Investigating the Effect of Network Traffic Signal Timing Strategy with Dynamic Variable Guidance Lanes

Abstract

This paper aims to investigate the effect of network signal timing strategy with dynamic variable guidance lanes based on a two-step approach, where the first step is an interactive traffic signal optimization model for each single interaction (e.g., lane allocation plans, cycle length) in the network, and the second refers to network signal control (e.g., split, off-sets). The optimization problem in the first step is solved using the Non-dominated Sorting Genetic Algorithm (NSGA-ΙΙ), and the network signal control problem in the second step is solved through SYNCHRO. To verify the effect of dynamic variable guidance lanes and also the reliability and validity of the proposed approach, a numerical case study is carried out. The results show that the average vehicle delay in the entire road network was reduced by 25.06% after optimization using the proposed model. Moreover, the sensitivity of influencing factors of the proposed model is also analyzed. The results show that when the traffic flow is increased by 60% of the original traffic flow, the optimization effect of the model is more significant. However, when the lane capacity is more than 1300 pcu/h, the vehicle delay will increase slowly. To sum up, this method can improve the regional traffic efficiency of the traffic-stressed lanes and further promote the full utilization of space-time resources of the road network.

1. Introduction

With the development of traffic planning and control techniques over several decades, urban traffic congestion is still one of the main issues that traffic engineers need to fix. On the one hand, the idea of travel demand management has been proposed, and there are numerous studies and applications aiming to relieve traffic congestion from the demand side [1,2]. On the other hand, there are still many studies focusing on the supply side. For instance, some investigate the home–work relationship and try to solve the congestion issue by reshaping urban spatial resources, which further influences peoples’ choices of workplace and residence [3,4]; some investigate the traditional traffic signal control strategies but in a real-time context to reduce the traffic delay at intersections [5,6].

From the perspective of traffic supply, traffic signal control is still one of the approaches to deal with traffic congestion. However, with the increasing of car ownership, isolated signal control for a single interaction is proved to be insufficient, and therefore some researchers have turned to coordinated (either arterial or network) signal controls. In fact, there are some mature commercial software tools or systems for such signal control strategies, such as SCATS and SCOOT [7,8,9,10]. Nevertheless, with the development of city size and urban population, some other approaches come into practice as well. The dynamic variable guidance lane is one of them [11].

A dynamic variable guidance lane is a specific lane whose turning direction is changeable (normally, it is changeable between turning left and going straight). By setting a variable guidance lane, the capacity of an intersection can be further improved [12]. For instance, in a certain time period, the going-straight traffic flow is dominated in an entrance of an intersection, and the direction of the variable guidance lane can be set as going straight; in another time period, the turning-left traffic flow becomes dominated, and the lane’s direction can be correspondingly set as turning left. In this sense, a variable guidance lane improves the capacity of an intersection by optimizing the spatial and temporal resources of the intersection [12].

To sum up, the variable guidance lane is proposed to solve the unbalance of different turning movements in the same entrance of an intersection. In the last century, it has been widely used to solve the problem of imbalanced traffic flow during daily commuting peaks [13].

Generally, there will be the following situations. In the first one, there are many vehicles in the left-turn lane and the queue length is increasing when the left-turn lane is in a red-time phase, while there are only a few vehicles in the going-straight lane when the corresponding phase is in green time. This phenomenon results in the waste of green time of the going-straight phase. The second is exactly the opposite. In this one, there are fewer vehicles in the left-turn lane when the responding phase is green time. However, the phase for the going-straight lane is still in red time, and straight-moving vehicles have to wait at the stop line. In both situations, the increase in the queue length further affects the service level at the upstream intersection. Therefore, the switching of driving direction of the variable guidance lanes at intersections and the optimization of the network signal timing strategy seems an effective approach to improving the overall service level of the road network.

Based on the above considerations, this paper attempts to contribute to the literature of traffic signal control by studying network signal control and the setting of variable guidance lanes together. To this end, a network signal timing strategy with the existence of dynamic variable guidance lanes is developed through a two-step approach, where the first step is an interactive traffic signal optimization model for each single interaction (e.g., lane allocation plans, cycle length) in the network, and the second refers to network signal control (e.g., split, off-sets).

This study aims to explore the interactive relationship between variable guidance lane design and signal control by establishing a dynamic two-step approach in order to mutually match lane function setting and signal control and to improve the operation efficiency of the whole road network. Combing the network coordinated signal control, the proposed approach is different from the previous method of setting variable guidance lanes regarding the following aspects. First, the premise of the model is that the middle lane of each entrance in a road network can be a variable guidance lane, rather than only a single entrance at a certain intersection depending on the manager experience. Second, with the objective of minimizing the road network total vehicle delay, the model answers the question of which direction the variable guidance lanes should run. Third, once the optimal variable guidance lane design scheme of each entrance at the intersection is determined, the network signal control strategy is optimized correspondingly. In particular, the network signal control parameters are determined by the optimization results in the first step (lane driving direction and single-intersection signal cycle). Using this proposed approach, we successfully extended the problem to combine both time and space, improving the efficient utilization of temporal and spatial resources, which enables treating the traffic demand in different time periods flexibly.

The remainder of the paper is organized as follows. Section 1 reviews the network signal control techniques. Section 2 introduces the proposed two-step approach. In Section 3, a numerical case is used to verify the effect of dynamic variable guidance lanes and also the reliability and validity of the proposed approach. Section 4 analyzes the proposed approach’s results. Section 5 analyzes sensitivity of the proposed model. Finally, Section 6 provides an overall conclusion and future research directions.

2. Literature Review

2.1. Network Signal Control and Optimization Methods

By definition, network signal control is a unified signal coordination control system for some intersections with strong correlation in the road network [14]. From a systematical perspective, the intersections in a road network cannot be independent from each other, especially in the context of higher-saturation flows. In this sense, the signal control strategies for these intersections also are not independent. Based on this idea, network traffic signal control was proposed and has become a popular topic, especially with the development of intelligent transportation techniques.

The research on network signal control originated in the last century. In the 1960s, the government of the United Kingdom adopted a combination method to achieve network signal coordination control for two dimensions, becoming the first practical application of network signal control in the world. The control system was further developed into TRANSYT, which is widely used by traffic engineers now. Later, the government of the United Kingdom continued to develop and design an adaptive control system based on TRANSYT called SCOOT, which detects the traffic flow at intersections in real-time and changes the signal control strategies adaptively. The SCOOT system has been tested and evaluated in numerous field trials using floating vehicle measurement technology. Results show that it can reduce vehicle delays by an average of 12% compared to the state-of-the-art scheduled fixed-time control calculated using TRANSYT. However, the SCOOT system cannot perform well in the context of higher-saturation traffic flows [15,16].

Another widely used system for network signal control is SCATS, which was developed in the 1970s by the Roads and Transport Authority of New South Wales, Australia [17]. It works by modifying traffic signal timings in real time in response to the changes in traffic demand and system capacity. Traffic sensors are used to monitor traffic flow conditions, based on which signal control timing is conducted to minimize the stops and delays of vehicles at intersections. Through this way, SCATS attempts to minimize the likelihood of traffic congestion at intersections [18]. However, similar to the SCOOT system, the SCATS system can better improve the overall performance of the road network in the state of unsaturated traffic flow, but the system cannot handle coordinated control in the oversaturated state, where the final coordination effect of the system is actually equivalent to that of separate-intersection signal control.

At present, the studies about network signal control mainly follow two research lines. On the one hand, considerable studies [19,20,21,22,23] are carried out on the basis of arterial coordinated signal control. These studies have been devoted to computing the parameters of network signal control, such as cycle lengths, green splits, and off-sets. On the other hand, some studies [24,25,26,27] have integrated signal control timing for single intersections in the road network.

Arsava [19] developed an asymmetrical Multi-BAND (AM-BAND) model by relaxing the symmetrical progression band requirement in a Multi-BAND model. The proposed AM-BAND model is formulated as a mixed-integer linear program. Zhang [20] proposed two models to tackle traffic signal coordination problems for long arterials and networks. The first model (Model MaxBand LA) can optimize arterial partition plans and signal coordination plans of all the subsystems simultaneously. The second one (Model MaxBand GN) directly optimizes the off-sets for all the signals in a network. Hu [21] divided the intersection into boundary intersection and internal intersection, and an improved Webster delay model based on off-set coordination was proposed. Luca [22] proposed a network signal control method using daily traffic flows. Regarding on-line traffic control, a hybrid approach combining interacting-intersection optimization (i.e., optimizing the parameters such as the green time, the off-sets, and the phase sequences) and the link metering control was considered. Wang [23] proposed an efficient origin–destination bandwidth (OD band) model, which provided dedicated progression bands for arterial traffic flows based on the real-time dynamic matrix of their estimated OD pairs. Wada [24] considered an optimal coordinated traffic signal control under both deterministic and stochastic demands. This study presented a new mixed-integer linear program (MILP) for deterministic signal control optimization. Li [25] proposed a novel dynamic multi-objective (i.e., travel delay and intersection capacity) optimization method for designing predictive controls of network signal strategy. Yu [26] proposed a Q-learning algorithm combined with the green signal ratio optimization method, based on which an optimization model for the coordinated control of the green time at intersections was established. Jia [27] applied metaheuristic techniques for signal timing optimization as one of the practical solutions to enhance the performance of transportation networks. Li [28] proposed a multi-objective optimization method for signal control design at intersections in urban traffic networks. The cell transmission model was employed for macroscopic simulation of the traffic. Additional rules were introduced to model different route choices from origins to destinations. A multi-objective optimization problem (MOP) was formulated considering four measures of network traffic performance.

2.2. Variable Guidance Lane and Its Development

A variable guidance lane is a lane whose movement direction for vehicles can be changed according to the direction of dominated traffic flow. Normally, variable guidance lanes are adopted to deal with traffic congestion and the phenomenon caused by the separation of work and residence locations (see Figure 1 as an example). In the last century, some researchers [12] have carried out studies on variable guidance lanes and proposed corresponding traffic management methods, which have since been used and are mainly used to solve the problem of unbalanced traffic flow during a certain time period (e.g., morning peak hour) and to deal with the influence of special important events, such as emergency evacuation, road construction, and particular traffic management.

In the literature, a series of optimization models have been developed and tested for the setting of variable guidance lanes. Zhou [13] introduced the intelligent dynamic optimization model of the variable lane control system used in the George Massey tunnel in southern Vancouver. A program for the variable guidance lane system was developed that can estimate real-time traffic demand more accurately. Urbina [29] conducted a study on emergency evacuation plans using variable guidance lanes in multiple states in the United States, focusing on the use of variable guidance lane flow in modeling and the role of intelligent transportation systems in emergency evacuation plans. Nassiri [30] studied the real-time adjustment technology of variable guidance lanes. An off-line scheme was used to adjust the variable lane through a logit model, and the lane direction was adjusted in real time. The test results on a road network in Texas showed a 16 percent increase in road capacity comparing to the case without variable guidance lanes. Hausknecht [31] proposed a real-time strategy for operating variable guidance lanes with the use of traffic sensors. According to these data, the traffic management department changes the direction of the variable guidance lanes artificially.

Zhou [32] used the traffic flow and other traffic information obtained from video detection to propose a variable guidance lanes decision algorithm based on non-parametric regression, which can intelligently change the variable lanes with real-time traffic flow. Zeng [33] analyzed the spatiotemporal relationship of signal-controlled intersections, and a combination model of variable guidance lane function and signal control phase was established. Zhao [34] proposed the concept of variable guidance lane control for intersections where emergency vehicles have priority and established a comprehensive optimization model of lanes and signal control aiming at zero delay of emergency vehicles and minimum total delay of other vehicles at the intersection. Song [35] provided a comprehensive overview of the state-of-the-art research on predicting and detecting the surrounding vehicles’ lane change maneuvers. First, various driver behavior modeling and classification methods were reviewed and analyzed. Next, the primary sensing devices equipped on intelligent vehicles and their impacts on lane change inference systems were discussed.

2.3. Conclusions from the Literature Review

As demonstrated in the literature review, network signal control is still a topic of ongoing research. In the area of signal control, the coordinated control model and the green wave model were proposed, and the research objectives include minimization of vehicle delay and maximization of traffic capacity. In terms of variable guidance lanes, many existing studies aim to improve the performance of each individual intersection. Several studies have proposed different signal control optimization models for variable guidance lanes, which normally aim at the minimization of vehicle delay or queue length and the maximization of interaction capacity.

However, there are three issues in these studies: (1) the research on network signal control and variable guidance lanes is carried out separately and independently, and the consistency of time and space is not fully considered; (2) unlike the premise of this paper’s model, which is that the middle lane of each entrance at an intersection can be a variable guidance lane, these studies assume it can be set at only a single entrance at a certain intersection depending on the manager experience; (3) although the topics of network signal control and variable guidance lanes are of interest, the relationship between them is not actually fully investigated.

To address the above defects, this paper attempts to contribute to the literature on traffic signal control by studying network signal control and the setting of variable guidance lanes together. To this end, a network signal timing strategy with the existence of dynamic variable guidance lanes is developed through a two-step approach, where the first step is an interactive traffic signal optimization model for each single interaction (e.g., lane allocation plans, cycle length) in the network, and the second refers to network signal control (e.g., split, off-sets).Using this proposed approach, we successfully extended the problem to combine both time and space, improving the efficient utilization of temporal and spatial resources, which enables treating the traffic demand in different time periods flexibly.

In addition, it is worth noting that the purpose of this paper is not to propose a new mesoscopic model but to investigate the effect of network signal control strategy with consideration of variable guidance lane control. This study also uses simulation software to analyze and compare the optimization results obtained by the model. The simulation is also used to analyze how traffic flow and lane capacity influence the proposed model.

3. Methodology

3.1. General Framework

The network traffic signal control strategy with variable guidance lanes is presented in this section, aiming at optimizing design of the variable guidance lanes and network signal control strategy. Specifically, a two-step approach is proposed, where the first step is an interactive traffic signal optimization model for each single interaction in the network, and the second refers to network signal control. The following introduces the details of the two-step approach.

In the literature, the optimized objectives for intersection signal control vary (e.g., capacity, travel cost, fuel consumption, or air pollution). In this current paper, the considered objective function is the minimization of vehicle total delay in a road network.

In the first step, the setting scheme of the variable guidance lanes at a single intersection is carried out, in which the turning direction of the variable guidance lanes and other parameters of single timing for each interaction in the network are optimized. Specifically, a bi-level model from Zhao et al. (2022) is adopted, whose solutions are found through the NSGA-II algorithm. In the second step, the network signal control is performed, in which the parameters for network signal control such as common cycle, green time, and off-sets are optimized. Specifically, network signal control is carried out based on single-intersection optimization. In this case, once design schemes for all considered single intersections are determined, the common cycle length, the green time and the node off-sets are optimized based on the objective of network total delay minimization and are computed. In Figure 2, the network traffic control procedure with variable guidance lanes is shown in more detail.

3.2. The Two-Step Approach

In this section, we describe the details of the proposed two-step approach. In terms of the bi-level model in the first step, authors have conducted a related study (Zhao et al., 2022). For the sake of simplicity of the paper, we are not going to repeat the model in this section. Readers can see the attached Appendix A for the details. This proposed approach is based on a previous interaction model, a single-intersection optimization model considering variable guidance lane. In order to reduce the computational complexity and model error, two-step approach can avoid error effect in the calculation result of each step and improve the robustness. Therefore, we used two-step approach in this study.

In the second step, based on the results of the bi-level model, the network signal control is conducted, which introduces the delay in crossing signalized intersections and proposes the off-set optimization model using the vehicle delay. The most important point is that on the basis of previous model, the design scheme of the variable guidance lane was obtained, and therefore the critical lane (i.e., the variable guidance lane, in this case) and the coordinated traffic flow and phase for the road network signal control optimization in this study could be determined. The following describes the details in the second step.

3.2.1. Vehicle Delay of Road Network

As stated above, the total vehicle delay was considered as objective function (even though other measure of performances could be introduced) in this paper.

In actual urban traffic operation, vehicles wait in stop lines due to the influence of signal control, which causes vehicle delays. Meanwhile, there is another kind of delay due to acceleration and deceleration through the intersection. Therefore, the vehicle delay consists of these two parts, as shown in Formula (1).

$$\min {\displaystyle \sum _i{\displaystyle \sum _j{\displaystyle \sum _k\left(D_{ijk}+D_{ijk}^{\prime }\right)}}}$$

(1)

where D_ijk is the vehicle delay in the k lane of the j entrance at the i intersection, (s); $D_{ijk}^{\prime }$ is vehicle delay in crossing the intersection of the k lane in the j entrance lane at the i intersection, (s).

The vehicle delay D_ijk is obtained by subtracting the theoretical travel time from the actual travel time, as shown in Formula (2).

$$D_{ijk}=N_{ijk}/S_{ijk}-\left(N_{ijk}\cdot J/v_{ijk}\right)$$

(2)

where N_ijk is actual queue length of the k lane of the j entrance at the i intersection, (pcu); S_ijk is saturated flow rate of the k lane of the j entrance at the i intersection, (pcu/s). J is the length of each vehicle, (m); v_ijk is the average speed of vehicles in the k lane of the j entrance at the i intersection, (m/s).

Vehicle delay crossing the intersection $D_{ijk}^{\prime }$ is caused by vehicle acceleration and deceleration and queue dissipation at the intersection. In order to get closer to the actual operating situation, based on the above statements, the delay in crossing the intersection is computed as follows:

$$D_{ijk}^{\prime }=N_{ijk}·((v_{ijkt}-v_{ijk0})/a-(L_{ijk}/v_{ijk}))$$

(3)

where v_ijkt is the vehicle speed of the k lane in the j entrance lane passing through the i intersection, (m/s); v_ijk0 is the initial vehicle speed of the k lane in the j entrance lane passing the i intersection, (m/s); L_ijk is the length of the intersection (the distance from the k lane in the j entrance lane at the i intersection stop line of the upstream entrance to the exit of downstream intersection), (m).

3.2.2. Signal Control Optimization of Road Network

1. Signal Cycle formulation

Assuming that the phase composition and sequence are explicitly considered, the signal cycle length of each intersection is calculated by Formula (4). In this case, the signal cycle is computed based on the Webster [36] formula. Nevertheless, any other formula can be used as well.

$$C_i=\left(1.5L_i+5\right)/\left(1-Y_i\right)$$

(4)

$$L_i={\displaystyle \sum _{n=1}^N{l}_n}$$

(5)

$$Y_i={\displaystyle \sum _{n=1}^N{y}_n={\displaystyle \sum _{n=1}^N\max \left({\mathrm{y}}_{nk}\right)}}$$

(6)

where l_n is lost time of the n phase, (s); y_nk is flow ratio of the k lane in the n phase; N is the number of phases of the i intersection.

2. Common signal cycle of road network

After having calculated the cycle length of each single intersection, it is necessary to determine the grid network common cycle and phase sequence to facilitate the coordinated signal control of a network and to provide a reasonable signal timing plan for critical traffic flows.

$$C_m=\max (C_1,C_2\cdots C_i)$$

(7)

where C_m is the common signal cycle in the road network, (s).

3. Signal control optimization strategy

• Minimum green time of coordinated phase at critical intersection

Once the variable guidance lane design scheme and signal control period are determined, the critical phase at the critical intersections can be also determined on this basis, as follows:

$$t_{EGm}=\left(C_m-l_m\right)\times \frac{y_m}{Y_m}$$

(8)

where t_EGm is the minimum green time for coordinated phase, (s); l_m is total lost time of the critical intersections, (s); y_m is the coordination phase of critical intersections and the critical traffic flow ratio, (s); Y_m is the sum of the critical traffic flow ratios of each phase at critical intersections, (s).

It needs to be emphasized that if d = 1 (see Appendix A for details), meaning the variable guidance lane is a left-turn lane, then y_m = max (y_ij−l, y_ij−v); if d = 0, meaning the variable guidance lane is a going-straight lane, then y_m = max (y_ij−sr, y_ij−v).

The calculation of the flow ratio of each lane in each phase is shown in Formulas (9)–(11):

$${\mathrm{y}}_{ij-l}=q_{ij-l}/\left(S_{ij-l}(1+d_{ij})\right)$$

(9)

$$y_{ij-v}=\left(q_{ij-l}\cdot d_{ij}+q_{ij-s}\cdot (1-d_{ij})\right)/2S_{ij-v}$$

(10)

$$y_{ij-sr}=q_{ij-sr}/\left(S_{ij-sr}(2-d_{ij})\right)$$

(11)

where y_ij−l is the flow ratio of the left-turn lane of the j entrance at the i intersection; y_ij−v is the flow ratio of the variable guidance lane of the j entrance at the i intersection; y_ij−sr is the flow ratio of the straight and right-turn lane of the j entrance at the i intersection.

$$Y_m={\displaystyle \sum _{n=1}^N\max \left({\mathrm{y}}_n\right)}$$

(12)

where y_n is traffic flow ratio of phase n at critical intersection.

• Minimum green time of non-coordinated phases at non-critical intersection

On the basis of the critical intersections and critical phase, the other non-coordinated phases at non-critical intersection can be also determined as follow:

$$t_{EGn}=C_m\times q_n/\left(S_n\times x_p\right)=C_m\times y_n/x_p$$

(13)

where t_EGn is the minimum green time of the n phase in the non-coordinated phases at non-critical intersection, (s); q_n is the critical traffic flow of the n phase in the non-coordinated phase at a non-critical intersection, (pcu/h); S_n is saturated flow of the critical lane of the n phase in the non-coordinated phase at non-critical intersection, (pcu/h); y_n is traffic flow ratio of the critical lane of the n phase in the non-coordinated phase at non-critical intersection; x_p is saturation of non-coordinated phases at non-critical intersections.

If d = 1, meaning the variable guidance lane is left-turn lane, then y_n = max (y_ij−sr, y_ij−v); if d = 0, meaning the variable guidance lane is straight lane, then y_n = (y_ij−l, y_ij−v).

• Effective green time of the coordinated phases at non-critical intersections

In order to have better coordinated control performance and proper off-set, it is necessary to calculate the critical phase green time of non-critical intersections, as shown here:

$$t_{EG}=C_m-L_n-{\displaystyle \sum _{n=1}^k{t}_{EGn}}$$

(14)

where t_EG is minimum green time of the coordinated phase, (s); L_n is total lost time at non-critical intersections, (s); K is the total number of the non-coordinated phases at non-critical intersections.

4. Off-set optimization model

Once the signal control of each single intersection is optimized, combined with the minimized vehicle delays calculated in Section 3.2.1 and Section 3.2.2, the off-set optimization model can provide a more efficient coordination signal control strategy for the traffic flow that selects the variable guidance lanes. The off-set model Formula (15) is shown as follows:

$$O_{i,i+1}=L_{i,i+1}/v_t+l_s+D_{i,i+1}$$

(15)

where O_i,i+1 is the off-set of the coordinated phase between intersection i and intersection i + 1, (s); L_i,i+1 is the distance from the stop line at the entrance of intersection i to the stop line of the intersection i + 1, (m); D_i,i+1 is the vehicle delay of the coordinated phase between intersection i and intersection i + 1, (s).

Different from previous studies about network signal control, this study directly incorporates variable guidance lanes and signal coordination control into an integrated two-step framework. The idea is straightforward: once the vehicle delay is optimized, the traffic demand can be changed and assigned; further, the model in the first step optimizes the signal timing plan of each single intersection, and the model in the second step optimizes the coordinated network signal control.

The first and the second steps are essentially connected via the parameters d and C, which are optimized by the two -step model in the first step and are introduced into the second step to determine the critical traffic flow and other parameters. Another point that needs to be emphasized is the off-set optimization model between each intersection. It is also optimized on the basis of the vehicle delay calculated in the first step.

4. Numerical Case

In this section, a numerical case study is carried out, where the network signal control strategy with variable guidance lanes is optimized using the proposed two-step approach, and the final corresponding total vehicle delay is computed using the SYNCHRO simulation software. In particular, sensitivity analysis is also carried to investigate the effect of traffic flows and capacity.

Case Description

In this numerical case, four intersections (labeled by 1 to 4) are consisted as the road network. The middle lane of each entrance of each intersection is set as the variable guidance lane, which can change the driving direction (go straight or turn left) according to the traffic flow. The network is shown in Figure 3.

In addition to signal timing plan of the intersections, other data are needed in this case study. They are traffic flow of each lane, length of entrance lane, vehicle speed, and actual length of the vehicle. The traffic volume can be obtained by video detectors. According to the traffic volume and the characteristics of the traffic flow, the entire day is divided into five time periods: the time period of 0:00–6:00 is the free-flow period, during which the average traffic volume is the smallest; 6:00–9:00 is the morning peak period, during which the traffic volume rises to the highest; 9:00–16:00 is the noon period, during which the traffic volume is stable; 16:00–19:00 is the evening peak, the other time during which traffic volume reaches the highest; 19:00–0:00 is the evening period, when the traffic volume in this period is stable again.

Table 1. All-day traffic volume of each entrance at the 4 intersections.

Intersection No.	Time Periods	South (pcu/h)			North (pcu/h)			West (pcu/h)			East (pcu/h)
		LT	TH	RT	LT	TH	RT	LT	TH	RT	LT	TH	RT
1	0:00–6:00	74	63	28	39	27	12	34	68	10	48	12	7
	6:00–9:00	392	296	132	384	98	25	352	290	37	255	71	19
	9:00–16:00	572	218	79	645	171	29	455	364	85	417	121	54
	16:00–19:00	310	107	46	289	99	24	208	164	63	261	62	49
	19:00–0:00	149	76	23	174	71	13	97	116	21	149	35	12
2	0:00–6:00	84	135	45	63	36	9	30	69	16	54	84	16
	6:00–9:00	330	468	80	231	193	36	297	378	72	360	468	105
	9:00–16:00	492	540	95	531	356	84	495	582	124	594	693	89
	16:00–19:00	198	273	60	228	186	49	192	294	65	300	384	126
	19:00–0:00	120	183	37	156	105	17	96	165	40	48	147	31
3	0:00–6:00	30	69	14	63	81	12	45	72	13	93	114	20
	6:00–9:00	363	402	51	222	294	33	195	279	28	231	312	67
	9:00–16:00	540	522	102	483	513	105	288	384	63	408	510	138
	16:00–19:00	289	245	67	252	297	46	126	135	85	177	204	92
	19:00–0:00	90	165	34	156	213	69	99	120	26	147	183	26
4	0:00–6:00	48	75	17	42	60	14	51	78	10	33	54	15
	6:00–9:00	339	453	94	303	540	76	180	246	85	345	444	134
	9:00–16:00	438	504	125	486	609	111	318	405	70	360	507	91
	16:00–19:00	147	228	87	264	291	63	81	120	56	123	210	72
	19:00–0:00	81	129	23	159	225	58	99	144	48	96	162	51

Note: LT represents left-turn lane; TH represents going-straight lane; RT represents right-turn lane.

shows the statistics of travel volume of each entrance lane with different turns in the five periods. Note that the data we used in this numerical case cannot exactly reflect any situation in the real world, and they are just used to show the reliability and validity of the proposed model.

Table 2. Original signal timing plans before optimization.

Intersection No.	Time Period	Phase 1 (s)	Phase 2 (s)	Phase 3 (s)	Phase 4 (s)	Cycle (s)
						——
1	0:00–6:00	16	20	25	28	89
	6:00–9:00	20	25	29	32	106
	9:00–16:00	24	27	26	25	102
	16:00–19:00	32	28	30	24	114
	19:00–0:00	22	25	20	24	91
2	0:00–6:00	25	28	22	25	100
	6:00–9:00	30	25	26	32	113
	9:00–16:00	25	28	24	26	103
	16:00–19:00	25	30	35	25	115
	19:00–0:00	20	24	28	22	94
3	0:00–6:00	18	22	20	24	84
	6:00–9:00	26	30	28	25	109
	9:00–16:00	24	28	25	20	97
	16:00–19:00	28	30	34	26	118
	19:00–0:00	20	20	22	24	86
4	0:00–6:00	20	24	24	20	88
	6:00–9:00	26	35	28	30	119
	9:00–16:00	25	28	32	24	109
	16:00–19:00	25	35	30	28	118
	19:00–0:00	20	18	22	25	85

presents the original signal timing plans for intersections in the network, including the phase sequence, green time, and cycle length. Note that for network signal control, the phase sequence for all intersections must be the same.

Finally, the non-dominated sorting genetic algorithm II (NSGA-II) was selected in this study. In particular, the NSGA-II algorithm, allowing for the computation of an approximation of the entire Pareto front, guarantees the exploration of a wide solution space [37]. The implementation regarding the proposed model was worked out in RStudio and run on a server machine that has an Intel(R) Xeon(R)CPU E7-7500, clocked at 2.7 Ghz, with 32 GB of RAM.

5. Result and Discussion

The all-day traffic data in Table 1 are used as research data, and current signal timing in Table 2 are used as original signal timing schemes in this section. Firstly, the proposed approach optimizes the variable guidance lane scheme and each intersection signal cycle, and the results are shown in

Table 3. The model optimization results before coordination.

Intersection No.	Time Period	South	North	West	East	Cycle(s)	Delay(s)
		d1	d2	d3	d4	C	D
1	0:00–6:00	0	0	0	0	92	15.38
	6:00–9:00	1	1	0	1	127	21.23
	9:00–16:00	1	0	0	0	114	19.04
	16:00–19:00	0	1	0	1	100	16.73
	19:00–0:00	0	0	0	0	96	16.07
2	0:00–6:00	0	0	0	0	93	15.58
	6:00–9:00	0	1	0	1	121	20.23
	9:00–16:00	0	1	0	0	105	17.23
	16:00–19:00	1	0	0	0	111	18.45
	19:00–0:00	0	0	0	0	95	15.83
3	0:00–6:00	0	0	0	0	91	15.14
	6:00–9:00	1	1	0	0	116	19.29
	9:00–16:00	0	0	0	1	103	17.16
	16:00–19:00	0	0	1	1	108	18.03
	19:00–0:00	0	0	0	0	88	14.59
4	0:00–6:00	0	0	0	0	92	15.30
	6:00–9:00	0	0	1	0	113	18.76
	9:00–16:00	0	0	0	0	100	16.64
	16:00–19:00	0	1	0	1	104	17.27
	19:00–0:00	0	0	0	0	94	15.74

Note: 0 means going-straight direction, and 1 means left-turn direction.

. Secondly, effect of variable guidance lanes. are shown in Table 4. Thirdly, the network signal timing and off-set are optimized, and the optimization results are shown in Table 5. Table 6 shows the effect of network coordinated signal control with variable guidance lane.Finally, the simulation is used to verify the approach, and the final results for each intersection are shown in Table 7.

5.1. Effect of Variable Guidance Lanes

Table 3 shows the results of the first step, namely the design scheme of variable guidance lane and the optimal signal cycle length of each intersection. It can be observed from Table 3 that the design plan of the variable guidance lane and the signal cycle for each time period are different (because of the changes in traffic volume and the saturation of each driving direction during different time periods), where 0 represents that the lane driving direction is going-straight, and 1 represents that the lane driving direction is left-turning. Taking the intersection 1 as an example, from 6:00 to 9:00, due to the increase in left-turning volume during the morning rush hour, the driving direction of the variable guidance lanes of the North, South and East entrance is switched to left, and the optimal signal cycle is 127 s. Similarly, the driving direction of the variable guidance lane of the South entrance is switched to left and the optimal signal cycle is 114 s from 9:00 to 16:00. From 16:00 to 19:00, the variable guidance lanes of the North and East entrance are switched to left, and the optimal signal cycle is 100 s. During the other two periods, from 0:00 to 6:00 and from 19:00 to 0:00, these traffic volumes are smaller compared to the overall day. Therefore, the driving direction of the variable guidance lane does not need to be switched. The driving direction remains going-straight, and the optimal signal cycles are 92 s and 96 s, respectively. Moreover, the model can also provide the vehicle delay in different time periods.

The entire delay of the four intersections that were optimized by the proposed approach is shown in Table 4. It can be seen that: (1) during the period from 0:00 a.m. to 6:00 a.m., the entire delay is 92.43 s before optimization and drops to 75.38 s after optimization; (2) during the period from 6:00 a.m. to 9:00 a.m., the entire delay is from 88.88 s before optimization and 74.11 s after optimization, a reduction by 16.61%; (3) from 9:00 a.m. to 16:00 p.m., the entire delay is 88.38 s before optimization and 70.71 s after optimization, a reduction by 19.99%; (4) from 16:00 to 19:00, the entire delay is 82.47 s before optimization and 67.08 s after optimization, a reduction by 18.66%; (5) from 19:00 p.m. to 0:00 a.m., the entire delay is 87.18 s before optimization and 76.41 s after optimization. The entire delay can be reduced on average by 12.35%.

It can be seen that upon implementing the variable lane design into the road network, the entire delay of four intersections is significantly reduced when the traffic flow does not change during each time period. The model optimization results show that the total vehicle delay is reduced by 17.14%. To conclude, the proposed approach exhibits a better performance in reducing vehicle delay and can improve the level of service and operation efficiency of the intersections in a road network.

Table 4. Effect of variable guidance lanes.

Time Period	Total Vehicle Delay (s)
	Before Optimization	After Optimization	Vehicle Delay Reduced
0:00–6:00	92.43	75.38	18.45%
6:00–9:00	88.88	74.11	16.61%
9:00–16:00	88.38	70.71	19.99%
16:00–19:00	82.47	67.08	18.66%
19:00–0:00	87.18	76.41	12.35%
Average	17.14%

Table 4. Effect of variable guidance lanes.

Time Period	Total Vehicle Delay (s)
	Before Optimization	After Optimization	Vehicle Delay Reduced
0:00–6:00	92.43	75.38	18.45%
6:00–9:00	88.88	74.11	16.61%
9:00–16:00	88.38	70.71	19.99%
16:00–19:00	82.47	67.08	18.66%
19:00–0:00	87.18	76.41	12.35%
Average	17.14%

5.2. Effect of Network Coordinated Signal Control with Variable Guidance Lane

The results for the network coordinated signal control are presented in Table 4, which shows the green times and off-set under the selected common signal cycle length that minimizes the deterministic total vehicle delay. Normally, the largest signal cycle length from the first step is selected as the common cycle length, as the second-last column shows in Table 5. The common cycle lengths of the four intersections during the five time periods are 93 s, 127 s, 114 s, 111 s, and 96 s, respectively. It should be emphasized that the intersection 1 is set as the base intersection when calculating the off-set. In addition, the off-set of each intersection in the same time period is different, which is determined by the intersection distance, variable guidance lane design, and critical traffic flow.

Table 5. Optimized signal timing schemes after network coordination.

Intersection No.	Time Period	Phase 1 (s)	Phase 2 (s)	Phase 3 (s)	Phase 4 (s)	Cycle (s)	Off-Set (s)
						——	——
1	0:00–6:00	19	25	22	27	93	-
	6:00–9:00	32	40	24	31	127	-
	9:00–16:00	36	29	24	25	114	-
	16:00–19:00	22	34	27	28	111	-
	19:00–0:00	30	25	19	22	96	-
2	0:00–6:00	21	26	24	22	93	33
	6:00–9:00	25	36	24	42	127	42
	9:00–16:00	30	32	28	24	114	33
	16:00–19:00	26	34	28	23	111	43
	19:00–0:00	20	28	25	23	96	32
3	0:00–6:00	18	24	28	23	93	36
	6:00–9:00	36	40	28	23	127	46
	9:00–16:00	30	30	25	29	114	38
	16:00–19:00	23	27	29	32	111	48
	19:00–0:00	20	25	28	23	96	33
4	0:00–6:00	19	26	28	20	93	35
	6:00–9:00	25	35	37	30	127	46
	9:00–16:00	25	30	32	27	114	34
	16:00–19:00	23	33	27	28	111	45
	19:00–0:00	19	28	26	23	96	33

Table 5. Optimized signal timing schemes after network coordination.

Intersection No.	Time Period	Phase 1 (s)	Phase 2 (s)	Phase 3 (s)	Phase 4 (s)	Cycle (s)	Off-Set (s)
						——	——
1	0:00–6:00	19	25	22	27	93	-
	6:00–9:00	32	40	24	31	127	-
	9:00–16:00	36	29	24	25	114	-
	16:00–19:00	22	34	27	28	111	-
	19:00–0:00	30	25	19	22	96	-
2	0:00–6:00	21	26	24	22	93	33
	6:00–9:00	25	36	24	42	127	42
	9:00–16:00	30	32	28	24	114	33
	16:00–19:00	26	34	28	23	111	43
	19:00–0:00	20	28	25	23	96	32
3	0:00–6:00	18	24	28	23	93	36
	6:00–9:00	36	40	28	23	127	46
	9:00–16:00	30	30	25	29	114	38
	16:00–19:00	23	27	29	32	111	48
	19:00–0:00	20	25	28	23	96	33
4	0:00–6:00	19	26	28	20	93	35
	6:00–9:00	25	35	37	30	127	46
	9:00–16:00	25	30	32	27	114	34
	16:00–19:00	23	33	27	28	111	45
	19:00–0:00	19	28	26	23	96	33

To further examine the effects of the network coordinated signal control, the design scheme of the variable guidance lanes was fed into the SimTraffic simulation module in Synchro 11, and the results (the final delay) from the proposed two-step approach were compared with the original single timing strategy. The index delay per vehicle was chosen as the criterion, because it can be used to verify the model optimization results directly and easily.

In order to collect the simulation results, the following inputs must be defined:

-

The study time length is 15 min;

-

The simulation interval length is 3600 s;

-

The free speed is 30 km/h;

-

Speed limit is 60 km/h;

-

The lost time for each phase of all intersections is 2 s;

-

Yellow time is 3 s.

Table 6 shows the entire vehicle delay of four intersections before optimization obtained by the Synchro simulation based on the traffic flow data (Table 1) and original signal control timing (Table 2) and the results after optimization of the proposed two-step approach.

Table 6. Effect of network coordinated signal control with variable guidance lane.

Time Period	Vehicle per Delay (s)
	Before Optimization	After Optimization	Vehicle Delay Reduced
0:00–6:00	84.25	61.34	27.19%
6:00–9:00	79.28	57.72	27.19%
9:00–16:00	78.91	61.82	21.66%
16:00–19:00	78.86	59.70	24.30%
19:00–0:00	79.00	58.89	25.46%
Average	25.06%

Table 6. Effect of network coordinated signal control with variable guidance lane.

Time Period	Vehicle per Delay (s)
	Before Optimization	After Optimization	Vehicle Delay Reduced
0:00–6:00	84.25	61.34	27.19%
6:00–9:00	79.28	57.72	27.19%
9:00–16:00	78.91	61.82	21.66%
16:00–19:00	78.86	59.70	24.30%
19:00–0:00	79.00	58.89	25.46%
Average	25.06%

It can be found that after the optimization, the vehicle delay of each entrance lane has been significantly reduced as follows: (1) from 0:00 a.m. to 6:00 a.m., average vehicle delay is reduced from 84.25 s to 61.34 s; (2) from 6:00 a.m. to 9:00 a.m., average vehicle delay is reduced from 79.28 s to 57.72 s; (3) from 9:00 a.m. to 16:00 p.m., average vehicle delay is reduced from 78.91 s to 61.82 s; (4) from 16:00 p.m. to 19:00 p.m., average vehicle delay is reduced from 78.86 s to 59.70 s; (5) from19:00 p.m. to 0:00 a.m., average vehicle delay is reduced from 79.0 s to 58.89 s.

Table 6 is a comparison of simulation results before and after optimization. It can be seen that under the condition that the traffic flow does not change during each time period, implementing the design of variable guidance lanes and network coordinated signal control timing, the entire delay of vehicles is significantly reduced. The entire delay of vehicles decreased by 25.06%. It can be seen that network coordinated signal control with variable guidance lanes can improve the service level and operating efficiency of the intersection.

5.3. Results for Each Intersection

Table 7 shows the specific results of the effect of the variable guidance lanes and network signal control.

Figure 4 shows the average vehicle delays of four intersections in one day. The abscissa is the five time periods of one day, and the ordinate is the average vehicle delay at the intersection. In Figure 4, 1 represents the effect of a variable guidance lane before optimization; 2 represents the effect of a variable guidance lane after optimization; 3 represents the effect of network coordinated signal control before optimization; 4 represents the effect of network coordinated signal control after optimization. Figure 4 shows this in detail. Again, the results confirm the effects of variable guidance lanes and network coordinated signal control. One thing that should be noted is that the delays calculated by the model and Synchro have minor differences. Although the difference is minor, we think the causes may be diverse; therefore, it is neither appropriate nor possible to investigate the effect of network coordinated signal control without variable guidance lanes in this case.

Table 7. Results for each intersection.

Time Period	Intersection No.	Vehicle per Delay (s)
		Effect of Variable Guidance Lane			Effects of Network Coordinated Signal Control
		Before Optimization	After Optimization	Delay Reduced	Before Optimization	After Optimization	Delay Reduced
0:00–6:00	1	21.31	17.38	18.44%	19.84	14.29	27.97%
	2	25.63	21.23	17.17%	23.38	16.12	31.05%
	3	25.12	20.04	20.22%	22.41	15.25	31.95%
	4	20.37	16.73	17.87%	18.62	15.68	15.79%
6:00–9:00	1	21.59	19.07	11.67%	19.45	13.1	32.65%
	2	19.11	15.58	18.47%	18.56	14.27	23.11%
	3	24.52	20.23	17.50%	21.03	14.56	30.77%
	4	23.66	19.23	18.72%	20.24	15.79	21.99%
9:00–16:00	1	23.51	18.45	21.52%	21.97	16.34	25.63%
	2	21.12	17.83	15.58%	17.68	14.26	19.34%
	3	20.73	15.14	26.97%	18.72	14.37	23.24%
	4	23.02	19.29	16.20%	20.54	16.85	17.96%
16:00–19:00	1	20.42	17.16	15.96%	20.11	16.27	19.09%
	2	23.92	19.03	20.44%	21.26	15.55	26.86%
	3	18.98	15.59	17.86%	19.35	14.67	24.19%
	4	19.15	15.3	20.10%	18.14	13.21	27.18%
19:00–0:00	1	22.43	19.76	11.90%	20.46	14.52	29.03%
	2	21.05	18.64	11.45%	19.27	14.69	23.77%
	3	25.42	21.27	16.33%	20.98	16.45	21.59%
	4	18.28	16.74	8.42%	18.29	13.23	27.67%
Average				17.14%			25.06%

Table 7. Results for each intersection.

Time Period	Intersection No.	Vehicle per Delay (s)
		Effect of Variable Guidance Lane			Effects of Network Coordinated Signal Control
		Before Optimization	After Optimization	Delay Reduced	Before Optimization	After Optimization	Delay Reduced
0:00–6:00	1	21.31	17.38	18.44%	19.84	14.29	27.97%
	2	25.63	21.23	17.17%	23.38	16.12	31.05%
	3	25.12	20.04	20.22%	22.41	15.25	31.95%
	4	20.37	16.73	17.87%	18.62	15.68	15.79%
6:00–9:00	1	21.59	19.07	11.67%	19.45	13.1	32.65%
	2	19.11	15.58	18.47%	18.56	14.27	23.11%
	3	24.52	20.23	17.50%	21.03	14.56	30.77%
	4	23.66	19.23	18.72%	20.24	15.79	21.99%
9:00–16:00	1	23.51	18.45	21.52%	21.97	16.34	25.63%
	2	21.12	17.83	15.58%	17.68	14.26	19.34%
	3	20.73	15.14	26.97%	18.72	14.37	23.24%
	4	23.02	19.29	16.20%	20.54	16.85	17.96%
16:00–19:00	1	20.42	17.16	15.96%	20.11	16.27	19.09%
	2	23.92	19.03	20.44%	21.26	15.55	26.86%
	3	18.98	15.59	17.86%	19.35	14.67	24.19%
	4	19.15	15.3	20.10%	18.14	13.21	27.18%
19:00–0:00	1	22.43	19.76	11.90%	20.46	14.52	29.03%
	2	21.05	18.64	11.45%	19.27	14.69	23.77%
	3	25.42	21.27	16.33%	20.98	16.45	21.59%
	4	18.28	16.74	8.42%	18.29	13.23	27.67%
Average				17.14%			25.06%

6. Sensitive Analysis

This section aims to analyze the sensitivity of the traffic volume and capacity to the proposed approach.

First, the traffic volume of each intersection is increased from 10% to 15%, 150% of the original traffic, with an interval equaling 5% from 6:00 a.m.–9:00 a.m. The two-step approach calculates the design plans of the variable guidance lanes and the signal control common cycles in terms of different traffic flow increments. The average vehicle delays in terms of different traffic flow increments are obtained by the proposed model.

Figure 5 shows the impact of traffic flow on average vehicle delay and common signal cycle. It can be seen that when the flow is not saturated, the average vehicle delay gradually increases with the increase in traffic flow. However, when the traffic flow is increased to 120%, the vehicle delay gradually increases. At the same time, the average vehicle delay before and after optimization is compared. It is found that the two-step approach for network signal control strategy with variable guidance lanes proposed in this study can effectively reduce the average vehicle delay, especially when the traffic flow is increased by 60% of the original traffic flow. This further illustrates the two-step approach has more significant improvement benefits under saturation and oversaturation conditions.

Figure 5 also reveals the influence of different traffic flows on the optimal common cycle obtained by the two-step model, from which conclusions can be made. First, as the flow increases, the signal control cycle also increases. Second, when the traffic flow is increased by 60% of the original flow, the increase is relatively large. Third, due to the increase in traffic flow, the red time of each phase will also be extended, which further causes delays to increase, so the increase is relatively small or even has a downward trend.

Next, the capacity of each lane is also changed from 200 or 300 to 1800 (pcu/h) with an interval equaling 100. The impact of road capacity on vehicle delay and signal cycle is analyzed from 6:00 a.m.–9:00 a.m. It can be seen from Table 6 that in terms of certain traffic flow, the greater the capacity of the lane, the smaller the delay. However, as traffic capacity increases, design schemes of variable guidance lanes and signal timing schemes will also change, and average vehicle delays will slowly increase (Figure 6). Figure 6 shows the impact of capacity of the variable guidance lane in the north entrance on the common signal cycle at the intersection 3. It can be found that as the lane capacity increases, the signal cycle will increase. However, when the capacity is more than 1300 pcu/h, the vehicle delay will increase slowly. In order to ensure that the average delay of vehicles is minimized in this case, the signal common cycle does not increase dramatically.

7. Conclusions, Limitation and Future Work

Variable guidance lanes are an effective solution to improve the traffic capacity of urban road network, which can optimize the space-time resources distribution of each lane at the intersection. Network signal control is also believed to be an effective approach to deal with traffic congestion and operation efficiency at intersections. Therefore, this study aims to investigate the effect of network signal control strategy with variable guidance lanes.

In this study, a two-step approach is developed, where the first step is an interactive traffic signal optimization model for each single interaction (e.g., lane allocation plans, cycle length) in the network, and the second refers to network signal control (e.g., split, off-sets).

Combing the network coordinated signal control, the proposed approach is different from the previous method of setting variable guidance lanes regarding the following aspects. First, the premise of the model is that the middle lane of each entrance in a road network can be variable guidance lane, only a single entrance at a certain intersection depending on the manager experience. Second, with the objective of minimizing the road network total vehicle delay, the model answers the question of which direction the variable guidance lanes should run. Third, once the optimal the variable guidance lane design scheme of each entrance at the intersection is determined, the network signal control strategy is optimized correspondingly. In particular, the network signal control parameters are determined by the optimization results in the first step (lane driving direction and single-intersection signal cycle).

Using this proposed approach, we successfully extended the problem to combine both time and space, improving the efficient utilization of temporal and spatial resources, which enables treating the traffic demand in different time periods flexibly.

Furthermore, the final result analysis is as follows. First, the total vehicle delay at the road network is significantly reduced, by 25.06%. Second, we analyze the impact of traffic volume and lane capacity on the model. The results show that the average delay and signal cycle calculated by the model are positively correlated with traffic volume. Conversely, the lane capacity is negatively correlated with vehicle average delay, but it is positively correlated with signal control cycle.

Although we investigated and verified the relationship between network signal control and variable guidance lanes, some issues need to be further studied and resolved. This study compared the current vehicle delays with the optimized vehicle delays by the proposed approach. The simulation also was used to verify the approach, and the obtained results support our approach. It is best that obtained results can be compared with existing research methods, but there is no similar existing research. The existing research does not have research methods for studying the relationship between the variable guidance lane and the network signal control, so this problem is our future work. In particular, the variable guidance lane scheme and optimal network signal control strategy are not static, as they depend on the traffic demand and drivers’ driving behavior and travel route choice habits. In addition, it would also be valuable to consider time-dependent traffic demands and various phase sequence.