delay. By comparing the average vehicle
delay, it is found that the new algorithm includes a more comprehensive and universal range of
phase combination schemes. The control scheme corresponding to the minimum delay is
selected as the optimal control scheme for the intersection, providing a reference for the
generation of phase combination schemes at signalized intersections in the autonomous driving
environment.
Keywords
traffic engineering, signal intersection, movement overlap, phase combination scheme, raffic
engineering, siautomated vehiclesaal in 1
1. Introduction
According to statistics from the Ministry of Public Security, as of September 2023, the total
number of motor vehicles in China has reached 430 million, including 330 million
conventional cars and 18.21 million new energy vehicles. Urban traffic congestion has
become a daily occurrence, with congestion at intersections being particularly severe, and
its impact far exceeds that of regular road sections. Researching the traffic conditions at
intersections and optimizing signal intersection control schemes is one of the effective
means to alleviate intersection congestion [1].
CITI’2024: 2nd International Workshop on Computer Information Technologies in Industry 4.0, June 12–14, 2024,
Ternopil, Ukraine
∗ Corresponding author.
† These authors contributed equally.
46461558@qq.com (Z. Yu); 2423425917@qq.com (C. Zhou); traffic_xwb1910@whut.edu.cn (W. Xiao)
0000-0003-3412-1639 (Z. Yu); 0000-0002-9496-2395 (C. Zhou); 0000-0001-5476-8670 (W. Xiao)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
As smart transportation and the proliferation of new energy vehicles continue to
develop, some functions of autonomous driving have gradually been implemented on new
energy vehicles. Vehicles in the autonomous driving environment can safely drive based
on predefined lane trajectories using electromechanical technology [2]. The existing phase
stream combination method of the Ring Barrier System (RBS) for reducing phase green
light losses does not meet the requirements of the autonomous driving environment as it
fails to consider the relationships between different inlet streamlines flowing into the
same outlet [3]. Currently, research on intersection control in the autonomous driving
environment focuses on vehicle-to-vehicle information transmission and real-time
optimization of intersection control timing schemes by accurately collecting inbound
traffic flow parameters using advanced autonomous driving technology [4, 5], but does
not consider the compatibility of refined streamlines.
Therefore, our research team has developed a more comprehensive algorithm for
determining signalized intersection phase stream combinations, taking into account the
compatibility between cross-flow, diversion flow, and merging flow [6]. To validate the
effectiveness and compatibility of the new algorithm, this paper compares the new scheme
with the RBS phase combination scheme, divergence phase combination scheme, and
combination phase combination scheme using existing timing models. The feasibility of
the new scheme is verified, and the optimal intersection control scheme is further derived.
2. Intersection Streamline Overlay Algorithm
The research team has comprehensively studied a more comprehensive algorithm for
determining the phase stream combination at signalized intersections. The algorithm
takes into account the compatibility of conflicting, diverging, and merging relationships
among the flow streams, specifically refining the merging relationships previously
identified as conflicts into compatible relationships in the context of automated driving
environments.
Next, all stream combinations are evaluated based on the requirement that phase
stream combinations must be compatible, and considerations such as lane-sharing
conditions for stream lane settings, in order to identify all feasible phase stream
combinations.
Subsequently, the phase combination control scheme, which includes all intersection
streams and the continuity of successive movements within the cycle, is used as a filtering
condition to derive viable phase stream combination schemes.
Once the feasible phase combinations are determined, they are synthesized with the
intersection signal timing model to calculate the phase stream timing. Only when the
resulting control scheme is complete and compatible with the intersection control can it
be considered finalized.
At the current stage, numerous signal timing models are available for determining
phase combinations, with the HCM2010 timing model being one of the more conventional
options. Therefore, the paper employs the HCM2010 timing model to calculate the timing
for the feasible phase combination schemes determined by the algorithm. During the
signal timing process, input parameters such as stream arrival patterns, stream saturation
flow rates, and yellow phase timing are required. By inputting these parameters, the
timing model can compute the green phase timing for the respective stream, thus
determining the signal timing for the intersection phases. For a detailed understanding of
the timing process, reference can be made to HCM2010 [7].
Upon determining the signal timing for all feasible phase combinations, the average
vehicle delay for different schemes is calculated, and the control scheme with the least
average delay is chosen as the preferred signal intersection control scheme. This approach
aims to further reduce intersection vehicle delay and improve the intersection control
scheme.
3. Algorithm Validation and Analysis Example
To validate the effectiveness of the paper’s algorithm, a verification analysis is conducted
using a specific example. In the context of complex urban road networks with numerous
intersections and random arrival patterns for vehicles at various entry points, diverse lane
configurations exist at urban road intersections. The algorithm in the paper is designed for
signalized intersections with different lane configurations, and to further demonstrate the
feasibility and effectiveness of the algorithm, verification analysis is carried out on a
selected urban signalized intersection with a predetermined lane configuration. Assuming
that at the intersection, right-turn lanes are all equipped with exclusive right-turn lanes
using channelization islands, the right-turn streams are not controlled by signals. The
specific lane configuration and corresponding symbols for the streams are represented as
shown in figure 1.
Figure 1: Lane Movement Layout of Experiment Intersection
According to the thesis algorithm the relevant parameters are determined sequentially
as follows: the set of all streamlines at the intersection
Ψ {σ12 , σ13 , σ 22 , σ 23 , σ 32 , σ 33 , σ 42 , σ 43} ,The total number of flow lines is 8, namely Ψ 8
C82 28
.Streamlines are paired to form sets Θ ,set Θ have altogether group element,
Θ
that is, it contains 28 sets ξ ， ξ 1, 2, , 28 . Based on the two-flow line compatibility
relationship, compatible flow line pairs can be determined, where the set of diverging
{σ , σ13},{σ 22 , σ 23},{σ32 , σ33},{σ 42 , σ 43} ;the set
compatible flow line pairs are respectively 12
of pairs of opposite-compatible flow lines is respectively
{σ12 , σ32 },{σ13 , σ33 },{σ 22 , σ 42},{σ 23 , σ 43} ;the set of merging compatible flow line pairs are
{σ12 , σ 43 },{σ33 , σ 42 } .From this it is possible to determine the set of streamline
respectively
X {{σ12 , σ13},{σ 22 , σ 23},{σ32 , σ33}, {σ 42 , σ 43},{σ12 , σ 32 },{σ13 , σ 33},
compatible pairs
{σ 22 , σ 42 },{σ 23 , σ 43}, {σ12 , σ 43 },{σ33 , σ 42 }} ,a total of 10 groups are assembled X δ ，
assume δ 1, 2, ,10 .Then the set of non-compatible streamline pairs X total 18
Φ {σ 22 , σ 23} ,Only one set of
groups,not listed.Collection of all shared lane flow lines
Ψ1 {σ 22 , σ 23 } ,so the set Ψ {{σ 22 , σ 23 }} .From this it can
shared lane flow groups, the
be determined that the set Ω ，Total elements 1023 groups of elements,the number is
large so it is not listed. According to the method of determining phase flow line
combinations, all sets of phase flow line combinations can be calculated
Λ {{σ12 , σ13 },{σ 22 , σ 23 },{σ32 , σ33 },{ σ 42 , σ 43 },{σ12 , σ 32 },{σ13 , σ33},{σ12 , σ 43 },{σ33 , σ 42 }}
,there are a total of 8 sets of phase flow line combinations.
Once the phase streamline combinations are determined, the phase combination
scheme needs to be determined Pυ ,Through the calculation, it can be seen that there are
109,200 sets of all phase combination programs. Not all the phase combination scheme
can be used as the intersection control phase scheme, it is necessary to carry out condition
judgment on the scheme, and the scheme that meets the setting conditions can be used as
the feasible phase combination scheme. Because of the number of calculations of the
intersection is large, so the Python software is used to program the judgment. Through the
programming judgment to get to meet the conditions of the feasible phase combination
scheme group has a total of 400 groups, including four-phase 48 groups, five-phase
combination scheme 264 groups, six-phase combination scheme 88 groups, see Table 1.
According to Table 1, the algorithm proposed in the paper not only includes traditional
phase combination schemes, but also all phase combination schemes that can be obtained
by the RBS, thereby verifying the generality of the algorithm in determining intersection
phase combination schemes. After determining all feasible phase combination schemes,
the effectiveness of the algorithm is analyzed by combining actual traffic flow analysis. The
traffic flow at the intersection reaches a random nature, and in the autonomous driving
environment, the traffic flow of each lane at the intersection can be directly obtained
through wireless communication technology, thus assuming a set of random traffic flows
for each lane at the intersection as shown in Table 2.
Table 1
FPC Schemes
w mw Fw Phase Number
1 4 { 12 , 13 },{ 22 , 23 },{ 32 , 33 },{ 42 , 43 } 4
{12 , 13},{ 22 , 23 },{ 42 , 43},{ 32 , 33}
2 4
{12 , 13},{ 32 , 33},{ 22 , 23},{ 42 , 43}
3 4
{12 , 13 },{ 32 , 33 },{ 42 , 43},{ 22 , 23}
4 4
{ 22 , 23 },{ 32 , 33},{ 42 , 43},{ 12 , 43},{ 12 , 13 }
49 5 5
{ 22 , 23 },{ 32 , 33 },{ 12 , 13 },{ 12 , 43 },{ 42 , 43 }
50 5
{ 22 , 23 },{ 32 , 33},{ 13 , 33},{ 42 , 43},{ 12 , 43 }
51 5
{ 22 , 23 },{ 32 , 33},{13 , 33},{ 12 , 13},{ 42 , 43}
52 5
{ 22 , 23 },{ 32 , 33},{ 13 , 33},{ 12 , 13 },{12 , 43},{ 42 , 43}
313 6 6
{ 22 , 23 },{ 32 , 33 },{ 13 , 33},{ 33 , 42},{ 42 , 43},{ 12 , 43 }
314 6
{ 22 , 23 },{ 32 , 33},{ 12 , 32 },{12 , 13},{12 , 43 },{ 42 , 43}
315 6
{ 22 , 23 },{ 32 , 33},{ 33 , 42 },{ 42 , 43 },{12 , 43 },{12 , 13 }
316 6
{12 , 43 },{ 12 , 32 },{ 32 , 33},{ 33 , 42 },{13 , 33},{ 22 , 23 }
399 6
{12 , 43 },{12 , 32 },{12 , 13},{13 , 33},{ 33 , 42 },{ 22 , 23}
400 6
Table 2
Traffic Volume of the Movements
Streamline Traffic Streamline Traffic
Flow(pcu/h) Flow(pcu/h)
12 550 32 550
13 750 33 350
22 550 42 800
23 500 43 450
For all feasible phase combination schemes obtained based on the above, the traffic
signal timings were determined and the average vehicle delay was calculated. The study
focuses on researching phase streamlining combinations at signalized intersections in the
context of autonomous driving. Throughout the timing calculation process, the base timing
model remains unchanged, with input parameters such as a vehicle start-up delay of 1.8
seconds (3 seconds for conventional driving), a saturation flow rate of 2000 pcu/h/lane
(1650 pcu/h/lane for conventional driving)[8], and a yellow light duration of 3 seconds.
The calculated average vehicle delay for all feasible phase combination schemes is shown
in Figure 2.
Figure 2: Average Delay of FPC Schemes
From Figure 2, it is evident that different phase combination schemes at signalized
intersections have a significant impact on intersection control effectiveness. The minimum
average delay per vehicle for a specific stream is 79.3 seconds/pcu, while the maximum
value is 173.03 seconds/pcu, representing a difference of more than 2 times. This
indicates that phase combination schemes have a substantial influence on intersection
control effectiveness, emphasizing the importance of selecting an appropriate phase
combination scheme.
Further, the calculation reveals that there are four sets of phase combination schemes,
numbered 316, 329, 360 and 373, corresponding to the minimum average vehicle
delay:；； ；,the 4 groups of phase combination program has the same phase flow line
combination with different phase sequence. The four groups of phase combination scheme
has phase streamline combination of the same phase sequence is different, thus also
verified that when the streamline vehicle reaches a fixed situation, the same phase
streamline combination scheme with different phase sequences, the control effect on the
intersection is the same. In the choice of intersection signal phase combination scheme,
can choose any one phase combination scheme as the actual use of the program.A
protected phase setup is used for the left-turn flowline of the intersection, and since there
are shared lanes in the east inlet flowline of the intersection, there is no opposite-side
control scheme (OS) for the arithmetic example intersection. Conventional signal control
schemes are only DS, CS and RBS.By adopting the phase combination scheme
corresponding to number 316 as the best control scheme for the example intersection, it is
compared and analyzed with the conventional phase combination scheme, and the results
of the analysis are shown in Table 3.
The algorithm proposed in the paper was compared with the conventional control
scheme, and it was found that the average vehicle delay was reduced by 3.77 seconds per
passenger car unit (pcu), 4.19 seconds per pcu, and 12.68 seconds per pcu, respectively.
This indicates that the algorithm proposed in the paper can further reduce vehicle delays
at intersections and improve intersection control efficiency.
Table 3
Movements' Timing and Average Delay of the Control Schemes
Phase flow Streamline green time/s Non- Non-
Scheme w combination English English
program 12 13 22 23 32 33 42 43 or Math or Math
{ 22 , 23},{ 32 , 33 },{ 33 , 42 }
PM 316 { 42 , 43},{ 12 , 43},{ 12 , 13 } 31 25 22 22 18 22 26 28 109 79.3
{ 22 , 23},{ 42 , 43 },{ 13 , 33},
RBS 65 { 12 , 13 },{ 12 , 32 } 29 27 22 22 20 18 26 26 107 83.07
{ 12 , 13},{ 22 , 23 },
DS 1 { 32 , 33},{ 42 , 43 } 28 28 22 22 19 19 26 26 107 83.49
{ 22 , 23},{ 42 , 43},
CS 5 { 13 , 33},{ 12 , 32 } 27 24 23 23 27 24 27 27 113 91.98
To further validate the feasibility and effectiveness of the proposed method in the
paper, VISSIM was used for verification. The timing schemes corresponding to the
conventional signal control scheme and the PM (propose method) scheme obtained from
calculations were input into the simulation software. By setting up detectors in the
simulation, different phase combination control schemes corresponded to simulation
indicators, such as average delay, traffic flow, average queue length, and average number
of stops. Specific simulation comparison results are shown in Figure 3.
Figure 3: Comparison of Simulation Results
The simulation results found that the phase combination scheme obtained by the thesis
algorithm improves the simulation indexes to different degrees compared with the other
schemes, which shows that the thesis algorithm can further improve the intersection
signal control, and further verifies the feasibility and effectiveness of the thesis method.
4. Conclusion
By combining the existing timing models, the optimal control scheme for the intersection
in the true sense is calculated. Through the calculation examples and simulation analysis,
it is found that the algorithm can further reduce the average delay of vehicles in the
intersection flow lines and improve the intersection control efficiency. However, the thesis
research only considers the compatibility relationship between motor vehicle flow lines,
and the compatibility relationship between the flow lines of multiple transportation
modes will be considered comprehensively to study the intersection control scheme.
Meanwhile, with the development and upgrading of automatic driving technology, the
unsignalized processing of intersections under the automatic driving environment is
studied, and how the streamline vehicles can realize non-stopping passage in the case of
unsignalized control of intersections is analyzed.
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