Sage Journals: Discover world-class research

Abstract

To improve traffic congestion of urban intersections, this article presents a cooperative vehicle intersection control scheme without using any traffic lights, based on model predictive control theory. The assumptions are that all vehicles are fully automated and that a control unit is installed at the intersection to coordinate vehicle movements. Using connected vehicles technology, vehicles approaching the intersection from all directions are globally coordinated by integrating their states all together. The trajectories of vehicles are predicted and adjusted based on collision avoidance under relevant constraints and preferences. The control scheme prevents each pair of conflicting vehicles from approaching conflicting areas at the same time and minimizes the total collision risks of all pairs of conflicting vehicles. The simulation platform was developed to quantifiably evaluate the overall performance of the scheme. Simulation results show that the proposed scheme can significantly improve the mobility, safety, and environmental aspects of the intersection compared with conventional actuated controls. In addition, we also found that better performance can be achieved when the intersection is being operated under oversaturated conditions, and the market penetration rates of equipped vehicles exceed 30%.

Keywords

Intelligent transportation system cooperative vehicle intersection control connected vehicles collision avoidance model predictive control actuated controls

Introduction

Mobility, environmental impacts, and safety are the major concern areas of transportation systems, especially at intersections. The intersection management has become difficult because the number of vehicles is increasing. Statistics show that about 40% of traffic accidents occur at intersections and 21.5% of traffic fatalities are intersection related.¹ In the traditional traffic control paradigm, intersections are regulated by yield-stop traffic lights or signs. The vehicles must stop if the right of ways are not obtained, even no other vehicles are present, which greatly restricts the traffic capacity of intersections and increases inconveniences of frequent stops and idling. In other words, traffic lights are not able to adapt to varying traffic conditions, resulting in heavy traffic congestions, crashes, fuel waste, and exhaust emissions.

The connected vehicles (CV) provide a two-way wireless communication environment, enabling vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications.² Therefore, the intersections can be controlled cooperatively with vehicles and infrastructures. With a CV environment, vehicles could obtain adequate maneuvers from the controller to cross the intersection safely, and thus, traffic operations at intersections could be manipulated without using stop-and-go style traffic lights. Considering ever-increasing transportation demands, an innovative traffic control paradigm for intersection based on CV, which can smooth the traffic flows and improve the safety and efficiency of intersections, is highly expected.

Many previous studies have attempted to solve the safety and efficiency problems of intersections based on CV, but few studies have been found in the literature that investigated the impacts of various traffic conditions and market penetration rates, except for Lee and Park.³ Some studies failed to consider the acceleration or deceleration behavior of vehicle, assuming that the vehicle speed is constant, for example, Yusuke et al.⁴ In addition, some studies even could not guarantee collision avoidance between vehicles.

To deal with these mentioned issues, we present a model predictive control (MPC)-based cooperative control scheme for unsignalized intersections. The main goals of this article are to check the feasibility and the potential benefits of cooperative vehicle intersection control (CVIC) scheme and offer proper suggestions for infrastructure investments. The remainder of this article is organized as follows: section “Related works” briefly reviews related works. Section “Methodology” describes the formulation of a constrained nonlinear optimization problem in the MPC framework, including assumptions and constrains related to the intersection operation, and presents the coordination control strategy. Section “Results and discussions” describes the details about numerical simulation and discusses the simulation results. Finally, section “Conclusion” presents conclusions and recommendations for future work.

Related works

Considering the current publications in the cooperative control area, there have been several intersection-control-related studies. These studies were conducted to examine the potential benefits about traffic safety, mobility, and the environment. This section presents a summary of such research efforts to date.

Dresner and Stone⁵ presented an autonomous intersection management system, consisting of an intersection agent and multiple vehicle agents. The intersection zone was divided into a number of grid cells, and the intersection agent gathered individual vehicles’ driving information, coordinated all the reservation requests of temporal-spatial cell occupancies from vehicle agents, and provided right of ways to ensure a safe crossing. However, this method did not coordinate the vehicles globally, so the system may face a situation where it cannot operate optimally; Lee and Park⁶ proposed a CV-based cooperative control algorithm for effective intersection operations. By minimizing the total trajectories overlaps of vehicle from all conflicting directions, the optimal maneuvers for vehicles were obtained. However, the system simply attempted to avoid the presence of any pair of conflicting vehicles in the intersection at the same time.

Nevertheless, the system did not consider any constraints for crossing collision avoidance, resulting sometimes in unfeasible solution conditions; Y Zheng et al.⁷ developed a distributed cooperative control algorithm without using any other infrastructures, embedding wireless communication devices inside the vehicles. The algorithm minimized the total collision probability of conflicting vehicles approaching the intersection, and hence, safe maneuvers can be obtained. However, the feasibility of system architecture should be examined further before real implementation; SI Guler et al.⁸ proposed an intersection control algorithm to reduce the traffic congestion. The algorithm utilizes the information from CV to improve traffic operations without requiring any additional infrastructures. The driving strategies can be obtained by optimizing the car departure sequences; Kamal et al.⁹ proposed a vehicle intersection coordination scheme (VICS) to improve traffic operations. The VICS coordinates the movements of automated vehicles all together based on avoidance of collision risks. Specifically, the scheme prevents each pair of conflicting vehicles from approaching their crossing collision points at the same time. However, the VICS did not consider the impact of market penetration rates on the scheme.

Despite the contributions made by previous studies, a common limitation is the assumption of a 100% market penetration rate of equipped vehicles, except for Lee and Park.³ In addition, few studies have explicitly examined the impact of different traffic-congested levels on the system. Several studies did not coordinate the vehicles globally, just simply avoided the presence of conflicting vehicles in the intersection at the same time, and hence, the designed system is easy to fall into unfeasible conditions. Moreover, most studies were performed with only a few vehicles, which are insufficient to reflect the real traffic conditions.

Recently, a MPC approach was presented to optimally adjust vehicle speeds for freeway traffic.¹⁰ By maneuvering vehicles, the traffic flow can be smoothed. The information from the CV environment can be efficiently addressed in the MPC framework.^11,12 The dynamics of all vehicles are described using a set of difference equations. With the current vehicle states, we can forecast the future states of vehicle flows. The coordination scheme will track every vehicle and determine optimal control sequences of vehicles by solving previous difference equations.

To explicitly assess the safety impact of the CVIC scheme, this article employs the surrogate safety assessment model (SSAM)¹³ to measure safety. In addition, the Virginia Tech microscopic (VT-micro) model¹⁴ is used to evaluate the energy and environment impacts. Our main contributions can be summarized as follows: (1) present a novel coordination control strategy for intersections removing the traffic lights, (2) perform a series of simulations under varying congested conditions and market penetration rates, and (3) proper suggestions for real implementation are provided.

Methodology

In this article, a typical urban intersection shown in Figure 1 was studied. The approaches to the intersection are clock labeled from 1 to 8, and arrow marked on lanes indicating the allowable driving direction. The vehicles keep to the right side according to the traffic rules in China. To formulate the proposed coordination control scheme, some variables and parameters are defined as follows:

P: total phase number

l: lane identifier

$L_{i}$ : total number of lanes of phase i

$N_{il}$ : total number of vehicles on lane l of phase i

b: width of lane

$v_{d}$ : desired velocity of vehicle

u: acceleration or deceleration rate that depends on magnitude is positive or negative

$x_{i}$ : the remaining distance from the center point of the vehicle i to the intersection stop line

$R_{c}$ : radius of turning path

t: time step counter

$τ$ : duration of unit time step

$θ$ : the heading angle of vehicle

Figure 1.

The typical urban intersection.

The CVIC scheme allows vehicles with conflicting movements to cross the unsignalized intersection at high speeds. The assumptions are that all vehicles are fully identical and automated, and the vehicles can perfectly follow lateral trajectories of preceding vehicles and generate sufficient lateral acceleration to safely navigate the turning curve.

The vector $x = [x_{1}, x_{2}, \dots, x_{N}]$ is defined as the current position of N vehicles on approaches 1 to 8 and vectors v and u denote the velocity and acceleration of the same set of vehicles, where $x, v, u \in R^{N}$ , N is the total number of vehicles. For simplicity, lane changing is not allowed while driving, and only the longitudinal motion of the vehicle is studied. The discrete time state equations describing the longitudinal motion of vehicle i are given in equations (1) and (2).

$x_{i} (t + 1) = x_{i} (t) τ - \frac{1}{2} u_{i} (t) τ^{2}$ (1)

$v_{i} (t + 1) = v_{i} (t) + u_{i} (t) τ$ (2)

Constraints and preferences

Since the vehicles interact with each other under the CV environment while traveling, several constraints and preferences are required to ensure safety. These mainly include the following: (1) the maximum acceleration and deceleration rates, (2) the minimum headway, and (3) the minimum allowable distance.

Maximum acceleration and deceleration rates

In fact, $u_{min}$ and $u_{max}$ are not necessarily the same for all vehicles, but depend on the performance of vehicle model. However, for simplicity, constant magnitudes are considered as the limits for this article. The final form was derived after considering other constrains, where $t_{0}$ represents the initial time.

$u_{i} \geq max (u_{min}, \frac{- v_{i}^{2} (t)}{2 x_{i} (t_{0})}, \frac{v_{min}^{2} - v_{i}^{2} (t)}{2 (x_{i} (t_{0}) - x_{i} (t))})$ (3)

$u_{i} \leq min (u_{max}, \frac{v_{max}^{2} - v_{i}^{2} (t)}{2 (x_{i} (t_{0}) - x_{i} (t))})$ (4)

Minimum headway

The minimum headway defines the minimum distance to the vehicle in front that must be available for the lane changing. The safety distance between two consecutive vehicles is constrained to avoid rear end collisions, and generally interpreted as either a spacing or a headway, and it is believed that the later would be more proper. The trajectory of the vehicle is a feasible function of time, and the trajectories of two consecutive vehicles i and $i + 1$ are denoted as $x_{i} (t)$ and $x_{i + 1} (t)$ , respectively. Note that the vehicle $i + 1$ is further to the intersection than vehicle i, and $h - s$ is denoted by h, the minimum headway constraint is derived in equation (5).

$D (\frac{1}{2} u_{i} (t) - u_{i + 1} (t)) R^{2}) - R (u_{i} (t) h - v_{i} (t) + v_{i + 1} (t)) + D > 0$ (5)

$D = \frac{1}{2} u_{i} (t) h^{2} - v_{i} (t) h - x_{i} (t_{0}) + x_{i + 1} (t_{0})$

$R = \frac{1}{u_{i + 1} (t)} (- v_{i + 1} (t) + \sqrt{v_{i + 1}^{2} (t) + 2 u_{i} (t) x_{i + 1} (t_{0})})$

Minimum allowable distance

To ensure no collision occurs between a pair of vehicles with different crossing approaches, a nonlinear inequality constraint is defined in equation (6). Satisfying this constraint means that the optimal solutions of CVIC scheme are found inside the safe areas. Thus, collision free between vehicles around the intersections can be guaranteed.

$(x_{i} (t) + d_{ϕ_{i} ϕ_{j}})^{2} + (x_{j} (t) + d_{ϕ_{j} ϕ_{i}})^{2} \geq R_{min}^{2}$ (6)

where $d_{ϕ_{i} ϕ_{j}}$ and $d_{ϕ_{j} ϕ_{i}}$ are the distances from the crossing collision point to the ends of lanes $l_{i}$ and $l_{j}$ , respectively. For the case shown in Figure 2, the lane width is b, $d_{ϕ_{i} ϕ_{j}} = b / 2$ , and $d_{ϕ_{j} ϕ_{i}} = 3 b / 2$ . $R_{min}$ represents a constant value that denotes the minimum allowable gap between centers of two conflicting vehicles to avoid a potential collision.

Figure 2.

Example of distance at the intersection.

Derivation of the performance index

The necessary condition for avoiding a collision of any pair of vehicles is to prevent them from approaching conflicting areas at the same time. Based on this idea, a risk indicator $r_{i, j} (t)$ is introduced to quantitatively describe the potential collision risk of conflicting vehicles, and it is computed using equation (7).

$r_{i, j} (t) = e^{- \frac{1}{δ} {(x_{i} (t) + d_{ϕ_{i} ϕ_{j}}))^{2} + (x_{j} (t) + d_{ϕ_{j} ϕ_{i}})}^{2}}$ (7)

where $δ$ is a scaling parameter. It can be easily observed from equation (7) that $r_{i, j} (t)$ is a monotonic decreasing function satisfying $r_{i, j} (t) \in (0, 1)$ . To decrease computational complexity, a threshold value $ε$ was employed. If $r_{i, j} (t) \geq ε$ , it implies that a potential collision will occur, so the vehicle speeds must be adjusted.

The conflicting relationship between phases can be represented by function $g_{i, j} (t)$ : if there is a collision relationship, $g_{i, j} (t) = 1$ , otherwise, $g_{i, j} (t) = 0$ . The collision relationship is defined as occurring if the bounding boxes of vehicles overlapped at some point in time.

Only crossing conflict and rear end conflict are considered. Function $f_{i, j} (t)$ in equation (8) was proposed to describe the potential risks between two conflicting vehicles.

$f_{i, j} (t) = g_{i, j} (t) \times r_{i, j} (t) = {\begin{matrix} e^{- \frac{1}{δ} {(x_{i} (t) + d_{ϕ_{i} ϕ_{j}})^{2} + (x_{j} (t) + d_{ϕ_{j} ϕ_{i}})}^{2}} \\ 0 \end{matrix}$ (8)

This article considers trajectories of vehicles with a constant acceleration between $u_{min}$ and $u_{max}$ . The trajectory of a vehicle can be identified by the tuple $(u, v, x, θ)$ . With the real-time information, future trajectories of all vehicles can be predicted. Then, a new function $F (t)$ describing the total collision risks is defined in equation (9). The article defined a performance index J, which is calculated using equation (10), and the goal is to minimize the performance index J over a finite time horizon $[0, T]$ by determining a sequence of control inputs $u_{1} (t), u_{2} (t), \dots, u_{N} (t)$ subjected to the previous constraints.

Note that the integral interval of equation (9) is defined according to equations (3) and (4), and variables $u_{down}$ and $u_{up}$ are also defined to simplify the derivation process, where $u_{down} = max (u_{min}, \frac{- v_{i}^{2} (t)}{2 x_{i} (t_{0})}, \frac{v_{min}^{2} - v_{i}^{2} (t)}{2 (x_{i} (t_{0}) - x_{i} (t))})$ and $u_{up} = min (u_{max}, \frac{v_{max}^{2} - v_{i}^{2} (t)}{2 (x_{i} (t_{0}) - x_{i} (t))})$ .

$F (t) = \sum_{i = 1}^{P} \sum_{k = 1}^{L_{i}} \sum_{m = 1}^{N_{ik}} \sum_{j = 1}^{P} \sum_{l = 1}^{L_{j}} \sum_{n = 1}^{N_{jl}} \int_{u_{down}}^{u_{up}} \int_{u_{down}}^{u_{up}} g_{m, n} (t) r_{m, n} (t) dmdn$ (9)

$\begin{array}{l} \min_{u (t)} J = \sum_{t = 0}^{T - 1} F (t) + \sum_{t = 0}^{T - 1} \sum_{i = 0}^{N - 1} w_{u} u_{i}^{2} (t) \\ + \sum_{t = 0}^{T - 1} \sum_{i = 0}^{N - 1} w_{v} {(v_{i} (t) - v_{d})}^{2} \end{array}$ (10)

where N is the total number of vehicles, and $v_{d}$ is the desired velocity, which has a significant influence on the traffic capacity of the intersection. $w_{u}$ and $w_{v}$ are the constant weights. It can be seen from equation (10) that there are three terms in performance index J. The first term is related to the total collision risks between vehicles. The second term represents the cost of accelerations, and the last term denotes the cost of deviation from vehicles’ desired velocities. Minimizing the last two terms can ensure steady driving and smooth the vehicle flows.

The performance index J presented in equation (10) is considered a nonlinear constrained optimization problem, and we solved this problem using the modified shuffled frog leaping algorithm (SFLA)¹⁵ and the continuation and generalized minimum residual (C/GMRES) method.¹⁶ The two algorithms try to search for optimal solutions in parallel. Note that the C/GMRES method does not require iterative searches, and the study in Kamal et al.¹⁷ showed that the computational time required to solve an optimization problem is not long.

Coordination control strategy

The coordination scheme takes advantage of the space and time of intersection by preventing conflicting vehicles from entering the intersection at the same time. To this end, the intersection control unit (ICU) was designed to gather vehicular information, estimate potential conflicts, and provide optimal maneuvers to vehicles through wireless communication using the standard communication protocol as defined in wireless access in vehicular environment/dedicated short range communication (DSRC).^2,18 The priority and non-priority approaches are determined based on a comparison of the total number of vehicles. The assumption is that the vehicles on priority approaches need not change their states. Each vehicle broadcasts its driving information, including precise position and instantaneous velocity and acceleration rate to neighboring vehicles and infrastructures.

If the conflicts are expected, the ICU divides all vehicles into a series of conflicting pairs (CPs) based on the vehicles’ states. If the vehicle has no conflicts with others, and it can maintain original speed to cross the intersection. Otherwise, the vehicles’ trajectories are adjusted to avoid the crashes, and the vehicles pass through the intersection with adjusted acceleration/deceleration rates. When the vehicles have crossed the intersection, they will transmit a message to ICU and will not participate in cooperative collision avoidance.

However, the optimization techniques cannot always guarantee the feasibility of optimal solutions. In case that no optimal solutions are obtained or the system fails, the ICU will enter emergency mode, disseminating the slow command to guide vehicles to slow down. The vehicles on priority approaches will pass through the intersection at original speeds, while vehicles on non-priority approaches have to brake hard and wait before the stop line. When no vehicles exist on the priority approaches, vehicles on non-priority approached speed up. Meanwhile, the ICU keeps checking new vehicles approaching the intersection. If new vehicles are present, the ICU will disseminate the stop command, and the vehicles will slow to a stop outside of the intersection zone, waiting for the next command. In addition, a maximum waiting time $t_{max}$ is introduced to avoid a situation in which the vehicles on non-priority approaches cannot obtain the right of ways for a long time. Once the waiting time reaches $t_{max}$ , the ICU will disseminate guidance information and release the traffic flow. Figure 3 illustrates the overall implementation logic of the CVIC scheme. Figure 4 describes the conflict scenarios between vehicles.

Figure 3.

The overall implementation logic of the CVIC scheme: (a) the overall flowchart of the CVIC scheme and (b) emergency mode logic.

Figure 4.

Conflict scenario between the vehicles.

Results and discussions

Experimental setup

An isolated intersection was created by the VISSIM for experimental evaluations. The intersection has four approaches and each approach has two through lanes and a single left-turn lane. Taking into consideration the required computational time, 40 volume scenarios covering the volume to capacity ratios (v/c) ranging from 0.1 to 1.5 were designed. With a 3600-s simulation period, 40 replications were executed for each scenario using different random seeds, and thus, a total of 1600 simulations were conducted.

To compare the performances of the CVIC scheme, the coordinated actuated control system was used with same replication times and simulation period. The Synchro software was used to obtain the traffic signal timing plan.¹⁹ Note that Synchro is a macroscopic and deterministic model for modeling and optimizing cycle times and splits. And we converted the v/s ratios to the corresponding v/c ratios for all scenarios with the optimal timing plans. The evaluation results of actuated controls produced the same measurements as used in the proposed scheme.

To evaluate the sustainability impacts covering mobility, safety, energy, and the environment, the simulation platform was developed, incorporating three distinct programs: (1) the microscopic traffic simulator VISSIM 4.3,²⁰ (2) SSAM software, and (3) optimization methods are implemented through MATLAB. Figure 5 illustrates the overall structure diagram of the simulation platform.

Figure 5.

Structure diagram of the simulation platform.

As Table 1 summarizes, the measures of effectiveness (MOEs) used in this study include three categories: mobility, safety, and sustainability. The mobility measures come directly from the VISSIM program, while the safety and sustainability measures must be evaluated using indirect methods. For the mobility aspects, the total stopped delay time, the total travel time, and the total throughputs were used. In assessing the safety aspects, the time to collision (TTC), the post encroachment time (PET), and the number of conflicts were used as safety surrogate measures. To estimate the benefits of sustainability, the trajectory data of vehicles were analyzed using the VT-micro model, which requires instantaneous velocity and acceleration/deceleration rate. For the purpose of this study, carbon dioxide (CO₂) emissions and fuel consumptions were computed.

Table 1.

Summary of the MOEs.

MOE category	MOE	Unit
Mobility measure	Total stopped delay time	h
	Total travel time	h
	Total throughputs	Vehicles
Safety measure	TTC	s
	PET	s
	Number of conflicts	Times
Sustainability measure	CO₂ emissions	kg
Sustainability measure	Fuel consumption	kg

MOE: measures of effectiveness.

Before implementing the scheme, it was necessary to determine the values of several parameters. For the experimental road network, the length of each link was set to 600m, and the assumption was that all the lanes had the same width, $b = 4 m$ , $R_{min} = 6 m$ . The minimum radius of the turning path $R_{c}$ was set to 30m for the left turn. The driving and control parameters were set as follows: $v_{max} = 22.23 m / s$ , $v_{min} = 0 m / s$ , $u_{max} = 4 m / s^{2}$ , $u_{min} = - 4 m / s^{2}$ , $v_{d} = 16.67 m / s$ , $w_{u} = 10$ , $w_{v} = 0.6$ , and $h = 1 s$ , $t_{max} = 100 s$ . The discrete time step was defined as $τ = 0.05 s$ and the prediction horizon $T = 5 s$ . The parameters for the risk function were set to $δ = 2$ and $ε = 0.005$ . The length and width of the vehicles were set to 4.5 and 1.75 m, respectively.

When all the simulations were completed, the resulting trajectory data for the vehicles were fed into the SSAM software. If both the TTC and PET values of a pair of conflicting vehicles are found to be within threshold values, the SSAM program identifies it as a conflict event. This article selected 1.5 and 5 s for TTC and PET as the corresponding threshold values, respectively, based on previous studies.^21,22

The vehicles are all equipped with wireless communication device inside, and the range of the wireless communication is within a 150-m radius. The IEEE 802.11p model²³ was used to simulate the physical and medium access control layers. Regarding the communication protocols, each vehicle broadcasted driving information at every 100 ms, and the ICU transmitted optimal maneuvers to vehicles at the same time interval as defined in SAE-J2735.²⁴ The dissemination of safety critical information is broadcasted periodically and becoming standardized in the form of cooperative awareness messages²⁵ and basic safety messages.²⁶

Results

Performance comparison and analysis

This section examines the overall performances of scheme under 100% market penetration rates. Compared with the actuated control (AC) system, the proposed scheme significantly improved the mobility, safety, and environmental measures. All the data in the table below are statistically significant at a 5% confidence level.

Mobility analysis

The total stopped delay time was dramatically reduced between 80.6% and 100% depending on the traffic volume, and the total travel time and the total throughputs were also improved to different degrees. However, the AC system sometimes was superior to the CVIC scheme (e.g. the total throughputs in case 5). Taking into consideration that the scheme is designed to smooth traffic flows for a traffic-lightless intersection, such improvements verify the promising benefits of the scheme, as summarized in Table 2.

Table 2.

Mobility improvements.

Case	Measure	AC		CVIC		p-value	Gain (%)
Case	Measure	Mean	SD	Mean	SD	p-value	Gain (%)
1	Total stopped delay time	13.9	1.6	0.50	0.5	0.001	96.4
	Total travel time	37.4	2.2	32.3	0.7	0.002	13.6
	Total throughputs	1360	0.2	1482	0.0	0.001	8.97
2	Total stopped delay time	19.6	0.1	3.8	0.0	0.001	80.6
	Total travel time	46.2	0.2	35.0	0.0	0.000	24.2
	Total throughputs	1186	0.4	1302	1.3	0.018	9.78
3	Total stopped delay time	22.7	0.3	1.5	0.1	0.001	93.4
	Total travel time	60.5	0.6	39.8	0.0	0.000	34.2
	Total throughputs	964	0.8	1105	0.0	0.000	14.6
4	Total stopped delay time	18.4	1.1	1.6	0.2	0.001	91.3
	Total travel time	57.5	0.6	46.3	0.1	0.002	19.5
	Total throughputs	1278	0.9	1380	0.5	0.000	7.98
5	Total stopped delay time	12.2	0.8	0	0.1	0.000	100
	Total travel time	71.3	1.0	57.8	0.0	0.000	18.9
	Total throughputs	912	0.7	874	0.3	0.001	−4.17

Safety analysis

Table 3 shows that the TTC and PET of the scheme were all less than that of the AC system for each volume. Indeed, smaller TTC and PET indicate a more dangerous situation. The CVIC scheme appeared to decrease safety performance; however, the number of conflicts for each volume was significantly reduced. While the CVIC seemed to incur more dangerous situations, the frequency was reduced, resulting in safer conditions. This is likely because the scheme is designed to coordinate the movements of all vehicles to guarantee safety even if crossing the intersection at high speeds.

Table 3.

Safety improvements.

Case	Measure	AC		CVIC		p-value	Gain (%)
Case	Measure	Mean	SD	Mean	SD	p-value	Gain (%)
1	TTC	1.42	2.0	0.83	0.4	0.001	41.5
	PET	3.21	1.8	1.76	0.6	0.000	45.2
	Conflicts	449	1.3	328	0.6	0.012	26.9
2	TTC	1.29	1.0	0.65	0.0	0.000	49.6
	PET	3.06	1.2	1.62	0.0	0.000	47.1
	Conflicts	398	0.5	346	0.1	0.002	13.1
3	TTC	1.28	0.7	0.47	0.1	0.001	63.3
	PET	3.15	0.5	1.44	0.0	0.000	54.2
	Conflicts	224	0.9	153	0.1	0.000	31.7
4	TTC	1.26	0.8	0.53	0.2	0.001	57.9
	PET	3.18	0.4	0.96	0.0	0.000	69.8
	Conflicts	158	1.5	107	0.3	0.000	32.2
5	TTC	1.26	0.2	0.73	0.5	0.001	42.1
	PET	3.08	0.5	1.25	0.1	0.000	59.4
	Conflicts	415	0.3	328	0.0	0.000	20.9

TTC: time to collision; PET: post encroachment time.

Figure 6 illustrates the conflict comparison under two systems: the red and blue filled triangles represent the crossing conflict and rear end conflict, respectively. Note that lane changing conflict is not considered in this study. It can be seen from Figure 6 that the scheme can reduce the number of conflicts, especially the crossing conflict, and ensure a safe crossing.

Figure 6.

Conflict comparison under two systems: (a) conflicts in actuated control system and (b) conflicts in cooperative control system.

Emissions and energy analysis

The results from Table 4 reveal that the scheme is able to effectively improve air quality and provide energy savings. One can expect percentages of reduction ranging from 13.5% to 58.6% for CO₂ emissions and 14.7% to 52.4% for fuel consumptions. Obviously, such benefits would result from smoothness in traffic flows by reducing unnecessary stops and idling. More specifically, the scheme ensured vehicles’ steady driving while crossing the intersection.

Table 4.

Environmental improvements.

Case	Measure	AC		CVIC		p-value	Gain (%)
Case	Measure	Mean	SD	Mean	SD	p-value	Gain (%)
1	CO₂ emissions	885.6	32.5	694.8	56.3	0.001	21.5
1	Fuel consumptions	479.5	18.6	314.8	37.0	0.000	34.3
2	CO₂ emissions	945.4	22.1	615.2	68.3	0.036	35.0
2	Fuel consumptions	529.1	15.9	346.6	67.4	0.018	34.5
3	CO₂ emissions	527.9	8.9	354.0	24.6	0.000	32.9
3	Fuel consumptions	243.2	5.7	150.7	11.8	0.000	38.0
4	CO₂ emissions	850.4	10.0	735.6	19.6	0.000	13.5
4	Fuel consumptions	241.0	6.4	210.2	5.9	0.000	12.7
5	CO₂ emissions	499.0	3.8	355.4	3.2	0.001	28.8
5	Fuel consumptions	353.7	2.0	231.9	1.8	0.000	34.4

CVIC: cooperative vehicle intersection control.

Impact of traffic congestion conditions

Figure 7 shows the impacts of varying traffic congestion conditions on the performances. The CVIC outperformed the AC over all traffic conditions for the total stopped delay time, as shown in Figure 7(a). However, the total travel time showed marginal improvements under uncongested conditions (e.g. the v/c ratio is less than 0.7). Similar results were obtained from the total throughputs. It is pointed out that the v/c ratio less than 1.0 indicates that the intersection has sufficient capacity to handle approaching vehicles. Figure 7(b) illustrates that vehicles can maintain free-flow speeds although they have to stop before the intersection if the right of ways is not obtained under the AC system when a v/c ratio is 0.7 or less. On the contrary, vehicles are manipulated to cross the intersection at optimal speeds without waiting before the stop line in the CVIC. If the free-flow speeds are above the optimal speeds, the total travel time of the AC system is shorter than that of the CVIC. However, the scheme achieved better performances with the rapid increase in traffic volume, and then improvements of the total travel time significantly increased. The total throughputs were similar to the case of the total travel time, but its boundary v/c ratio was 0.8, as shown in Figure 7(c).

Figure 7.

Improvement under varying congested conditions: (a) total stopped delay time, (b) total travel time, (c) total throughputs, (d) conflicts, (e) CO₂ emissions, and (f) fuel consumptions.

Figure 7(d) shows that the proposed scheme can greatly reduce the number of conflicts, especially when the v/c ratio is approximately 0.8–1.1, but the reduction was insignificant under uncongested conditions. Regarding the assessment of safety, addressing the severity of crashes based on their type falls outside the purview of this article. Moreover, the scheme also contributed to improving exhaust emissions and fuel consumption, as illustrated in Figure 7(e) and (f), respectively. One can conclude that the proposed scheme can more efficiently utilize the intersection areas under oversaturated conditions, compared with the conventional AC system, when removing the traffic lights.

Impact of market penetration rates

The full automation of the vehicles will be a long time coming, and thus, it might not be realistic to assume that all the vehicles are fully automated, even in the distant future. Normal vehicles and equipped vehicles will inevitably exist at the same time in road networks. Obviously, the performance of the proposed scheme is affected by the ratios of equipped vehicles. To look into the relationship between the two, the entire market penetration rates were uniformly divided into five levels: 10%, 30%, 50%, 70%, 90%, and 100%. Figure 8 illustrates the impacts of varying market penetration rates.

Figure 8.

Improvement under varying market penetration rates: (a) 10% market penetration rates, (b) 30% market penetration rates, (c) 50% market penetration rates, (d) 70% market penetration rates, (e) 90% market penetration rates, and (f) 100% market penetration rates.

Generally speaking, more improvements could be expected by applying the proposed scheme. With a 100% market penetration rates, at least 30% of the total travel time could be achieved. Regarding the sustainability, CO₂ emissions and fuel consumption showed promising benefits over the entire market penetration rates, even under low penetration rates (e.g. 10%). However, the reduction in the total amount of CO₂ emissions and fuel consumption grew smaller as the market penetration rates increased. This is likely because the vehicle speeds were adjusted to smooth traffic flow. For the safety, the number of conflicts fell at all the market penetration rates, and the system improvements generally showed a rising trend.

Therefore, it can be concluded as follows. First, the system’s benefits would begin to be obtained when the market penetration rates of equipped vehicles exceeded 30%. Second, a 100% market penetration rate does not guarantee the most benefits.

Discussion

Based on the simulation results, we can draw a conclusion that the CVIC scheme is beneficial in terms of reducing traffic congestions, improving road efficiency, and alleviating environmental problems around intersections. Results may seem sufficient, but we believe they are largely due to the assumptions made: (1) all the vehicles are fully automated, (2) a coordination control unit is installed at the intersection, manipulating the movements of all vehicles, and (3) communication performance is perfect without considering any transmission latencies, signal fading, and so on. Future studies should examine the feasibility of relevant assumptions and preferences.

Many researchers have studied the distributed architectures; these systems were not robust enough when the number of vehicles increases beyond the road capacity. However, such architectures are worth further exploration due to the potentials in the development of automation technology. With respect to the wireless communication, perfect communication conditions are nearly impossible to achieve in reality. Hence, it is essential to establish an additional module to explicitly consider imperfect communications. However, this article mainly focused on the design of a coordination control strategy; its objective was not to develop new communication protocols. The protocols on V2V and V2I communications should be validated and determined before deploying the scheme.

For safety reasons, driving backward is not permitted at any time. Lane changing while crossing the intersection was also not considered, but the scheme can be extended to coordinate lane changing from a far distance by integrating more vehicles. This article did not examine the impacts of the parameter values either, which should depend on the performance of the vehicles, control strategies (e.g. a concern for safety or efficiency), and so on. For simplicity, the parameter values were specified in this article, such as the maximum acceleration and deceleration rates. These values should be acceptable based on the previous studies conducted by Dresner and Stone⁵ and Lee and Park.⁶

For the AC system, the greatest contributions to environmental impacts resulted from over acceleration/deceleration and idling. The mentioned actions could be alleviated if there were less need for stopping. This is the reason why cooperative control scheme greatly outperformed the AC system. The number of vehicles left stopped and idling in the AC environment is likely a result of the traffic signals being restricted to the optimized timing plan. The improvements this scheme made are also apparent in the environmental impacts from the reduced emissions.

Conclusion

This article presented a CVIC scheme using MPC and examined the mobility, safety, energy, and environment aspects of the scheme under the CV environment. Based on a simulation-based study at an isolated intersection, automated vehicles were globally coordinated to cross the intersection safely and quickly. The control inputs of vehicles were optimized by minimizing the total collision risks of all pairs of conflicting vehicles. Simulation results have shown that the proposed scheme is effective in smoothing traffic flow compared to conventional actuated controls. Given 100% market penetration rates, the control algorithm significantly improved the performances of the intersection, and 30% market penetration rates is the break-even point. Therefore, the performances would be improved at 30% or higher. In addition, the results also indicated that better performances could be achieved when the intersection is being operated under oversaturated conditions.

However, several challenges still need to be addressed. First, future researches should test the coordination scheme in more complicated and realistic traffic scenarios. Second, the article evaluated the performances just for an isolated intersection, and thus, the scheme must be extended to include more intersections along the road network. Third, more realistic V2V/V2I communication protocols based on DSRC and SAE J273 protocols should be developed and implemented.

Footnotes

Academic Editor: Hai Xiang Lin

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This study was financially supported by the National Natural Science Foundation of China (no. 51575229),the National Distinguished Young Scholar Foundation Candidate Cultivation Program of Jilin University,and the National Key Research and Development Program of China (no. 2017YFB0102600).

References

Fatality analysis reporting system (FARS) . Washington, DC: NHTSA, http://www.nhtsa.gov/FARS

Connected vehicles research, 2011, http://www.its.dot.gov/connected_vehicle/connected_vehicle.htm

Lee

Park

Development and evaluation of a cooperative vehicle intersection control algorithm under the connected vehicles environment. IEEE T Intell Transp 2012; 13: 81–90.

Yusuke

Yusuhisa

Fukuda

et al . Zipping, Weaving: control of Vehicle Group Behavior in Non-signalized Intersection. In: Proceedings of the 2004 IEEE international conference on autonomous agents and multiagent system, New Orleans, LA, 26 April–1 May 2004, vol. 2, pp.530–537. New York: IEEE.

Dresner

Stone

A multiagent approach to autonomous intersection management. J Artif Intell Res 2008; 31: 591–656.

Lee

Park

Sustainability assessments of cooperative vehicle intersection control at an urban corridor. Transport Res C 2013; 32: 193–206.

Zheng

Lisheng

Gao

et al . Development of a distributed cooperative vehicles control algorithm based on V2V communication. Proced Eng 2016; 137: 649–658.

Guler

Menendez

Meier

Using connected vehicle technology to improve the efficiency of intersections. Transport Res C 2014; 46: 121–131.

Kamal

MAS

Imura

Hayakawa

et al . A vehicle-intersection coordination scheme for smooth flows of traffic without using traffic lights. IEEE T Intell Transp 2015; 16: 1136–1147.

10.

Hegyi

De Schutter

Hellendoorn

Optimal coordination of variable speed limits to suppress shock waves. IEEE T Intell Transp 2005; 6: 102–112.

11.

Baskar

De Schutter

Hellendoorn

Traffic management for automated highway systems using model-based predictive control. IEEE T Intell Transp 2012; 13: 838–847.

12.

Zegeye

De Schutter

Hellendoorn

et al . A predictive traffic controller for sustainable mobility using parameterized control policies. IEEE T Intell Transp 2013; 13: 1420–1429.

13.

Gettman

Head

Surrogate measures of safety from traffic simulation models. Transp Res Record 2003; 1840: 104–115.

14.

Rakha

Ahn

Integration modeling framework for estimating mobile source emissions. J Transp Eng 2004; 130: 183–193.

15.

Eusuff

Lansey

Pasha

Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization. Eng Optimiz 2006; 38:129–154.

16.

Ohtsuka

A continuation/GMRES method for fast computation of nonlinear receding horizon control. Automatica 2004; 40: 563–574.

17.

Kamal

MAS

Mukai

Murata

et al . Model predictive control of vehicles on urban roads for improved fuel economy. IEEE T Contr Syst T 2013; 21: 831–881.

18.

Balke

Songchitruksa

Zeng

. Potential connected vehicle applications to enhance mobility, safety environmental security. College Station, TX, http://texashistory.unt.edu/ark:/67531/metapth281728/.

19.

Husch

Albeck

Trafficware SYNCHRO 6 user guide. Sugar Land, TX: Trafficware, 2004.

20.

VISSIM 4.30 user manual. Karlsruhe: PTV, 2007.

21.

Hyden

The development of a method for traffic safety evaluation: the Swedish conflicts technique. Lund: Department of Traffic Planning and Engineering, Lund University, 1987.

22.

Sayed

Brown

Navis

Simulation of traffic conflicts at unsignalized intersections with TSC-Sim. Accident Anal Prev 1994; 26: 593–607.

23.

Eckhoff

Sommer

Dressler

. On the necessity of accurate IEEE 802.11p models for IVC protocol simulation. In: Proceedings of the 75th IEEE VTC-Spring, Yokohama, Japan, 6–9 May 2012, pp.1–5. New York: IEEE.

24.

SAE J2735:2009. Dedicated short range communications (DSRC) message set dictionary.

25.

Intelligent transport systems (ITS); Vehicular communications; basic set of applications; part 2: specification of cooperative awareness basic service (ETSI, TS 102 637–2 V1.1.1), 2010, http://www.etsi.org/deliver/etsi_en/302600_302699/30263702/01.03.02_60/en_30263702v010302p.pdf

26.

SAE J2945.1:2011. DSRC message communication minimum performance requirements: basic safety message for vehicle safety applications.

Research on cooperative vehicle intersection control scheme without using traffic lights under the connected vehicles environment

Abstract

Keywords

Introduction

Related works

Methodology

Constraints and preferences

Maximum acceleration and deceleration rates

Minimum headway

Minimum allowable distance

Derivation of the performance index

Coordination control strategy

Results and discussions

Experimental setup

Results

Performance comparison and analysis

Mobility analysis

Safety analysis

Emissions and energy analysis

Impact of traffic congestion conditions

Impact of market penetration rates

Discussion

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References