Green Wave Arterial Cooperative Control Strategy Based on Through-Traffic Priority

Abstract

Mainline coordinated control is usually based on fixed speed and statistical traffic flow by period. However, in actual operation, the vehicles parked in front of the intersection and the arriving vehicles often fluctuate, and the through-traffic green time is wasted due to phase transition, which leads to mismatches between the signal plans and actual traffic flow requirements, affecting the traffic efficiency of the intersection. To address the above issues, using vehicle–road collaborative control (VRCC), by calculating the phase difference lead time and phase difference of adjacent intersections, the green extension time for the green wave through-traffic phase, and the guiding vehicle speed, the goal of reducing the detention volume of through traffic, reducing the waste of through-traffic green time caused by phase transitions and improving the throughput of through traffic can be achieved. The speed of the green wave traffic flow is increased by guiding vehicles to form saturated platoons during green periods. Finally, PTV VISSIM 4.3 was used for simulation verification, and the results showed that compared to not implementing the control strategy, the average delay on the arterial road was reduced by 85.1%, the average number of stops was reduced by 84.3%, the average travel time was reduced by 34%, and the average queue length was reduced by 62.6%. This significantly improved the efficiency of traffic on the arterial road and effectively reduced congestion.

1. Introduction

With the acceleration of urbanization, road congestion has become a challenging problem that plagues urban development and residents’ travel. Traffic signal control is one of the most effective means to solve traffic congestion problems in traffic management and control, and is the foundation of realizing intelligent transportation [1,2,3]. The coordinated control of green waves on the mainline is one of the main methods of traffic signal control, enabling vehicles to pass through the mainlines without stopping or with minimal stops. It plays a vital role in alleviating traffic congestion and improving the traffic efficiency of urban road networks [4,5]. However, the current application of the mainline green wave coordinated control system on mainlines only works well during off-peak hours. When the number of left- and right-turn vehicles on the mainline increases during peak hours, the number of through vehicles stuck at intersections also increases. At that time, the green wave coordinated control on the mainline could not adapt to the dynamic changes in traffic flow during peak hours, and the green wave effect was reduced.

Therefore, recent research has aimed to optimize signal timing to adapt to the dynamic fluctuations of traffic volume, reduce the green time waste during transitions between phases, optimize the green wave control effect during peak periods, reduce congestion on mainlines, and improve the adaptability of the mainline green wave coordinated control under saturation conditions [6,7,8]. In traditional traffic control systems, due to the limitations in information exchange between vehicles and roads, parameters such as driving speed and the initial queue length of road sections can only be estimated using empirical formulas and then set as fixed values [9,10]. Scholars have proposed signal control schemes as a starting point for mainline green wave coordination in saturation conditions. For example, Lv et al. [11] proposed a novel dynamic two-way green wave coordinated control strategy by combining genetic BP neural networks with traditional analytical algorithms to maximize the green wave bandwidth of main roads. Zhang et al. [12] proposed a comprehensive mixed-integer nonlinear programming model and compared it with traditional genetic algorithms and heuristic algorithms based on genetic algorithms, to demonstrate the effectiveness of the proposed model and algorithm. Wang et al. [13] proposed a novel dynamic model to simulate urban traffic flow. By defining an objective function based on traffic flow, congestion, and waiting time, and using an optimization algorithm based on Bellman’s principle of optimality, the effectiveness of the algorithm was verified through numerical experiments. Keyvan Ekbatani et al. [14] established a macroscopic traffic signal feedback model by analyzing the operational states of different traffic flows at intersections, with the goal of maximizing the traffic flow exiting the selected regional road network. Jing et al. [15] considered the volatility of vehicle speeds and speed constraints under saturation conditions and proposed a formula for calculating the percentage of speed fluctuation. They designed a dual-objective control model that aims to maximize both the two-way green wave bandwidth and the maximum percentage of speed fluctuation. However, in the practical traffic applications of the above studies, these parameters could influence the signal at intersections. If the estimated values are too low or too high, it will affect the effectiveness of the coordinated control and even cause failure.

In recent years, with the accelerated popularization of new technologies such as 5G, artificial intelligence, big data, the Internet of Things, and vehicle–road collaboration control (VRCC), as well as their integration with the transportation field, the intelligent transportation industry has been gradually upgraded. Using VRCC to improve mainline green wave coordinated control methods and strategies, traffic congestion can be better alleviated [16,17,18]. Scholars have also conducted research on this topic. Xu et al. [19] studied coordinated control technology based on traffic signal optimization and speed control. They calculated the optimal signal timing and vehicle arrival times to optimize vehicle braking force and proposed a coordinated control method for signal timing and speed optimization, thereby reducing vehicle travel time and fuel consumption. Song et al. [20] utilized Internet of Vehicles (IoV) technology to intelligently control intersections by optimizing green light duration, demonstrating that this method can effectively reduce the number of queued vehicles. Li et al. [21] considered the optimization of signal timing and phase differences, further transforming the signal optimization and coordination problem into a two-level signal control problem. Consequently, they proposed a predictive two-level iterative solution method. Ghoul et al. [22] adjusted the system in real time based on real-time traffic information at intersections and combined it with dynamic vehicle speed guidance, proposing a signal–vehicle-coupling control scheme that can effectively reduce the conflict rate and vehicle delays at intersections. Wang et al. [23] combined vehicle speed and signal timing optimization to maximize the capacity of arterial roads, establishing a control model for speed control and arterial signal coordination.

In their study of vehicle speed guidance technology, Yang et al. [24] proposed a trunk line coordination control method based on vehicle speed guidance, to address the issue of frequent stops at intersections. This method aims to reduce vehicle delays and the number of stops. Wu et al. [25] established speed guidance models for green and red light situations, respectively, to optimize vehicle arrival times and signal timing parameters, exploring the relationship between speed and signal timing. Bie et al. [26] proposed a prediction model based on public transportation travel time, using dynamic control to determine the headway on bus-only lanes, thus improving vehicle operation efficiency. Wu et al. [27] developed a new method combining ramp control and speed guidance for urban expressway entrance ramps, centered on Model Predictive Control (MPC), through the analysis of MPC and macroscopic traffic flow, further enhancing traffic efficiency and safety. However, these studies still have limitations, such as considering only single operating conditions and lacking flexibility to adapt to dynamic changes in traffic volume during peak periods. From the above research, the existing research results on trunk line signal coordination control and vehicle speed guidance provide important theoretical support for alleviating urban traffic congestion. Nevertheless, most current studies still focus on traditional models, where the adaptation process to changes in traffic factors such as traffic flow and section speed is merely passive, without actively adjusting signal timing. Thus, they cannot effectively address the changes caused by traffic flow fluctuations.

This article focuses on the mainline green wave coordinated control of signalized intersections along urban arterials. It presents the one-way green wave VRCC method under saturation conditions. The main contributions are as follows:

(1) In response to dynamic changes in traffic flow, the paper proposes strategies for extending green light duration and dynamically adjusting phase differences. These strategies allow the real-time adjustment of green light periods based on vehicle arrivals, reducing the wastage of green time during phase transitions.

(2) The paper designs a vehicle speed guidance strategy that directs vehicles to pass through intersections at appropriate speeds, thereby reducing queue lengths and travel times at intersections.

(3) The proposed control strategies were validated using PTV VISSIM 4.3 simulation software. The results show that, compared to scenarios without the control strategy, the average delay on the arterial road decreased by 85.1%, average stops reduced by 84.3%, the average travel time dropped by 34%, and average queue length shortened by 62.6%, significantly improving arterial road efficiency and alleviating congestion.

2. Methodology

This section first introduces the mechanism of green wave failure, laying the foundation for the subsequent work. Then, it presents the VRCC method, which aims to optimize traffic flow along urban arterials by enhancing the green wave effect. Using data from roadside equipment, the VRCC method combines green time extension and phase difference adjustment strategies to minimize delays, reduce queue lengths, and improve overall traffic efficiency.

2.1. Problem Description

Because traffic flow is always in a state of dynamic change, when the traffic saturation is low (Figure 1a), vehicle queues at the intersection have little significant impact on the operation of upstream vehicles. Vehicles can pass the intersection at the designed green wave speed. However, when the traffic flow reaches saturation (Figure 1b), as the number of left- and right-turn vehicles from upstream intersections continues to increase, the number of through vehicles queued at the intersection also continues to grow, which easily destroys the green wave effect. This will lead to long vehicle queues at downstream intersections. At intersections with limited queueing space, if the downstream queue has not fully dissipated, it will cause secondary stops for vehicles released at the beginning of the upstream green, leading to increased delays and even traffic congestion on the main road.

2.2. Proposed VRCC Method

The green wave VRCC method based on through-traffic priority includes three modules (Figure 2): an information acquisition module, a signal timing module, and a vehicle speed guidance module. First, the information acquisition module collects the left- and right-turn inflow volume at upstream intersections, the through queue volume at the current intersection in the previous cycle, and the vehicle arrival data at the end of the green wave through phase through the roadside equipment roadside unit (RSU). Then, it calculates the phase difference advance time and phase difference between adjacent intersections, as well as the green time extension time for the green wave through-traffic phase. Second, the signal timing module combines the green wave priority phase green time extension strategy and the phase difference dynamic adjustment strategy to adjust and update the signal timing plans for the current intersection and the downstream intersection in the current cycle. Third, the vehicle speed guidance module combines roadside equipment, edge computing equipment, on-board unit equipment (OBU), and roadside display equipment to implement a vehicle speed guidance strategy that enables the left, right, and through inflowing traffic at upstream intersections to form a platoon and catch up with the previous platoon, reducing green time waste during phase transitions. This reduces the through-traffic queue volume, increasing the through-traffic throughput, and reducing the through-traffic travel time.

Due to the complex and changeable road conditions, the following assumptions are made to facilitate the research on control and simplify the construction process of the control model:

(1) The model is designed for unidirectional green wave traffic, with the through direction of the mainline in the east selected as the unidirectional green wave direction. The green wave through-traffic volume at each intersection comprises left turns from the south, right turns from the north, and through traffic from the east.

(2) The signal timing at the mainline intersections adopts the overlapping phase method, and the westbound through-left direction is the first phase. The overlapping phases are as follows (Figure 3a): Phase 1 is westbound through-left, Phase 2 is westbound and eastbound through, Phase 3 is eastbound through-left, Phase 4 is northbound through-left-right, and Phase 5 is southbound through-left-right. Since the signal phase settings in the PTV VISSIM 4.3 simulation software need to be specific to each lane, the actual signal phase needs to be disassembled to be the same as the actual signal phase scheme. The disassembled phases are as follows (Figure 3b): Phase 1 is westbound left, Phase 2 is westbound through, Phase 3 is eastbound through, Phase 4 is eastbound left, Phase 5 is northbound through-left-right, and Phase 6 is southbound through-left-right.

(3) Right turns are controlled at the westbound entrance of the mainline intersection.

(4) The vehicles on the mainline arrive uniformly.

(5) The left-turn queues at downstream intersections do not overflow and do not cause congestion in the through-traffic flow.

2.3. Control Logic

The control logic of the mainline green wave VRCC strategy based on through-traffic priority mainly includes unidirectional green wave phase adjustment and single intersection signal cycling. The detailed control logic schematic is shown in Figure 4, and the phase difference operating times at each intersection are shown in

Table 1. Phase difference operating times at each signalized intersection.

Interval	Phase Condition	Celapsed Interval
A~B	Phases 1 and 2 are green	$t_{e-\mathrm{r}\left(i,0\right)}\le C_{elapsed}<t_{e-\mathrm{g}\left(i,0\right)}$
B	Phases 1 and 2 are yellow	$t_{e-\mathrm{g}(i,0)}\le C_{elapsed}<t_{e-\mathrm{r}(i,2)}$
B~C	Phases 2 and 3 are green	$t_{e-\mathrm{r}(i,2)}\le C_{elapsed}<t_{e-\mathrm{g}(i,1)}$
C	Phase 2 is yellow	$t_{e-\mathrm{g}(i,1)}\le C_{elapsed}<t_{e-\mathrm{r}(i,3)}$
C~D	Phases 3 and 4 are green	$t_{e-\mathrm{r}(i,3)}\le C_{elapsed}<t_{e-\mathrm{g}(i,3)}$
D	Phases 3 and 4 are yellow	$t_{e-\mathrm{g}(i,3)}\le C_{elapsed}<t_{e-\mathrm{r}(i,4)}$
D~E	Phase 5 is green	$t_{e-\mathrm{r}(i,4)}\le C_{elapsed}<t_{e-g(i,4)}$
E	Phase 5 is yellow	$t_{e-g(i,4)}\le C_{elapsed}<t_{e-\mathrm{r}(i,5)}$
E~F	Phase 6 is green	$t_{e-\mathrm{r}(i,5)}\le C_{elapsed}<t_{e-g(i,5)}$
F	Phase 6 is yellow	$t_{e-g(i,5)}\le C_{elapsed}<t_{e-\mathrm{r}(i,5)}+A$

.

2.3.1. One-Way Green Wave Phase Adjustment

Set the cycle to adjust the phase difference (absolute phase difference) in place. When the simulation time is an integer multiple of the simulation accuracy, if the current phase difference is greater than the initially set phase difference, it indicates that the phase difference at the intersection has been adjusted in place, and the cycle is calculated until the last intersection in the arterial system. When all intersections on the mainline have their phase differences adjusted in place, the calculation is ended. If the phase difference at the current intersection has not been adjusted in place, execute the initial default signal timing scheme; if the phase difference at the current intersection has already been adjusted in place, start the calculation. When the last second of the cycle is reached, then

$$C_{elapsed}=t_{e-\mathrm{g}(i,5)}+A-1$$

(1)

where $C_{elapsed}$ = phase difference operating time at each intersection, $t_{e-\mathrm{g}(i,5)}$ = time when the green ends, i = ith intersection, and $A$ = yellow and all-red times.

2.3.2. Cycle of Signal Timing Scheme for Intersections

At the end of the cycle, revert to the initial timing. In the previous cycle, due to the extended green time for through traffic in the east direction, the left turns from the south and right turns from the north were cut off early, achieving cycle balance. The cycle length remains unchanged, but the early cut-off of green time for north–south traffic affects the phase difference at the next intersection. At this point, reverting to the initial timing does not affect the current intersection.

3. Control Strategies

This section addresses the dynamic changes in the number of vehicles retained and arriving at intersections and the issue of wasted green light time for straight-through traffic due to phase transition times. A straight-through priority coordinated control strategy for arterial green wave traffic–road cooperation is proposed. By calculating the advance time and phase difference between two adjacent intersections, extending the green light duration for the green wave straight-through phase, and guiding vehicle speeds, the strategy aims to reduce the retention of straight-through traffic, minimize the green light time wasted during phase transitions, and increase the throughput of straight-through traffic.

3.1. Strategy 1: Green Phase Extension

3.1.1. Green Time Extension

A detector is installed at the stop line of the intersection’s entrance. A preset initial green time $g_i$ is set in the signal controller (Figure 5). When no vehicles passing through are detected during the last second before the green time for that phase ends, it can be replaced with other phases. When the detector detects a vehicle arriving at the stop line, the green time is extended by one preset unit green time $g_o$ until no arriving vehicles are detected or the green time for that phase has reached its maximum. Then, it is replaced with other phases. The initial green time equals the minimum value minus one unit of green time extension. The actual green time should be greater than or equal to the shortest green time $g_{min}$ and less than the maximum green time $g_{max}$.

3.1.2. Green Time Phase at Current Intersection after Green Time Extension

By using detectors to monitor the arrival of through vehicles, the green time for the westbound through phase can be extended to reduce through-traffic congestion. At the same time, cycle balancing is performed by reducing the green time for the eastbound left-turn phase, northbound through-left phase, and southbound through-left phase, thereby reducing the number of merging vehicles making left and right turns.

The phase order adopts the overlapping phase, and Phase 1 (westbound through) is the target priority phase, while the remaining phases are non-priority phases. Among them, the adjustable phases that can be shortened are Phase 3 (eastbound through-left), Phase 4 (northbound through-left), and Phase 5 (southbound through-left). The green time requirements for the priority phase adjustment are as follows: First, shorten the green time of Phase 3 to the minimum green time, and then uniformly shorten the green times of Phases 4 and 5.

Let the green times of Phases 1–5 be denoted by $g_{i,1}$, $g_{i,2}$, $g_{i,3}$, $g_{i,4}$, and $g_{i,5}$. Then, the specific calculations are as follows:

Step 1: When the required adjustment of green time satisfies

$$g_{de}\le g_{de,max\left(i,3\right)}$$

(2)

where $g_{de}$ = adjustment of amount of green time demand and $g_{de,max\left(i,3\right)}$ = maximum adjustable green time of Phase 3.

By shortening $g_{i,3}$ and keeping the other phases unchanged, the adjusted green time of each phase can be obtained as

$$\left\{\begin{array}{l}{g}_{i,3}=g_{i,3}-g_{de}\\ g_{i,1}=g_{i,1}+g_{de}\end{array}\right.$$

(3)

Step 2: When the required adjustment of green time $g_{de}$ satisfies

$$g_{de}>g_{de,max\left(i,3\right)}$$

(4)

then, $g_{i,3}$ must be shortened first to its minimum value $g_{min\left(i,3\right)}$, and $g_{i,4}$ and $g_{i,5}$ must be uniformly shortened one by one until the remaining required green time reduction $g_{min\left(i,3\right)}$ becomes 0.

After reducing the Phase 3 green time, the remaining required green time reduction is

$$g_{i,5left-de}=g_{i,5de}-g_{i,5de,max\left(i,3\right)}$$

(5)

The adjusted green times of Phases 1 and 3 can be obtained as

$$\left\{\begin{array}{l}{g}_{i,1}=g_{i,1}+g_{de,max\left(i,3\right)}\\ g_{i,3}=g_{i,3}-g_{de,max\left(i,3\right)}\end{array}\right.$$

(6)

Step 3: Calculate the green times of Phases 4 and 5 based on the conditions, as shown in

Table 2. Formulas for green times of Phases 4 and 5 for different conditions.

Conditions	${\mathit{g}}_{\mathit{i},4}$$\mathbf{and}{\mathit{g}}_{\mathit{i},5}$
$\begin{array}{l}{g}_{i,4}-g_{phase,4}\ge g_{min\left(i,4\right)}\\ g_{i,5}-g_{phase,5}\ge g_{min\left(i,5\right)}\end{array}$	$\begin{array}{l}{g}_{i,4}=g_{i,5}-g_{phase,4}\\ g_{i,5}=g_{i,5}-g_{phase,5}\end{array}$
$\begin{array}{l}{g}_{i,4}-g_{phase,4}<g_{min\left(i,4\right)}\\ g_{i,5}-g_{phase,5}\ge g_{min\left(i,5\right)}\end{array}$	$\begin{array}{c}{g}_{i,4}=g_{min\left(i,4\right)}\\ g_{i,5}=g_{i,5}-(g_{left-de}-g_{de,max(i,4)})\end{array}$
$\begin{array}{l}{g}_{i,4}-g_{phase,4}\ge g_{min\left(i,4\right)}\\ g_{i,5}-g_{phase,5}<g_{min\left(i,5\right)}\end{array}$	$\begin{array}{c}{g}_{i,4}=g_{i,4}-(g_{left-de}-g_{de,max(i,5)})\\ g_{i,5}=g_{min\left(i,5\right)}\end{array}$

, where $g_{phase,4}$ = green time adjustment required for Phase 4, $g_{min\left(i,4\right)}$ = minimum green time of Phase 4, $g_{phase,5}$ = green time adjustment required for Phase 5, and $g_{min\left(i,5\right)}$ = minimum green time of Phase 5, $g_{de,max(i,4)}$ = maximum adjustable green time of Phase 4, and $g_{de,max(i,5)}$ = maximum adjustable green time of Phase 5.

3.2. Strategy 2: Dynamic Offset Adjustment

In the VRCC context, the phase difference can be dynamically adjusted based on the vehicle speed under the real-time dynamic traffic flow state, to achieve optimal control of arterial coordination. Within the range of the guided vehicle speed, the phase difference is optimized and adjusted to achieve optimal control of the arterial traffic flow.

Before the current intersection returns to the initial timing, calculate the impact of the previous cycle’s phase difference on the downstream intersection: The extension of the green for the westbound through-left turn results in a decrease in the green time for the north–south through-left turn, which affects the volume of left and right turns from the previous cycle. Additionally, consider the volume of through traffic that was queued at the downstream intersection in the previous cycle, which ultimately affects the phase difference of the downstream intersection. The phase difference adjustment first estimates the initial queue length based on the initial input traffic volume, then sets an initial phase difference, and detects the left- and right-turn volumes and the through-traffic volume that was queued at the previous intersection by installing detectors before the stop line of the intersection. It calculates the new real-time phase difference, compares the initial phase difference with the real-time phase difference change, and calculates the advance or delay amount of the phase difference.

3.2.1. Phase Difference Advance Time and Value

Step 1: Calculate the through traffic queueing and left/right turn volumes at the downstream intersection by

$$\left\{\begin{array}{l}Ve{h}_{1(i+1)}={\displaystyle \frac{(Ve{h}_{l(i)}+Ve{h}_{r(i)})\times f_{s(i)}+Ve{h}_{unclear(i+1)}}{n_{s(i+1)}}}\\ t_{clean-s(i+1)}={\displaystyle \frac{3600\times Ve{h}_{1(i+1)}}{Ca{p}_{s(i+1)}}}\end{array}\right.$$

(7)

where $Ve{h}_{1(i+1)}$ = number of through vehicles in the downstream intersection’s single lane, $Ve{h}_{l(i+1)}$ = number of left-turning vehicles merging from the upstream intersection, $Ve{h}_{r(i+1)}$ = number of right-turning vehicles merging from the upstream intersection, $Ve{h}_{unclear(i+1)}$ = number of through vehicles queuing at the downstream intersection, $n_{s(i+1)}$ = number of through lanes at the downstream intersection, $t_{clean-s(i+1)}$ = green clearing time required for the remaining straight vehicles’ traffic volume (including the through-traffic queuing and left/right-turn merging traffic) to clear, and $Ca{p}_{s(i+1)}$ = traffic capacity of the downstream intersection’s through lanes.

Step 2: Based on the volume of left and right turns merging, determine whether the leading vehicle of the left turn will stop before the stop line of the intersection’s east entrance when traveling at the expected speed of the left turn. Calculate the phase difference advance time and phase difference in this situation.

(a)

A stop and queue will occur, when the left and right turns’ merge headway vehicle travels at the desired speed $V_{desire-l(i)}$ through the road section $L_{l-s(i)}$ between the intersections within the merge time $t_{lr(i)}$. Then, the following condition $V_{desire-l(i)}/3.6\times t_{lr(i)}>L_{l-s(i)}$ is met. At this time

$$\left\{\begin{array}{l}{t}_{O_{Si+1}(ad)}=t_{clean-s,1(i)}+t_{loss(i,0)}\\ O{S}_{new(i+1)}=t_1+t_2-t_{O{S}_{i+1}(ad)}\end{array}\right.$$

(8)

where $t_{O_{Si+1}(ad)}$ = phase advance time at the downstream intersection, $t_{clean-s,1(i)}$ = green clearing time for the left- and right-turn merging traffic within one cycle at the upstream intersection, $t_{loss(i,0)}$ = phase start loss time, $O{S}_{new(i+1)}$= real-time phase difference, $t_1$ = time required for the through merging traffic to catch up with the left-turning merging traffic, and $t_2$ = time required for the remaining distance to be traveled at the speed of the leading vehicle in the left and right straight-line queue.

(b)

No stopping or queuing occurs when the left and right turns’ merge headway vehicle travels at the desired speed $V_{desire-l(i)}$ through the road section $L_{l-s(i)}$ between the intersections within the left and right turn merge time $t_{lr(i)}$. Then, the following condition $V_{desire-l(i)}/3.6\times t_{lr(i)}\le L_{l-s(i)}$ is met. At this time

$$\left\{\begin{array}{l}{t}_{O_{Si+1}(ad)}=t_{clean-s,1(i)}\\ O{S}_{new(i+1)}=t_1+t_2-t_{O{S}_{i+1}(ad)}\end{array}\right.$$

(9)

The phase difference variation is obtained based on the difference $\mathsf{\Delta }O{S}_{(i+1)}=O{S}_{new(i+1)}-O{S}_{i+1}$ between the real-time phase difference and the initial phase difference.

3.2.2. Phase Difference Adjustment

At the end of the cycle of the current intersection i, estimate the non-priority green extension or truncation time for the downstream intersection i + 1 as follows:

Step 1: Determine the adjustable phase number under the running time of different cycles as follows:

$$Phase=\left\{\begin{array}{l}3\hspace{1em}\hspace{1em},\hspace{1em}{t}_{e-g(i,1)}\le t_{cycle(i)}<t_{e-g(i,3)}\\ 2\hspace{1em}\hspace{1em},\hspace{1em}{t}_{e-g(i,3)}\le t_{cycle(i)}<t_{e-g(i,4)}\\ 1\hspace{1em}\hspace{1em},\hspace{1em}{t}_{e-g(i,4)}\le t_{cycle(i)}<t_{e-g(i,5)}\end{array}\right.$$

(10)

where $Phase$ = number of phases, $t_{cycle(i)}$ = cycle running time, and $t_{e-g(i,m)}$ = green end time of the m-th phase. Note that when the cycle has run for a period during the fourth green phase and before, the number of phases can be adjusted to 3. When the cycle has run for a period during the green and yellow times of Phase 5, the number of phases can be adjusted to 2. When the cycle has run for a period during the green and yellow times of Phase 6, the number of phases can be adjusted to 1.

Step 2: Recalculate the maximum adjustable green time for each phase.

$$g_{n,max}=\left\{\begin{array}{l}{t}_{e-\mathrm{g}(i,3)}-t_{cycle\left(i\right)}-g_{min(i,3)}\hspace{1em},\hspace{1em}{t}_{e-\mathrm{g}(i,3)}-t_{cycle\left(i\right)}>g_{min(i,3)}\\ t_{e-\mathrm{g}(i,4)}-t_{cycle\left(i\right)}-g_{min(i,4)}\hspace{1em},\hspace{1em}{t}_{e-\mathrm{g}(i,4)}-t_{cycle\left(i\right)}>g_{min(i,4)}\\ t_{e-\mathrm{g}(i,5)}-t_{cycle\left(i\right)}-g_{min(i,5)}\hspace{1em},\hspace{1em}{t}_{e-\mathrm{g}(i,5)}-t_{cycle\left(i\right)}>g_{min(i,5)}\end{array}\right.$$

(11)

where ${\mathrm{g}}_{n,max}$ = maximum adjustable green time after adjustment.

Step 3: Allocate the phase difference changes to each reducible phase until the maximum adjustable green time for that phase becomes 0.

$$\left\{\begin{array}{l}\mathsf{\Delta }{g}_m+1\le g_{n,max(m)}\\ \mathsf{\Delta }{g}_m=\mathsf{\Delta }{g}_m+1\\ \left|\mathsf{\Delta }O{S}_{(i+1)}\right|=\left|\mathsf{\Delta }O{S}_{(i+1)}\right|-1\end{array}\right.$$

(12)

where $g_{n,max(m)}$ = maximum adjustable green time for the m-th phase, $\mathsf{\Delta }{g}_m$ = change in green time for each phase, and $\left|\mathsf{\Delta }O{S}_{(i+1)}\right|$ = absolute value of the phase difference change.

3.2.3. Update Signal Timing of Downstream Intersection

In the previous cycle, when the green of the westbound through phase was extended, and the green of the northbound left-turn and southbound right-turn merge was truncated to achieve a cycle balance, the red and green end times were updated. Then, the intersection returned to its initial timing without affecting the current intersection. The adjusted total amount and the adjusted cycle length are shown in Equation (13).

$$\left\{\begin{array}{l}{g}_{de,max(i,m)}=g_{i,m}-g_{min(i,m)}\\ g_{de,all(i)}=g_{de,max(i,3)}+g_{de,max(i,4)}+g_{de,max(i,5)}\\ t_{lr\left(i\right)}=g_{i,4}+g_{i,5}+2\times A\\ C=g_{i,0}+g_{i,2}+g_{i,4}+g_{i,5}\end{array}\right.$$

(13)

where $g_{de,max(i,m)}$ = maximum adjustable green time for the m-th phase at the i-th intersection, $g_{i,m}$ = current green time for the m-th phase at the i-th intersection, $g_{min\left(i,m\right)}$ = minimum green time for the m-th phase at the i-th intersection, $g_{de,all\left(i\right)}$ = total maximum adjustable green time for all phases, $C_i$ = current cycle duration for the i-th intersection, $t_{lr\left(i\right)}$ = left- and right-turn merge time at the i-th intersection, and $A$ = yellow and all-red times.

After the phase adjustment, update the signal timing of each phase at the downstream intersection. The changes in the red end time $t_{r-g(i,m)}$ and green end time $t_{e-g(i,m)}$ of each phase are shown in

Table 3. Red end time and green end time for each phase.

Phase	Red End Time	Green End Time
Westbound left turn	$t_{e-r(i,0)}=0$	$t_{e-g(i,0)}=t_{e-r(i,0)}+g_{i,0}$
Westbound through	$t_{e-r(i,1)}=0$	$t_{e-g(i,1)}=t_{e-r(i,1)}+g_{i,1}$
Eastbound through	$t_{e-r(i,2)}=t_{e-g(i,0)}+A$	$t_{e-g(i,2)}=t_{e-r(i,2)}+g_{i,2}$
Eastbound left turn	$t_{e-r(i,3)}=t_{e-g(i,1)}+A$	$t_{e-g(i,3)}=t_{e-r(i,3)}+g_{i,3}$
Northbound through-left	$t_{e-r(i,4)}=t_{e-g(i,3)}+A$	$t_{e-g(i,4)}=t_{e-r(i,4)}+g_{i,4}$
Southbound through-left	$t_{e-r(i,5)}=t_{e-g(i,4)}+A$	$t_{e-g(i,5)}=t_{e-r(i,5)}+g_{i,5}$

.

3.3. Strategy 3: Speed Guidance

Vehicle speed guidance is required during the extension of green phases and the adjustment of phase differences for green wave priority. When the phase requires an extension or early interruption of the green period, the current vehicle position and the phase time of the traffic signal are used to calculate the vehicle guidance speed, which determines the appropriate vehicle speed at that time. By accelerating or decelerating to achieve the appropriate speed, the waste of green time during the transition between phases can be reduced. Without considering the possibility of secondary stops, there are several situations upstream merging vehicles may encounter when arriving at the intersection. Different speed guidance strategies should be developed based on different vehicle arrival conditions, as described next.

3.3.1. Scenario 1: Vehicles Arrive during Green Time

When a vehicle arrives during the green period and the queue of vehicles in the previous cycle has completely dissipated, the vehicle can pass through the intersection without stopping or slowing down. To improve the utilization rate of green lights and reduce vehicle travel time, vehicles can be guided to accelerate through the intersection (Figure 6).

3.3.2. Scenario 2: Vehicles Arrive during Green Time and Queue from Previous Cycle Exists

When a vehicle arrives during the green time and the vehicles queued in the previous cycle have not completely dispersed, the vehicle must slow down or stop before passing the stop line. If the green time is sufficient, to avoid the influence of the vehicles queued in front, the vehicle can be guided to slow down and follow the front vehicle, so that it can arrive at the stop line just when the vehicles queued in front have just dispersed (Figure 7a). If the green time is insufficient, the vehicle must pass the intersection during the next green period, at which time the vehicle can be guided to slow down to the allowable speed range, so that it can pass the stop line after the next green is turned on and avoiding stopping and reducing the starting loss time (Figure 7b).

3.3.3. Scenario 3: Vehicles Arrive during Red Time

When a vehicle arrives during the red period, the vehicle must slow down and stop, and wait for the next green to start and pass the stop line. At this time, the vehicle can be guided to accelerate, so that it can pass the intersection during the current green period, reducing delay and travel time; or the vehicle can be guided to decelerate and pass the stop line after the next green is turned on, avoiding stopping (Figure 8).

4. Simulation Experiments

To verify the optimization effect of the proposed strategy, this section uses the actual traffic environment of five consecutive intersections on Jinshan Avenue. PTV VISSIM 4.3 simulation software and Visual Studio 2020 development software are utilized to write a custom control program for simulation verification. By combining traffic flow, the remaining straight-through ratio, and minimum green light time, a multi-factor orthogonal adaptive experiment is designed. Finally, the results of each experiment are analyzed to explore the appropriate values for the relevant factors of the strategy method. These results are compared with other control methods to demonstrate the effectiveness and feasibility of the proposed coordinated control optimization method.

4.1. Experimental Design

The Jinshan Avenue in Fuzhou, China (Figure 9), which has five consecutive intersections, was selected to build the simulation platform. The Visual Studio 2012 programming environment is used to conduct secondary development on PTV VISSIM 4.3 to implement the control logic and control strategy of the algorithm. Among them, the coordinated direction of intersections 1 to 5 is the forward direction of control. The experiment first conducts an adaptive experimental analysis to optimize westbound through-traffic efficiency. Then, it selects the combination of influencing factors with better coordinated adaptive effects to design comparative experiments. Finally, under these optimal influencing factors, the MAXBAND method, the Improved MULTIBAND method, the method of only applying vehicle speed guidance, the method of not applying VRCC, and the research model method are simulated and compared and analyzed based on indicators. Through traffic surveys of individual intersections along Jinshan Avenue, the mainline peak traffic flows (on 10 November 2023) at each entrance to the outer intersections are as shown in

Table 4. Traffic flow (pcu/h) of each converging inlet road at peripheral intersections.

Intersection No.
1			2		3		4		5
East	South	North	South	North	South	North	South	North	South	North
1848	490	524	466	542	564	484	542	384	458	460

. The signal timing cycle at each intersection is 166 s, and the initial signal timing for each phase is shown in Figure 10.

Using the adaptive experiments, it can be seen from the control strategies that they are mainly affected by traffic volume, the remaining straight vehicles proportion of incoming traffic, and the minimum green time of non-priority phases. Therefore, the main purpose of the experimental design is to explore the adaptability of the proposed collaborative control strategy under changes in these three influencing factors. We analyze the optimization effect of three strategy combinations, including the green extension strategy for green wave priority phases, the dynamic adjustment strategy for phase differences, and the vehicle speed guidance strategy, compared to the scenarios where no control strategy is in place.

When the optimization effect is better, it proves that the proposed combination method has a higher degree of adaptability to the combination of influencing factors selected at this time. Therefore, the experiment designed a three-factor, four-level orthogonal experiment using SPSS 27 data analysis software, set the random number seed to 300, selected 0.8, 1.0, 1.2, and 1.4 as the coefficients for the current traffic flow V in different traffic flow analyses, and selected 50%, 60%, 70%, and 80% for the remaining straight vehicle proportion of incoming traffic. The minimum green time was selected as 10 s, 12 s, 14 s, and 16 s, and then 16 sets of experimental combinations were automatically generated, as shown in

Table 5. Factor orthogonal experimental design.

Experiment Number	Imported Traffic Volume (pcu/h) a	Remaining Straight Vehicles Proportion (%)	Minimum Green Time (s)
1	0.8 V	50	10
2	0.8 V	60	12
3	0.8 V	70	14
4	0.8 V	80	16
5	V	50	12
6	V	60	10
7	V	70	16
8	V	80	14
9	1.2 V	50	14
10	1.2 V	60	16
11	1.2 V	70	10
12	1.2 V	80	12
13	1.4 V	50	16
14	1.4 V	60	14
15	1.4 V	70	12
16	1.4 V	80	10

^a V = current traffic flow.

. In addition, 16 sets of control group experiments were set up with the same value of influencing factors but without the application of coordination control optimization.

4.2. Results

4.2.1. Comparison of Proposed Method and Control Groups

The simulation results are analyzed based on the traffic capacity and average delay of the westbound through vehicles of the controlled group (proposed method) relative to the uncontrolled group (Figure 11). By comparing and analyzing the traffic capacity, it can be found that the traffic capacity values of the controlled and uncontrolled groups in the scheme combinations with experiment numbers 1, 2, 5, 6, 9, 10, 13, and 19 are similar, with the optimization ratio fluctuating around 0%. The analysis shows that the remaining straight vehicle proportion of this group of schemes is 50% or 60%. This is because when the remaining straight vehicles proportion is low, there are also fewer through vehicles traveling westbound.

Both the controlled and uncontrolled vehicles can pass the intersection within one green time, which does not reflect the effectiveness of the control strategy. However, in the controlled group with experiment numbers 4, 7, 8, 11, 12, 15, and 16, the proposed method significantly improved traffic capacity compared to the uncontrolled groups, as the incoming traffic volume increased and the remaining straight vehicle proportion is raised. The most significant improvement is seen in the 12th group, which increased by 81.2%. This indicates that the three strategies can effectively increase the incoming traffic flow of each intersection under the connected vehicle environment, ensuring that the green time is fully used and increasing the through-traffic flow.

By comparing and analyzing the delay, after applying the coordinated control strategy, the average delay time of all scheme combinations has significantly decreased, with an obvious optimization effect. The average delay has decreased by 75.9%, with the most significant improvement seen in the 12th group, where the delay decreased by 86.9%. This is because vehicles without the connected vehicle control must queue up and wait for the red signal. When the traffic volume is large, if the vehicles cannot pass through during one green time, there will be significant delays. However, when the vehicles under the control arrive at the intersection, they will be able to reduce the through and left-turning traffic volume through phase difference dynamic adjustment and vehicle speed guidance. This will shorten the phase difference lead time and reduce the phase difference, enabling the vehicles to pass each intersection continuously without stopping, thus reducing the delay time of the vehicles.

4.2.2. Comparison of Proposed and Existing Optimization Methods

Table 6. Comparison of simulation results of proposed and existing methods.

Method	Performance Indicator (% Reduction of Proposed Method)
	Average Delay (s)	Average Number of Stops	Average Travel Time (s)	Average Queue Length
No control strategy applied	278.5 (−85.1)	13.4 (−84.3)	482.2 (−34.0)	190 (−62.6)
MAXBAND	132.1 (−68.6)	5.5 (−61.8)	338.2 (−5.9)	87 (−18.4)
Speed Guidance	98.2 (−57.7)	4.4 (−52.2)	332 (−4.2)	75 (−5.3)
Improved MULTIBAND	55.7(−25.5)	3.3 (−36.4)	331(−3.9)	73 (−2.7)
Proposed Method	41.5 (n.a.)	2.1 (n.a.)	318.2 (n.a.)	71 (n.a.)

compares the results of the uncontrolled groups with the proposed method. As noted, the proposed method can reduce the waiting time at the intersection and reduce the frequency of vehicles’ starting, stopping, and idling before the intersection. This improves the delay and number of stops of the mainline vehicles. Compared with the no-control strategy, the proposed method reduces the average delay by 85.1%, the average number of stops by 84.3%, the average travel time by 34.0%, and the average queue length by 62.6%.

Compared with the MAXBAND method, which optimizes the phase difference of the coordinated intersections, the proposed method improves all indicators compared to the no-control strategy. The average delay is reduced by 68.6%, the average number of stops is reduced by 61.8%, the average travel time is reduced by 5.9%, and the average queue length is reduced by 18.4%. Compared with the Improved MULTIBAND method, the proposed method reduces the average delay by 25.5%, the number of stops by 36.4%, travel time by 3.9%, and queue length by 2.7%. This indicates that the model proposed in this article can more effectively reduce the average delay time and the average number of stops for vehicle platoons in the coordinated direction, achieving better arterial green wave coordination control results. Compared with the speed guidance method, the proposed method reduces the average delay by 57.7%, the number of stops by 52.2%, travel time by 4.2%, and queue length by 5.3%. This indicates that under the same speed guidance model, introducing inductive control for dynamic signal adjustment has a certain effect on reducing intersection delays and the number of stops. Thus, the model strategy constructed in this article can effectively improve the comprehensive efficiency of mainline coordinated intersections.

5. Conclusions

This article has proposed a green wave VRCC method based on through-traffic priority for signalized intersections. This method (1) uses data such as through-traffic detention and arrival-traffic volume collected by roadside equipment, (2) calculates the green time extension for the green wave through phase, the phase difference lead time and phase difference of adjacent intersections, and (3) performs green extension and phase difference adjustment. At the same time, it guides the vehicle speed to encourage the left- and right-merging traffic from the upstream intersections to form and pass through the intersection.

The validation results show that under the conditions of 1.2 times the actual surveyed traffic volume, 80% of the remaining straight vehicles traffic from merging traffic, and a minimum green time of 12 s, the proposed strategy reduces the average delay by 85.1%, the number of stops by 84.3%, travel time by 34%, and queue length by 62.6% compared to the strategy without control. The results indicate that the proposed control strategy can effectively reduce the travel time of through traffic, reduce vehicle detention volume, reduce green time waste caused by phase transitions, optimize the coordinated control effect of mainlines, and improve the efficiency of mainline traffic.

A distinct feature of the proposed method is that it ensures that the green time of the green wave phase is fully used, reducing green time waste during the transition between phases. The method also adapts to the complex and changing traffic environment, improves the green wave control effect during peak periods in the peak direction, guides the evacuation of traffic flows more efficiently, and reduces the impact of traffic flows on side roads. It plays an important role in improving traffic management, service levels, and traffic safety and in reducing environmental pollution. Further, the method significantly promotes social and economic industrial upgrading and provides social and economic benefits.

The study has some limitations. The focus of the research has mainly been on improving the traffic efficiency of single-direction vehicles, with less attention paid to the coordinated control of two-way traffic flow. Future work can focus on combining the characteristics of two-way traffic flow with patterns of intersection signal phase changes for further research. Additionally, the formation of vehicle platoons requires speed coordination between leading and following vehicles, and the speed guidance strategy proposed in this study considers few factors from this aspect. Subsequent research can incorporate vehicle following behavior and consider changes in vehicle acceleration and deceleration to achieve more precise speed guidance control for platooning.