Identification of Factors Influencing the Operational Effect of the Green Wave on Urban Arterial Roads Based on Association Analysis

Abstract

Green wave control is an important technology that synchronizes traffic signals to improve traffic flow on urban arterial roads. Current research has focused on optimizing and evaluating control schemes; however, their operational effect is easily affected by a variety of traffic and travel factors. This means it is important to study methods to identify the factors influencing the operational effect of the green wave on arterial roads. In this study, we conducted innovative research to identify these factors and made breakthroughs in optimizing and evaluating schemes of green wave control. We use the number of stops, travel time, and delays as representative evaluation indicators to assess the effects of four influencing factors: design speed, signal timing, pedestrian crossing, and heavy vehicles. An association analysis that combines sensitivity analysis and grey relational analysis was used to rank these factors in their degree of correlation. A case study was conducted based on the traffic data on Eshan Road in Wuhu City to verify the proposed method. The results of simulations in Vissim 7.0 showed that pedestrian crossing and heavy vehicles were the more important factors influencing the operational effect of the green wave. Moreover, implementing measures related to traffic management helped improve the effect to an extent greater than by optimizing the scheme for green wave control alone. Additionally, optimizing control schemes in the context of implementing measures related to traffic management significantly improved the operational effect of the green wave.

1. Introduction

On main urban roads, vehicles often encounter red lights at single-point signal-controlled intersections, which results in poor traffic flow. Green wave control technology, has therefore received close attention as an important means of urban traffic management [1,2,3]. It determines the traffic offset, which allows vehicles to enter a coordinated road and pass through several intersections without stopping based on the design speed and spacing between intersections [4]. Although green wave control can improve traffic efficiency on arterial roads, it often fails to achieve the desired operational effect owing to various factors [5,6], which has prompted extensive research.

Most research has focused on algorithms to optimize the green wave based on two classical strategies: bandwidth maximization and cost minimization. The former is based on graph-based and numerical methods and mathematical models. For example, Ji et al. [7] considered the influences of cruising speed and residual queues on traffic offset at a red light, and then optimized the classical bidirectional green wave graphic method. Zhang et al. [8] analyzed the shortcomings of the existing traditional numerical solution algorithm to solve the two-way green wave bandwidth problem and then improved it. Ma et al. [9] proposed a method to optimize the timing of traffic lights based on deep reinforcement learning to dynamically adjust the offset. Chen et al. [10] proposed a variable cycle-based method to optimize the bandwidth of the green wave and used it to optimize the green split in real time. Liang et al. [11] proposed an overlapping phase-based signal-control logic and a bus priority control algorithm under two-way signal coordination on arterial roads. Methods of optimization designed to minimize the cost seek to reduce the number of stops, queue length, and delays. For example, Yu et al. [12] proposed a coordinated green wave control model to optimize the distribution of adjacent intersections by minimizing delays. To minimize queue length, Zheng et al. [13] proposed two methods that use AI to coordinate traffic on arterial roads. The above studies investigated algorithms to optimize the green wave, but when applied to arterial roads different algorithmic models differed in adaptability [14]. Although different indicators were evaluated and verified by using traffic simulation, a unified method to assess the operational effect of the green wave on arterial roads remains elusive. As a consequence, no method is available to evaluate schemes of green wave control uniformly based on different algorithmic models.

Among the researchers who have sought to develop a unified method, Tian [15] evaluated the coordination-related performance of an adaptive system of signal control by using travel time and the number of stops as indicators. Chia et al. [16] evaluated the advantages and disadvantages of driving-based, coordination-based, and adaptive control strategies. Wang et al. [17] evaluated green wave coordination based on travel time, number of stops, and intersection delays. Ma et al. [18] selected delays, queue length, stopping rate, speed, and saturation to establish a grade evaluation and ranking model of operational efficiency on arterial roads. Liu et al. [14] designed an indicator to assess green wave-based coordination to evaluate different control schemes. Zhuo et al. [19] proposed a method of assessment based on grey relational analysis by using the travel time and the single-vehicle delay of the green wave as evaluation indicators. Lin [6] took the rate of use of green lights, delays, and number of stops as evaluation indicators and calculated the grey relational degree between several schemes and the ideal scheme. The above examples show that researchers have used the number of stops, travel time, delay, speed, and queue length to assess schemes of green wave control [6,17,18,19] based on simulations [14] and grey relational analyses [6,19]. These methods can be used to evaluate schemes of green wave control comprehensively and identify the optimal one. However, the operation of the green wave is affected design speed, signal timing, pedestrian crossing, and heavy vehicles, factors that interfere with achieving the desired objectives [20,21,22,23,24]. Moreover, the above studies did not interrelate the evaluation indicators. As a result, the most important factors influencing the operational effect of the green wave were not identified.

While many studies have been conducted on optimizing green wave control schemes, little work has been devoted to their assessment, and even fewer have investigated methods to identify the factors influencing their operational effects. Analyzing the association between the evaluation indicators and influencing factors can identify the most important factors influencing the operational effect of the green wave. This is important as it can be used to develop measures to optimize the operational effect of green wave control schemes.

This study makes the following innovative contributions on the identification of factors influencing the operational effect of the green wave on urban arterial roads: First, we combine sensitivity analysis and grey relational analysis to identify the most important factors influencing the operational effect of the green wave, and propose a method to identify the influencing factors. Second, we collected, cleaned, and matched traffic-related information such as data on multiple associated intersections on arterial roads. The effectiveness of the proposed method, which was verified in combination with actual cases, revealed that measures related to traffic management may be more effective for improving the operational effect of the green wave than those related to optimizing control schemes.

The remainder of this paper is arranged as follows: in Section 2, we detail the method used to calculate and analyze the association between the evaluation indicators and factors influencing the operational effect of the green wave. Section 3 describes the collection and matching of traffic-related data from a case study on the effects of the green wave on Eshan Road, Wuhu City, China. Section 4 contains a discussion and an analysis of the results, and Section 5 summarizes the conclusions of this study.

2. Methods

2.1. General Idea

The general idea of this paper is shown in Figure 1 and consists of two main parts. The first part is about the analysis of evaluation indicators and influencing factors. Through a literature review, it was found that there are many evaluation indicators for the operational effect of green wave with the most commonly used representative indicators being the average number of stops, average travel time, and average delay [6,17,18,19]. Therefore, we selected these three indicators for analysis. There are also many factors influencing the operational effect of the green wave. Physical factors such as the geometric design of intersections and spacing between intersections may prevent implementation of green wave schemes at intersections of arterial roads. However, the focus of this study was on arterial road intersections where green wave schemes have been implemented. Therefore, using a relatively reasonable geometric design and spacing of intersections, we selected non-physical influencing factors related to the operational effect of the green wave for further research. Based on the literature review, we selected four representative influencing factors for analysis: design speed, signal timing, pedestrian crossing, and heavy vehicle travel [20,21,22,23,24].

The second part is about the correlation analysis between evaluation indicators and influencing factors. To evaluate the operational effect of the green wave objectively, traffic simulation software such as Vissim was used to output the values of evaluation indicators under different conditions. To facilitate analysis, the value of influence corresponding to multiple evaluation indicators was further calculated so that the relationship between the value of influence and the influencing factors could be analyzed. Because the factors and the value of influence lack a data sequence directly used for association analysis, and the relationship between them is unclear, sensitivity analysis and grey relational analysis were combined to analyze the influencing factors and value of influence. Sensitivity analysis is mainly used to obtain a data sequence of the factors and value of influence. Grey relational analysis is mainly used to evaluate the ranking of the factors in their degree of correlation.

2.2. The Values of Evaluation Indicators and Influential Factors

2.2.1. The Values of Evaluation Indicators

(1)

Average number of stops

This refers to the number of stops made by vehicles passing through the green wave on a road in a coordinated direction. The value is denoted by “S” and is measured as number of stops/vehicle. The average number of stops was selected as the evaluation indicator to reflect the coordination effect of green wave control [6].

(2)

Average travel time

This refers to the time taken by vehicles to pass through the green wave in a coordinated direction. The value is denoted by “T” and is measured in hours/vehicle. The average travel time is selected as the evaluation indicator to reflect the traffic efficiency of the green wave [19].

(3)

Average delay

This refers to the time lost by vehicles while passing through signalized intersections on the green wave road. The value is denoted by “D” and is measured as s/pcu. The average delay is selected as the evaluation indicator to reflect the traffic benefit of the green wave [19].

S, T, and D can be obtained through Vissim simulation [14].

We needed to calculate the value of influence E based on S, T, and D data on the three indicators above to facilitate subsequent association analysis. The smaller the E, the smaller the influence on the operational effect of the green wave. This implied a better operational effect of the green wave. The E is calculated as follows.

We used Equations (1)–(3) to process the S_ij, T_ij and D_ij data relating to the S, T, and D to obtain non-dimensional S′_ij, T′_ij and D′_ij data. Then, the E_ij of E was calculated using Equation (4):

$$S_{ij}^{\prime }=\frac{S_{ij}}{\overline{S}},$$

(1)

$$T_{ij}^{\prime }=\frac{T_{ij}}{\overline{T}},$$

(2)

$$D_{ij}^{\prime }=\frac{D_{ij}}{\overline{D}},$$

(3)

$$E_{ij}=S_{ij}^{\prime }{\omega }_S+T_{ij}^{\prime }{\omega }_T+D_{ij}^{\prime }{\omega }_D,$$

(4)

where i indicates that there are multiple influential factors, and j indicates that each influential factors has multiple values. $\overline{S}$, $\overline{T}$ and $\overline{D}$ are the average values of S, T and D, and ${\omega }_S$, ${\omega }_T$ and ${\omega }_D$ are the weights of S, T and D, which was set to 1/3 to ensure simplicity of calculation. The range for value of influence E is (0, +∞).

2.2.2. The Values of Influential Factors

(1)

Design speed of the green wave

This refers to the optimal design speed of the vehicle starting from the starting intersection to ensure that it encountered a green light when arriving at the next intersection. The value is denoted by “V” and is generally in the range of 50–55 km/h [20]. We thus regard it as a factor influencing the operational effect of the green wave from the perspective of scheme optimization. Correspondingly, the value of i is 1, indicating the first influencing factors.

(2)

Signal timing scheme

The signal timing scheme includes a signal cycle, phase, and running time for each phase [21]. We thus regarded it as a factor influencing the operational effect of the green wave from the perspective of scheme optimization. To simplify the calculation, we used the signal cycle for quantitative analysis. The value was denoted by “C”, unit: s. Correspondingly, the value of i was 2, indicating the second influencing factors.

(3)

Pedestrian crossing

This refers to the behavior of pedestrians crossing the street at a non-signal crosswalk [22,23], which easily causes interference to vehicles on the green wave road, resulting in a reduction in speed. We thus regarded it as a factor influencing the operational effect of the green wave from the perspective of traffic management. We calculated the number of interferences caused by pedestrian crossing for quantitative analysis. The value is denoted by “L”, unit: times. Correspondingly, the value of i was 3, indicating the third influencing factors.

L was calculated as follows:

① The pedestrian flow P_m through the zebra crossing of the non-signal crosswalk m was calculated during the studied cycle. The number of interferences L_m of non-signal crosswalk m was calculated according to Equation (5).

$$L_m=k{P}_m,$$

(5)

where P_m is the flow of pedestrians crossing the non-signal crosswalk m; k is the ratio of influence that can be determined by calculating the mean of the ratio of actual interference to vehicles due to pedestrian crossings to the flow of pedestrians during the observation cycle.

② The average number of interferences L due to all non-signal crosswalks using Equation (6) was calculated:

$$L={{\displaystyle \sum }}_{m=1}^n{L}_m{\omega }_m,$$

(6)

where ${\omega }_m$ is the weight of the mth non-signal crosswalk.

(4)

Heavy vehicle traffic

Heavy vehicles travel at a slow speed, occupy adjacent lanes, and thus interfere with the normal movement of other vehicles [24]. They also affect the speed of traffic on the green wave road by increasing the number of stops and the average travel time. We thus regarded it as a factor influencing the operational effect of the green wave from the perspective of traffic management. We calculated the ratio of heavy vehicles on the road for quantitative analysis. The value is denoted by “H”, unit: %. Correspondingly, the value of i was 4, indicating the fourth influential factors.

H was calculated as follows:

① The number of heavy vehicles Q_nH and the total number of vehicles Q_n entering the upstream intersection of the road n in the studied cycle were obtained. Equation (7) was then used to compute the ratio H_n of heavy vehicles on road n.

$$H_n=\frac{Q_{nH}}{Q_n},$$

(7)

where Q_nH and Q_n are the number of heavy vehicles and the total number of vehicles on road n, respectively.

② The length l_n of each road was taken as the weight, and the ratio H of heavy vehicles on the entire studied road was then calculated according to Equation (8):

$$H={{\displaystyle \sum }}_{n=1}^N\frac{l_n}{l}{H}_n,$$

(8)

where l is the total length of the studied road and l_n is the length of the nth road.

2.3. Association Analysis of Evaluation Indicators and Influential Factors

2.3.1. Sensitivity Analysis of Influential Factors and Value of Influence

Sensitivity analysis is a method to measure the degree of influence of parameters on a system and can be divided into single-factor and multi-factor sensitivity analysis. Single-factor analysis refers to the technique in which the value of one uncertain factor is changed within a specific range at a given time while other factors are kept fixed, and then changes in the corresponding model are examined [25,26]. Single-factor sensitivity analysis, on the one hand, is an effective numerical processing method that can be used to obtain a data sequence of influential factors and the value of influence. On the other hand, by adjusting each influencing factor one by one, observing its impact on the value of influence can help determine which factors have a greater impact on the value of influence. Therefore, based on the theory of this method, the influencing factors of the operational effect of the green wave are taken as uncertain factors. The value of influence reflects the behavior characteristics of the system. A single-factor sensitivity analysis is proposed to calculate the values of influencing factors and value of influence. Specific analysis methods are as follows:

We used the value of influence as the index of sensitivity analysis and used influencing factors as the uncertain factors. The actual values of the design speed, signal timing, pedestrian crossing, and heavy vehicles were used as benchmark values to set the variation range in their values, as shown in Equations (9)–(12):

$$V_j\in \left[V_0-\Delta V,V_0+\Delta V\right],$$

(9)

$$C_j\in \left[C_0-\Delta C,C_0+\Delta C\right],$$

(10)

$$L_j\in \left[L_0-\Delta L,L_0+\Delta L\right],$$

(11)

$$H_j\in \left[H_0-\Delta H,H_0+\Delta H\right],$$

(12)

among these, V₀, C₀, L₀, and H₀, respectively, represent the actual values of V, C, L, and H; V_j, C_j, L_j, and H_j, respectively, represent the jth value of V, C, L, and H; and j values generally range from 1 to 5; that is, j = 1, 2, 3, 4, 5 [25,26], and $\Delta$V, $\Delta$C, $\Delta$L, and $\Delta$H, respectively, represent the variations of V, C, L, and H.

Under the premise that the benchmark values of other uncertain factors are taken, 5 different values of an uncertain factor are taken within its variation range, and the corresponding values of influence are calculated, respectively. For example, the values of C, L, and H are C₀, L₀, and H₀, respectively, and the values of V are V_j (j = 1, 2, 3, 4, 5). V is the first influencing factor, so the value of i is 1. The Vissim simulation software is used to output the values of S_1j, T_1j and D_1j corresponding to S, T, and D, and then E_ij of E is calculated by Equations (1)–(4). After all the numerical E_ij of E is calculated, the effects of V, C, L, and H on E are further analyzed by simple regression analysis. Origin software can be used to draw the diagram of the linear fitting of V, C, L, H and E, respectively. If the correlation coefficients R of V, C, L, H and E pass the test, V, C, L, H and E are obviously shown to be correlated; otherwise, there is no correlation.

2.3.2. Grey Relational Analysis of Influential Factors and Value of Influence

Grey relational analysis is used to measure the degree of correlation of factors, and it determines whether the reference and comparison sequences are closely related by determining the degree of geometric similarity between them. The more similar their geometric shapes, the greater the degree of correlation between them [25]. It is defined as: a certain parameter Y_i is the target parameter, and the values Y_ij on its sequence constitute a reference sequence, denoted as Y = {Y_ij}. The values X_ij of the influence parameters X_i on the same sequence form the comparison sequence, denoted X = {X_ij} [27,28,29]. Grey relational analysis does not need to make explicit assumptions about the linear or correlation relationship between evaluation indicators and influencing factors. The degree of correlation can be calculated between different factors and the operational effect of the green wave. Therefore, by referring to the theory of this method, we constructed the associated data sequence of the influencing factors and value of influence. The method of grey correlation analysis of factors and value of influence is proposed to evaluate the ranking of influential factors in degree of correlation. Specific analysis methods are as follows:

The V, C, L, and H are taken as the comparison sequence X, as shown in Equation (13):

$$X=\left[\begin{array}{c}{X}_1\\ ⋮\\ X_4\end{array}\right]=\left[\begin{array}{ccc}{x}_{11}& \cdots & x_{15}\\ ⋮& x_{ij}& ⋮\\ x_{41}& \cdots & x_{45}\end{array}\right]=\left[\begin{array}{c}\begin{array}{l}V\hfill \\ \begin{array}{l}C\hfill \\ L\hfill \end{array}\hfill \end{array}\\ H\end{array}\right]=\left[\begin{array}{l}\begin{array}{cc} V_1& \begin{array}{cc}{V}_2& \begin{array}{cc}{V}_3& \begin{array}{cc}{V}_4& V_5\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc} C_1& \begin{array}{cc}{C}_2& \begin{array}{cc}{C}_3& \begin{array}{cc}{C}_4& C_5\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc} L_1& \begin{array}{cc}{L}_2& \begin{array}{cc}{L}_3& \begin{array}{cc}{L}_4& L_5\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{cc}{H}_1& \begin{array}{cc}{H}_2& \begin{array}{cc}{H}_3& \begin{array}{cc}{H}_4& H_5\end{array}\end{array}\end{array}\end{array}\hfill \end{array}\hfill \end{array}\hfill \end{array}\right],$$

(13)

where x_ij is the jth value of the ith influential factor; the value of i ranges from 1 to 4; and the value of j ranges from 1 to 5.

The E is taken as the reference sequence Y, as shown in Equation (14):

$$Y=\left[\begin{array}{c}{Y}_1\\ ⋮\\ Y_4\end{array}\right]=\left[\begin{array}{ccc}{y}_{11}& \cdots & y_{15}\\ ⋮& y_{ij}& ⋮\\ y_{41}& \cdots & y_{45}\end{array}\right]=\left[\begin{array}{c}{E}_1\\ ⋮\\ E_4\end{array}\right]=\left[\begin{array}{l}\begin{array}{cc} E_{11}& \begin{array}{cc}{E}_{12}& \begin{array}{cc}{E}_{13}& \begin{array}{cc}{E}_{14}& E_{15}\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc} E_{21}& \begin{array}{cc}{E}_{22}& \begin{array}{cc}{E}_{23}& \begin{array}{cc}{E}_{24}& E_{25}\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc} E_{31}& \begin{array}{cc}{E}_{32}& \begin{array}{cc}{E}_{33}& \begin{array}{cc}{E}_{34}& E_{35}\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{cc} E_{41}& \begin{array}{cc}{E}_{42}& \begin{array}{cc}{E}_{43}& \begin{array}{cc}{E}_{44}& E_{45}\end{array}\end{array}\end{array}\end{array}\hfill \end{array}\hfill \end{array}\hfill \end{array}\right],$$

(14)

where y_ij is the jth value of influence corresponding to the ith influential factor.

Because the dimensions and values of V, C, L, and H are different such that they cannot be directly compared, x_ij and y_ij are standardized according to Equations (15) and (16) to form x′_ij and y′_ij:

$${x\prime }_{ij}=\frac{x_{ij}-min{x}_{ij}}{max{x}_{ij}-min{x}_{ij}},$$

(15)

$${y\prime }_{ij}=\frac{y_{ij}-min{y}_{ij}}{max{y}_{ij}-min{y}_{ij}}.$$

(16)

Equation (17) was used to calculate the absolute differences in the values of x′_ij and y′_ij to form a difference matrix Δ_ij:

$${\Delta }_{ij}=\left|{x’}_{ij}-{y’}_{ij}\right|.$$

(17)

Equations (18) and (19) eliminate the maximum and minimum values from the difference matrix, respectively.

$${\Delta }_{max}=max{\Delta }_{ij},$$

(18)

$${\Delta }_{min}=min{\Delta }_{ij}.$$

(19)

The difference matrix was used to calculate the correlation coefficients l_ij from Equation (20). Then Equation (21) was used to form the sequence of correlation coefficients L:

$$l_{ij}=\frac{{\Delta }_{min}+\rho {\Delta }_{max}}{{\Delta }_{ij}+\rho {\Delta }_{max}},$$

(20)

$$L=\left[l_{ij}\right],$$

(21)

where ρ is the coefficient of resolution, 0 < ρ < 1. The smaller the ρ, the greater the difference between correlation coefficient and another correlation coefficient, and the stronger is their capability of discrimination. In general, ρ is 0.5.

The degree of correlation Q_i is calculated from Equation (22):

$$Q_i=\frac{1}{n}{{\displaystyle \sum }}_{j=1}^n{l}_{ij},$$

(22)

where Q_i is the change in the interval [0, 1]. The closer Q_i is to 1, the stronger the correlation. The closer Q_i is to 0, the worse the correlation. According to the value of Q_i, the influencing factors can be divided into three levels. If Q_i is greater than 0.7, the corresponding ith influential factor is important; if Q_i is between 0.5 and 0.7, the ith influencing factor is relatively important; if Q_i is less than 0.5, the ith influencing factor is not important [30].

3. Results

As a national hub and an important node transportation corridor in China, Wuhu City widely uses green wave control technology on its arterial roads [31]. We chose Eshan Road in Wuhu City, as the green wave road for our case study. As shown in Figure 2, it is an arterial road with a coordinated direction from east to west for a total length of 5.8 km. It has six signalized intersections and three non-signaled crosswalks. We numbered the six intersections from west to east as 1, 2, 3, 4, 5, and 6 and the three non-signaled crosswalks as 7, 8, and 9. We used traffic data on a working day (21 September 2020) during the peak cycle (8:30–9:30) for calculation and analysis.

3.1. Data

We used bayonets and other equipment, installed by the municipal traffic management department to collect traffic data on arterial roads in the presence of the green wave and stored it in a database, which provided data support for the research and case verification.

3.1.1. Original Datasets

The first original datasets used here consisted of data collected by the bayonet equipment at major road intersections. Some of the data are shown in

Table 1. Bayonet data.

Intersection Number	Direction	License Plate	Vehicle Types	Recorded Time
1	East	*B2N13*	Small vehicle	2020/9/21 08:47
1	West	*A268H*	Small vehicle	2020/9/21 08:47
1	South	*B8549*	Small vehicle	2020/9/21 08:47
1	North	*A097A*	Heavy vehicle	2020/9/21 08:47

. The license plate information of the vehicles was concealed with “*”.

The second original dataset contained information on the canalization of the intersections and schemes of green wave control obtained from the local traffic police department and Baidu maps. Some of them are shown in

Table 2. Data on the canalization of the intersections and schemes of green wave control.

Intersection Number	Intersection Canalization			Green Wave Schemes
	Direction	Turning Direction	Number of Lanes	V	C	Phase	Timing	Offset
1	East	Left-turn	2	50 km/h	130 s		37	114 s
	East	Straight	3
	West	Left-turn	2				3
	West	Straight	3
	South	Left-turn	2				37
	South	Straight	4
	North	Left-turn	2				26
	North	Straight	4				27

.

The third original dataset contained information on the roads, and was obtained from Wuhu’s traffic police department. Some of them are shown in

Table 3. Road information.

Upstream Intersection Number	Downstream Intersection Number	Road Length (m)	Number of Non-Signal Crosswalks	Flow of Pedestrian Crossing (p/h)
1	2	1300	0	/
2	3	800	0	/
3	4	900	0	/
4	5	1300	1	80
5	6	1500	2	230

.

3.1.2. Data Matching

The first, second, and third original datasets were matched by the field “number of intersections” to obtain data on the trajectories of the vehicles. We then processed and cleaned the data to remove erroneous information and obtained information on the trajectories of vehicles for analysis. Some of the data are shown in

Table 4. Data on the trajectories of vehicles.

License Plate	Type of Vehicle	Upstream Intersection Number	Downstream Intersection Number	Road Length (m)	Starting Time	Ending Time
*PD0851*	Small vehicle	1	2	1300	2020/9/21 08:50	2020/9/21 08:51
*P5N512*	Small vehicle	2	3	800	2020/9/21 08:51	2020/9/21 08:52
*P28B96*	Small vehicle	3	4	900	2020/9/21 08:46	2020/9/21 08:48
*PD0209*	Small vehicle	4	5	1300	2020/9/21 09:15	2020/9/21 09:17
*PD0304*	Heavy vehicle	5	6	1500	2020/9/21 09:28	2020/9/21 09:29

.

We used the above data on the trajectories of vehicles to calculate the total flow through this section, and the ratios of heavy and light vehicles. The recorded times on the trajectories of the vehicles were then used to calculate the interval during which each passed through the green wave. This was used in turn along with the length of the road to obtain the average speeds of heavy and light vehicles. These data provide an important basis for the simulation and association analysis of traffic.

3.2. Association Analysis

3.2.1. Sensitivity Analysis

According to the data in Table 2, V₀ = 50 km/h and C₀ = 130 s.

The data required for L were obtained from the data in Table 3, and are shown in

Table 5. Data required for L.

Non-Signalled Crosswalks m	${\mathit{\omega }}_{\mathit{m}}$	Pm (p/h)	k
7	1/3	80	20%
8	1/3	145
9	1/3	85

. We observed the three non-signaled crosswalks to calculate the average ratio between the actual number of interferences caused by pedestrians crossing the street and the flow of pedestrian in 15 min units at 20%, i.e., k = 20%.

The data required for H were drawn from the data in Table 4, and their results are shown in

Table 6. Data required for H.

Road (W to E)	ln (m)	Qnh (pcu/h)	Qn (pcu/h)	Road (E to W)	Qnh (pcu/h)	Qn (pcu/h)
1–2	1300	0	314	6–5	45	1372
2–3	800	14	352	5–4	41	1268
3–4	900	55	969	4–3	2	137
4–5	1300	42	949	3–2	2	68
5–6	1500	38	928	2–1	41	769

.

Following this, we used Equations (5)–(8) to determine that L₀ = 20 times and H₀ = 3%.

Given V₀, C₀, L₀, and H₀, we used the steps provided in Section 2.3 to determine V_j, C_j, L_j, and H_j; j = 1, 2, 3, 4, 5; and we formulated 20 schemes. They are denoted by A1–A5, B1–B5, C1–C5, and D1–D5, and are shown in

Table 7. The values of the influential factors.

Schemes	V (km/h)	Schemes	C(s)	Schemes	L (Times)	Schemes	H (%)
A1	40	B1	110	C1	12	D1	1
A2	45	B2	120	C2	16	D2	2
A3	50	B3	130	C3	20	D3	3
A4	55	B4	140	C4	24	D4	4
A5	60	B5	150	C5	28	D5	5

.

The schemes for green wave control were calculated using a commonly applied graphic-based method [7,11]. When C₀ = 130 s, the schemes corresponding to the range of V of 40–60 km/h are shown in

Table 8. Schemes for green wave control with C₀ = 130 s, the range of V of 40–60 km/h (unit: s).

Intersection	Phase	Timing	V	Offset	Bandwidth	V	Offset	Bandwidth	V	Offset	Bandwidth	V	Offset	Bandwidth	V	Offset	Bandwidth
1		37	40 km/h	60	12	45 km/h	118	32.5	50 km/h	114	35	55 km/h	10	11.5	60 km/h	28	14.5
		3
		37
		26
		27
2		39		0			68			64			62			99
		46
		22
		23
3		30		49			51			49			106			119
		74
		26
4		26		59			120			117			117			123
		21
		26
		28
		29
5		29		31			56			50			46			46
		18
		29
		23
		31
6		47		0			0			0			0			0
		50
		16
		17

. When V₀ = 50 km/h, the schemes corresponding to the range of C of 110–150 s are shown in

Table 9. Schemes for green wave control with V₀ = 50 km/h, the range of C of 110–150 s (unit: s).

Intersection	Phase	C	Timing	Offset	Bandwidth	C	Timing	Offset	Bandwidth	C	Timing	Offset	Bandwidth	C	Timing	Offset	Bandwidth	C	Timing	Offset	Bandwidth
1		110	25	94	8.5	120	20	116	30	130	37	114	35	140	37	55	11.5	150	27	64	14.5
			8				16				3				8				23
			25				20				37				37				27
			25				29				26				29				33
			27				35				27				29				40
2		110	30	48		120	35	60		130	39	64		140	41	72		150	43	74
			46				46				46				53				58
			17				19				22				22				24
			17				20				23				24				25
3		110	25	34		120	25	50		130	30	49		140	29	128		150	31	135
			56				67				74				79				84
			29				28				26				32				35
4		110	29	33		120	20	108		130	26	117		140	25	127		150	23	137
			16				25				21				28				34
			29				20				26				25				23
			16				20				28				31				32
			20				35				29				31				38
5		110	28	30		120	25	50		130	29	50		140	21	59		150	21	53
			15				20				18				37				39
			28				25				29				21				21
			16				20				23				25				30
			23				30				31				36				39
6		110	39	0		120	43	0		130	47	0		140	48	0		150	52	0
			40				44				50				52				55
			15				16				16				19				21
			16				17				17				21				22

. The bandwidths in Table 8 and Table 9 are the average values of the bandwidths from east to west and west to east, respectively.

Single-factor sensitivity analysis was adopted; that is, the value of certain influencing factors changed with the scheme, and the actual value of other factors was adopted (in Table 7). Traffic data are shown in

Table 10. Flow-related data (Unit: pcu/h).

Intersection Number	East		West		South		North
	Left-Turn	Straight	Left-Turn	Straight	Left-Turn	Straight	Left-Turn	Straight
1	392	608	432	622	206	264	156	205
2	184	919	335	403	126	235	164	165
3	/	423	300	1082	/	/	345	/
4	398	1285	286	1038	153	203	105	165
5	429	1502	91	1058	111	219	132	405
6	1147	1220	187	1161	154	109	176	237

. The speeds of heavy and light vehicles were assumed to be 35 and 50 km/h, respectively. Through the Vissim simulation software, S, T, and D were output. Then, the E was calculated by Equations (1)–(4). The results are shown in

Table 11. Sensitivity schemes and outputs.

Schemes	V (km/h)	C (s)	L (times)	H (%)	S	T	D	E
A1	40	130	20	3	0.72	520.65	49.52	1.059
A2	45	130	20	3	0.58	487.13	50.22	0.971
A3	50	130	20	3	0.53	486.39	46.97	0.922
A4	55	130	20	3	0.74	524.16	47.51	1.058
A5	60	130	20	3	0.68	513.54	43.28	0.990
B1	50	110	20	3	0.73	525.69	36.07	1.002
B2	50	120	20	3	0.58	487.89	40.84	0.929
B3	50	130	20	3	0.53	486.39	46.97	0.945
B4	50	140	20	3	0.60	490.87	51.91	1.023
B5	50	150	20	3	0.62	517.77	57.86	1.092
C1	50	130	12	3	0.53	482.89	46.06	0.989
C2	50	130	16	3	0.53	485.20	46.09	0.991
C3	50	130	20	3	0.53	486.39	46.97	0.998
C4	50	130	24	3	0.54	488.26	47.02	1.006
C5	50	130	28	3	0.55	488.70	47.33	1.015
D1	50	130	20	1	0.52	481.60	45.60	0.978
D2	50	130	20	2	0.53	485.17	46.39	0.992
D3	50	130	20	3	0.53	486.39	46.97	0.997
D4	50	130	20	4	0.54	494.74	47.41	1.012
D5	50	130	20	5	0.54	495.16	48.47	1.020

.

Simple regression analysis was conducted on V, C, L, H, and E in Table 11. Origin software was used to draw a diagram of the linear fitting of V, C, L, H, and E. The results are depicted in Figure 3.

Figure 3a,b shows that the correlation coefficients R of the diagram of linear fitting corresponding to V, C, and E were −0.137 and 0.675, respectively. When the number of observed data items was n = 5, R_n-2 = 0.878 was obtained by querying the test table of correlation coefficients [32]. Because the absolute values of R were smaller than for R_n-2, no significant linear correlation was obtained among design speed, signal timing, or their values of influence. When V = 50 km/h, E was at a minimum, as shown in Figure 3a, and had its minimum value when C = 120 s as shown in Figure 3b.

Figure 3c,d shows that the correlation coefficients R of L, H, and E were 0.981 and 0.991, respectively. Because the absolute values of R were greater than R_n-2, pedestrian crossing and heavy vehicle travel significantly correlated positively with the value of influence. That is, as L and H increased, E gradually increased. This correlation was stronger for heavy vehicle traffic.

3.2.2. Grey Relational Analysis

We used Equation (13) to form the comparison sequence X as follows:

$$X=\left[\begin{array}{c}V\\ \begin{array}{c}C\\ \begin{array}{c}L\\ H\end{array}\end{array}\end{array}\right]=\left[\begin{array}{l}\begin{array}{cc} 40& \begin{array}{cc} 45& \begin{array}{cc} 50& \begin{array}{cc} 55& 60\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc}110& \begin{array}{cc}120& \begin{array}{cc}130& \begin{array}{cc}140& 150\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{l}\begin{array}{cc} 12& \begin{array}{cc} 16& \begin{array}{cc} 20& \begin{array}{cc} 24& 28\end{array}\end{array}\end{array}\end{array}\hfill \\ \begin{array}{cc}1& \begin{array}{cc} 2& \begin{array}{cc} 3& \begin{array}{cc} 4& 5\end{array}\end{array}\end{array}\end{array}\hfill \end{array}\hfill \end{array}\hfill \end{array}\right].$$

We also used Equation (14) to form the reference sequence Y as follows:

$$Y=\left[\begin{array}{c}{E}_1\\ \begin{array}{c}{E}_2\\ \begin{array}{c}{E}_3\\ E_4\end{array}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{cc}1.059& \begin{array}{cc}0.971& \begin{array}{cc}0.922& \begin{array}{cc}1.058& 0.990\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}1.004& \begin{array}{cc}0.931& \begin{array}{cc}0.947& \begin{array}{cc}1.023& 1.094\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}0.989& \begin{array}{cc}0.991& \begin{array}{cc}0.998& \begin{array}{cc}1.006& 1.015\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{cc}0.978& \begin{array}{cc}0.992& \begin{array}{cc}0.997& \begin{array}{cc}1.012& 1.020\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right].$$

Normalization was carried out through Equations (15) and (16), and the difference matrix was then obtained through Equation (17):

$$\Delta =\left[\begin{array}{c}\begin{array}{cc}1.000& \begin{array}{cc}0.105& \begin{array}{cc}0.500& \begin{array}{cc}0.239& 0.500\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}0.446& \begin{array}{cc}0.250& \begin{array}{cc}0.405& \begin{array}{cc}0.187& 0.000\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}0.000& \begin{array}{cc}0.179& \begin{array}{cc}0.151& \begin{array}{cc}0.093& 0.000\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{cc}0.000& \begin{array}{cc}0.089& \begin{array}{cc}0.043& \begin{array}{cc}0.065& 0.000\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right].$$

We also used Equations (18)–(21) to obtain the sequence of correlation coefficients L as follows:

$$L=\left[\begin{array}{c}\begin{array}{cc}0.333& \begin{array}{cc}0.827& \begin{array}{cc}0.500& \begin{array}{cc}0.677& 0.500\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}0.528& \begin{array}{cc}0.667& \begin{array}{cc}0.553& \begin{array}{cc}0.728& 1.000\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc}1.000& \begin{array}{cc}0.736& \begin{array}{cc}0.768& \begin{array}{cc}0.844& 1.000\end{array}\end{array}\end{array}\end{array}\\ \begin{array}{cc}1.000& \begin{array}{cc}0.848& \begin{array}{cc}0.921& \begin{array}{cc}0.885& 1.000\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right].$$

Finally, we used Equation (22) to calculate the degrees of correlation as Q_V = 0.567, Q_C = 0.695, Q_L = 0.870, and Q_H = 0.931. They were thus ranked as Q_H > Q_L > Q_C > Q_V.

The above results showed that Q_L and Q_H were higher than 0.7. They were thus important factors affecting the operational effect of the green wave that should be prioritized when formulating optimization measures. The Q_V and Q_C were 0.5–0.7, and thus they were relatively important factors in the optimization. Therefore, measures to optimize the green wave should start from two perspectives: appropriately restricting heavy vehicle traffic and pedestrian crossings in the context of traffic management, and optimizing signal timing and design speed to improve the operational effect.

3.3. Simulation-Based Verification

We designed four simulation-based schemes of verification to test the validity of the results of the above analysis. The results were used to verify the effect of the optimization and formulate optimal measures.

Scheme 1: No optimization measure was implemented. This was the control scheme.

Scheme 2: We optimized signal timing and design speed (scheme optimization). Webster’s method [33] was used to optimize the scheme for signal timing at the key intersection, and the optimal cycle was calculated to be 125 s. We analyzed the trajectory and bandwidth at different design speeds, and obtained an optimal design speed of 50 km/h. The optimal schemes for green wave control were calculated and represented graphically [7,11], as shown in

Table 12. Scheme for green wave control with a design speed of 50 km/h and signal cycle of 125 s (unit: s).

Intersection 1		Intersection 2		Intersection 3		Intersection 4		Intersection 5		Intersection 6
Phase	Timing	Phase	Timing	Phase	Timing	Phase	Timing	Phase	Timing	Phase	Timing
	34		31		26		25		33		45
	12		54		70		28		18		46
	34		19		29		25		33		15
	20		21				20		18		19
	25						27		23
Offset	108	Offset	59	Offset	50	Offset	109	Offset	54	Offset	0

. The time–distance diagram is shown in Figure 4.

Scheme 3: Limiting heavy vehicle traffic and pedestrian crossing (traffic management). This involved restricting heavy vehicles on the road through detours. The zebra crossing was eliminated to isolate the road.

Scheme 4: This involved optimizing the signal timing and design speed on the premise of limiting heavy vehicle traffic and pedestrian crossing. That is, we adopted the measures of Schemes 2 and 3 for the overall optimization of the system.

The S, T, and D were output by Vissim software according to the above four schemes, and the E was calculated according to Equations (1–4). The schemes and their results are shown in

Table 13. Schemes used for simulation-based verification and their outputs.

Simulation Schemes	V (km/h)	C (s)	L (times)	H (%)	S	T	D	E
Scheme 1	50	130	20	3	0.53	486.39	46.97	1.156
Scheme 2	50	125	20	3	0.47	459.21	39.76	1.030
Scheme 3	50	130	0	0	0.43	432.19	42.45	1.002
Scheme 4	50	125	0	0	0.32	401.42	32.33	0.812

.

The S, T, D, and E of the different schemes were compared as shown in Figure 5 and Figure 6.

Figure 5 and Figure 6 show that compared with Scheme 1, the average number of stops in Scheme 2 was smaller by 11.3%; the average travel time was shorter by 5.6%; the average delay was shorter by 15.4%; and the value of influence was smaller by 10.9%. The average number of stops in Scheme 3 was smaller by 18.9%; the average travel time was shorter by 11.1%; the average delay by 9.6%; and the value of influence decreased by 13.3% compared with Scheme 1. The average number of stops in Scheme 4 was smaller by 39.6%; the average travel time was shorter by 17.5%; the average delay by 31.2%; and the value of influence decreased by 29.8%.

4. Discussion

4.1. Identification of Influential Factors

A sensitivity analysis of the influential factors on the green wave road in Wuhu City showed there was no significant linear correlation among design speed, signal timing, and value of influence. When V = 50 km/h and C = 120 s, E was at a minimum, as shown in Figure 3a,b. This shows that both the design speed and the signal timing needed to be optimal for the green wave to perform well. There is more support for this view in the literature. For example, Tajalli et al. claimed that jointly optimizing the signal timing and the design speed of the green wave road significantly reduced traffic congestion [34]. However, the degrees of correlation of V, C, and E calculated by using grey relational analysis were 0.567 and 0.695, respectively. This showed that they are important factors influencing the operational effect of the green wave but not the most critical ones. That is, optimizing the scheme may not be the major means of ensuring the operational efficiency of the green wave. The correlation coefficients corresponding to L, H, and E were 0.981 and 0.991, respectively. This shows that they significantly correlated positively, and heavy vehicle traffic was more relevant to the green wave. Figure 3c,d show that E increased with L and H. This showed that the greater L and H, the greater the interference to the operational effect of the green wave. This was also supported by some studies. For example, Ci et al. claimed that pedestrian crossing is one of the most important factors influencing delays at intersections [23]. Ghanim et al. claimed that heavy vehicles occupied more space on the road and affected the speed of vehicles behind them [24]. The results of grey relational analysis showed that the degrees of correlation of L, H, and E were 0.870 and 0.931, respectively. This showed that pedestrian crossing and heavy vehicle travel influenced the operational effect of the green wave, and the latter was the most critical factor. Therefore, optimizing management may be the major means of ensuring operational efficiency of the green wave. This is also a new point of view put forward in this paper.

4.2. Effect of Different Optimization Measuress

To verify the validity of the results of identifying the factors influencing the operational effect of the green wave, we used four schemes and tested them by using simulations. Scheme 1 was the control scheme without any optimization. Scheme 2 optimized signal timing and design speed. Compared with Scheme 1, the average delay decreased to 15.4%. This indicated that the average delay was reduced by optimizing signal timing and design speed in the scheme used to control the green wave. This finding supported the view of Zhang et al.; that is, optimizing the signal cycle at each intersection of the green wave on arterial roads reduced overall delay [35]. Compared with Scheme 1, the average number of stops and average travel time in Scheme 3 decreased by 18.9 and 11.1%, respectively, showing that in the context of traffic management, reducing the ratio of heavy vehicles and pedestrian crossings reduced the average number of stops and average travel time. This supported Shelmakov’s view that strengthening the management of road traffic and banning large vehicles can improve the efficiency of traffic at intersections [36]. Scheme 4 optimized both the factors related to traffic management and those related to the optimization of schemes for green wave control. Compared with Scheme 1, the three evaluation indicators underwent the largest decline in Scheme 4: 39.6, 17.5, and 31.2%. This showed that the combined optimization of the scheme for green wave control and traffic management yielded the best results.

Further comparisons of the reduction in the values of influence of Scheme 2, 3, and 4 showed that Scheme 2 underwent the smallest decrease, 10.9%. Because there was no clear linear correlation among design speed, signal timing and value of influence, improving overall efficiency in this case depended on finding the optimal scheme for green wave control. Improvements to the operational effect of the green wave are thus limited. Scheme 3 recorded the second-smallest reduction in its value of influence, 13.3%. This is because pedestrian crossings, heavy vehicle traffic, and the value of influence correlated positively. This meant that such measures of traffic management as limiting pedestrian crossings and heavy vehicles can help improve the operational effect of the green wave. Scheme 4 recorded the largest decrease in the value of influence, 29.8%. This was larger than the sum of reductions recorded by Schemes 2 and 3 (24.2%) and indicated that optimizing schemes for green wave control under the premise of implementing measures of traffic management can significantly improve the operational effect of the green wave.

5. Conclusions

In this study, we made breakthroughs in optimizing and evaluating schemes of green wave control. Representative evaluation indicators and influencing factors were selected, and a sensitivity analysis and grey relational analysis were combined to conduct innovative research into methods to identify the factors influencing the operational effect of the green wave, for which we collected data on traffic on Eshan Road in Wuhu City. Following this, we proposed different methods of optimization and verified their effects through simulations in Vissim software. The results showed a significant positive correlation among pedestrian crossings, heavy vehicle traffic, and the value of influence. These are important factors influencing the operational effect of the green wave; however, there was no prominent linear correlation among design speed, signal timing, and value of influence. Through this study, it was found that measures related to traffic management may be more effective in improving the effect of the green wave than relying solely on optimizing the scheme for green wave control. Additionally, optimizing schemes for green wave control under the premise of implementing measures related to traffic management significantly improved the operational effect.

The significance of this paper is that it provides an effective method to identify factors influencing the operational effect of the green wave. It also provides feasible measures for improving its operational effect, which is important for improving traffic efficiency on arterial roads by guiding urban traffic management. Due to limitations imposed by the collected data, we selected representative evaluation indicators and influencing factors based on conventional analysis. In addition, only data on the traffic on a specific green wave road were used, which hindered generalizing the results of this study to green wave control at large. Especially in the analysis of the influencing factors, signal timing is a complex factor. How to carry out correlation analysis of influencing factors through traffic data of multiple green wave roads to determine their degree of influence under different conditions, is the next research work to be carried out.