Optimization of Autonomous Vehicle Safe Passage at Intersections Based on Crossing Risk Degree

Abstract

In the context of autonomous driving, ensuring safe passage at intersections is of significant importance. An effective method is necessary to optimize the passage rights of autonomous vehicles at intersections to enhance traffic safety and operational efficiency. This paper proposes an analytical model for assigning the right-of-way to autonomous vehicles approaching intersections from different directions. Assuming that fully autonomous vehicles equipped with advanced Vehicle-to-Everything (V2X) communication and real-time data processing can utilize gaps to proceed at unsignalized intersections in the future, the Crossing Risk Degree (CRD) indicator is introduced for safety assessment. A higher CRD value indicates a higher crossing risk. CRD is defined as the product of the kinetic energy loss from collisions between vehicles in the priority and conflicting fleets, and the probability of conflict between these two fleets. By comparing CRD values, the passage priority of vehicles at intersection entrances can be determined, ensuring efficient passage and reduced conflict risks. SUMO microsimulation modeling is employed to compare the proposed traffic optimization method with fixed signal control strategies. The simulation results indicate that under a traffic demand of 1200 vehicles per hour, the proposed method reduces the average delay per entry approach by approximately 20 s and decreases fuel consumption by about 50% compared to fixed-time signal control strategies. In addition, carbon emissions are significantly reduced. The findings provide critical insights for developing intersection safety management policies, including the establishment of CRD-based priority systems and real-time traffic monitoring frameworks to enhance urban traffic safety, symmetry, and efficiency.

1. Introduction

Autonomous driving refers to the technology that enables vehicles to operate independently without human intervention [1]. This technology relies on onboard sensors, computer vision systems, artificial intelligence, and machine learning algorithms, allowing vehicles to perceive their surroundings, recognize road signs and other vehicles, plan optimal routes, and execute driving maneuvers safely [2]. Numerous studies [3,4,5] have comprehensively demonstrated that the application of autonomous driving technology can enhance driving safety, reduce traffic accidents, improve traffic efficiency, conserve energy, and mitigate environmental pollution.

According to the Society of Automotive Engineers (SAE) in the United States, autonomous driving technology is categorized into levels 0–5 based on the degree of driver involvement: no automation, driver assistance, partial automation, conditional automation, high automation, and full automation [6]. The classification of autonomous driving levels in China aligns closely with the SAE levels [7], ranging from emergency assistance to fully autonomous driving. With continuous technological advancements, autonomous driving technology is evolving from driver assistance towards high automation and full automation, prompting the need for innovative traffic planning, control, and management strategies [8].

Scientific traffic planning is expected to optimize communication and cooperation between autonomous vehicles, facilitating the more efficient allocation of road resources, alleviating traffic congestion, enhancing road traffic efficiency, and improving traffic safety performance. Intersections, essential components of urban road systems, play a crucial role in road network connectivity but are also prone to traffic accidents, particularly at unsignalized intersections [9]. Existing research on intersection crossing strategies for autonomous vehicles primarily aims to enhance vehicle passage efficiency [10], improve intersection capacity [11], and prevent vehicle collisions [12]. Previous studies have demonstrated that vehicles at unsignalized intersections can utilize gaps in traffic to enhance passage efficiency while maintaining symmetry in coordinated vehicle movements.

To ensure the efficient passage of vehicles through intersections while reducing the risk of conflicts, this paper introduces Crossing Risk Degree (CRD), which integrates conflict probability and collision kinetic energy considerations. By comparing CRD values, the passage priority of autonomous vehicles at intersection entrances can be identified, potentially enhancing traffic safety and operational efficiency in autonomous driving environments. These insights underscore the need for policy interventions aimed at incorporating CRD-based frameworks into urban traffic management systems, thus promoting safer and more efficient road networks.

The remainder of this paper is organized as follows: Section 2 reviews the relevant research on intersection crossing strategies for autonomous vehicles. Section 3 introduces the proposed CRD indicator. Section 4 employs the SUMO microsimulation modeling package to validate the proposed model. Finally, the research findings are summarized in Section 5.

2. Literature Review

This section provides a comprehensive review of the research on traffic operations, control, and safety strategies for autonomous vehicles at intersections in both fully autonomous driving environments and mixed environments with autonomous and human-driven vehicles.

2.1. Fully Autonomous Driving Environments

In fully autonomous driving environments, research on unsignalized intersections has predominantly focused on leveraging Connected and Autonomous Vehicle (CAV) technologies to navigate intersections safely and efficiently through vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications. Chen and Englund [13] conducted an early comprehensive review of vehicle passage methods under unsignalized control, analyzing mechanisms to prevent traffic conflicts. Following this, Chen and Liu [14] proposed a gap-based speed control algorithm for self-driving vehicles aimed at minimizing fuel consumption, travel time, and vehicle conflicts. Zhou, Li, and Ma [15] utilized heuristic algorithms to optimize vehicle trajectories in a fully autonomous driving environment and later proposed an integrated optimization framework to enhance various traffic performance metrics. Building upon the research by Zhou, Li, and Ma [15], Ma et al. [16] proposed a comprehensive optimization framework that simultaneously considers travel time, fuel consumption, and safety risks to determine the optimal vehicle trajectory. He et al. [17] designed an unsignalized intersection with all-direction turning lanes (ADTLs) and introduced a conflict-avoidance-based method for coordinating vehicles from different approach lanes. Yu et al. [18] introduced a mixed-integer linear programming (MILP) model to optimize both vehicle trajectories and signal timings. In the same year, Feng, Yu, and Liu [19] proposed an integrated control framework to manage vehicle trajectories and traffic signals simultaneously, which has shown significant improvements in intersection operational efficiency. Guo, Li, and Ban [20] reviewed various studies on estimating intersection traffic flow conditions and optimizing signal timing using CAVs. They summarized six CAV-based traffic control methods and recommended selecting appropriate signal control methods based on different traffic flow conditions. Lu and Kim [21] developed an intersection traffic coordination algorithm based on discrete-time occupancy trajectories to ensure safe and efficient vehicle passage through intersections. Around the same time, Miculescu and Karaman [22] applied polling systems theory to schedule vehicles at intersections, a theory traditionally used to study queueing systems where a single server attends to multiple queues in a specific order. Choi, Rubenecia, and Choi [23] implemented a reservation-based scheduling method to coordinate vehicle passage at a single intersection, successfully achieving their objectives. Yu et al. [24] further advanced the field by proposing another mixed-integer linear programming model to optimize the entire road network, minimizing total delays. Wang, Cai, and Lu [25] introduced a collaborative autonomous traffic organization method for CAVs in a multi-intersection road network. Their method includes an autonomous crossing strategy for signal-free intersections, an improved trajectory optimization method for road segments, and a composite strategy for route planning within the road network. Additionally, Jiang et al. [26] proposed a bi-level control model based on the stochastic nature of vehicle arrivals, which also demonstrated significant improvements in intersection efficiency. Finally, Liu et al. [27] proposed a cooperative motion optimization strategy for autonomous vehicles at signalized intersections, utilizing a risk degree metric to assess conflict severity and optimize vehicle trajectories. Their approach allows AVs to select any exit lane to maximize spatial resource utilization and employs a linear control mechanism to adjust acceleration and speed based on post-encroachment time (PET) and conflict point occupancy time (CPOT). This method enhances intersection efficiency by dynamically managing AV movements and avoiding collisions through objective risk assessments, offering a complementary perspective to our CRD-based approach for unsignalized intersections [27].

2.2. Mixed Driving Environments

Intersection control in mixed traffic environments presents heightened complexity due to the inherent unpredictability of human driving behaviors. Conversely, research conducted in fully autonomous driving settings offers a more straightforward framework and generates abundant findings. Consequently, scholars have extended existing research to devise intersection passage strategies tailored for environments featuring a mix of autonomous and human-driven vehicles. These strategies can be broadly categorized into four domains: traffic signal control, vehicle trajectory planning, coordinated control of vehicle trajectories and traffic signals, and research focusing on dedicated CAV facilities.

In the realm of traffic signal control research, various studies have concentrated on optimizing vehicle passage sequences through diverse coordination methodologies. For example, Cabri et al. [28] developed an intersection management system based on an auction mechanism, where vehicles bid for the right-of-way to establish their priority. Liang, Guler, and Gayah [29] proposed a method that optimizes vehicle passage sequences by considering factors such as proximity to the intersection, distance, and speed, thereby enhancing traffic flow efficiency. These studies, leveraging innovative algorithms and models, effectively enhance traffic flow and mitigate vehicle delays. To optimize signal phase design at individual intersections, Feng, Zheng, and Liu [30] introduced a real-time, detector-free adaptive signal control algorithm suitable for environments with low connected vehicle (CV) penetration rates. This algorithm integrates a delay estimation model with an adaptive control algorithm to generate optimal signal timing plans, thereby minimizing vehicle delays. Islam, Hajbabaie, and Aziz [31] successfully optimized signal timings at intersections in mixed traffic environments using a distributed optimization and coordination algorithm in real-time. Furthermore, scholars such as Song and Fan [32] and Zhang et al. [33] employed deep reinforcement learning methods to control traffic signals at single intersections in mixed traffic environments. These studies leverage advanced algorithms and techniques to effectively improve the efficiency and adaptability of traffic signal control. Simultaneously, to further coordinate intersection signal control for road segments and networks, Wang et al. [34] proposed an adaptive traffic signal control method at the intersection level and a dynamic signal cascading control method at the road segment level. Additionally, Moradi et al. [35] developed a hierarchical control method with a three-layer structure to manage and estimate queue lengths at intersections and network load. These approaches significantly enhance the coordination of traffic signal control and the overall management of traffic flow.

In the domain of vehicle trajectory planning at intersections within mixed traffic environments, both Ma, Yu, and Yang [36] and Jiang et al. [37] considered lane-changing and car-following safety, establishing bi-level control models. These studies optimized vehicle paths and speeds, thereby enhancing intersection efficiency and safety, and demonstrated the potential for effective vehicle flow management and coordination in complex traffic scenarios. Yao and Li [38] proposed a decentralized control model aimed at identifying optimal vehicle trajectories that simultaneously minimize travel time, fuel consumption, and safety risks. Yu and Long [39] introduced a method to minimize the fuel consumption of individual Connected and Autonomous Vehicles (CAVs) in each cycle by controlling their driving trajectories and predicting the trajectories of manually driven vehicles. Conversely, Hajyan and Nikoofard [40] proposed a fuzzy logic controller for unsignalized intersections in mixed traffic environments, ensuring intersection safety by adjusting the speed of autonomous vehicles. Additionally, Chen et al. [41] effectively coordinated vehicle passage at intersections in mixed traffic environments by scheduling Connected and Autonomous Vehicles (CAVs) to control human-driven vehicles (HVs).

As research advances, an increasing number of scholars are integrating vehicle trajectories with traffic signals for collaborative control, substantiating the significant efficacy of joint optimization in enhancing intersection performance. For instance, Tajalli and Hajbabaie [42] formulated the joint optimization of signals and trajectory control as a mixed-integer nonlinear problem, while Guo and Ma [43] employed deep reinforcement learning to tackle signal optimization and simultaneously enhance trajectory control for Connected and Automated Vehicles (CAVs). These studies transcend mere signal optimization, integrating vehicle trajectories with signal control to achieve more efficient traffic flow. Certainly, while joint optimization strategies demonstrate remarkable efficiency improvements, their safety implications are also under scrutiny. Ghoul and Sayed [44] focus primarily on vehicular collision rates at intersections, whereas Niroumand et al. [45] place greater emphasis on the impact of autonomous driving behaviors on intersection performance and safety. It is imperative to note that while striving for traffic efficiency, ensuring the safety of the traffic system remains paramount, thus underscoring the significance of these studies in integrating considerations of both efficiency and safety.

Recent studies have proposed that enhanced traffic control and optimization can be achieved through the implementation of dedicated facilities for Connected and Automated Vehicles (CAVs), such as CAV-exclusive phases and lanes. Rey and Levin [46] introduced a blue signal phase exclusively permitting autonomous vehicle passage, aiming to alleviate traffic congestion in mixed traffic environments, and integrated this phase with traditional green phases to formulate multi-intersection control strategies. Furthermore, Niroumand et al. [47] introduced a white phase to regulate the trajectory of CAV and human-driven vehicle (HV) fleets passing through intersections, thereby optimizing signal phases. Additionally, Jiang and Shang [48] considered the impacts of CAV penetration rate and changes in traffic demand on lane utilization, proposing a dynamic allocation method for CAV-exclusive lanes, integrating signal optimization and trajectory control. Dai et al. [49] successfully reduced vehicle travel time through the joint optimization of signal control, lane configuration, and vehicle trajectories in mixed traffic environments. Conversely, Chen et al. [50] effectively alleviated congestion in conventional lanes by permitting autonomous vehicles to utilize Bus Rapid Transit (BRT) exclusive lanes.

In summary, the current research on intersection passage strategies for autonomous vehicles underscores the essential role of signal control in coordinating different vehicle types in mixed traffic environments. While intelligent systems can manage vehicles through signal-free intersections in fully autonomous environments, complex vehicle interactions and increased communication interference pose safety concerns at unsignalized intersections. Most research focuses on enhancing passage efficiency, intersection capacity, and collision prevention but lacks methods to reduce interaction risks. This study proposes a method assuming that vehicles can use gaps to navigate intersections in a fully autonomous environment, determining vehicle passage sequences at unsignalized intersections using the CRD indicator introduced here to reduce conflict risks and enhance traffic efficiency.

3. Methodology

This section details the approaches used to validate the proposed optimization method for autonomous vehicle passage at unsignalized intersections. To ensure clarity, all the notations used in this section are firstly summarized in

Table 1. Notations.

$H_{t0}$	The maximum allowable headway between any two vehicles within a traffic flow to be considered as part of a single platoon.
$m_1 \& m_2$	The weights of Vehicle 1 and Vehicle 2 before collision.
$m_3$	The combined weight of the two vehicles after collision.
${\overrightarrow{v}}_1 \& {\overrightarrow{v}}_2$	The velocity of Vehicle 1 and Vehicle 2 before collision.
$\theta$	The angle of collision between two vehicles.
$v_1 \& v_2$	The speeds of Vehicle 1 and Vehicle 2 before collision.
${\overrightarrow{v}}_3$	The combined velocity of the two vehicles after collision.
$v_3$	The combined speed of the two vehicles after collision.
$∆E$	The energy loss in a collision represents the difference between the pre-collision kinetic energy and the post-collision kinetic energy of the system.
$t_1 \& t_2$	The time for Vehicle 1 and Vehicle 2 to travel from the stop line to the conflict point.
$∆t$	The time interval during which two vehicles narrowly avoid a collision is referred to as the critical acceptable gap.
$p$	Lead vehicle conflict probability between priority vehicle platoon and conflict vehicle platoon.
$P_n$	The probability of a conflict occurring between a conflict vehicle platoon consisting of n vehicles and a priority vehicle platoon.
CRD	Crossing Risk Degree indicator.

.

This research focuses on autonomous vehicles approaching unsignalized intersections. Among all approaches to the intersection and entrance lanes, the lane with the vehicle closest to the stop line is defined as the priority direction, while all remaining lanes are collectively referred to as the conflict direction. This research employs the concept of headway to define a vehicle platoon; a platoon is considered when the headway between any two vehicles in traffic flow does not exceed a predetermined threshold, denoted as $H_{t0}$. Thus, a platoon of vehicles with headway not exceeding $H_{t0}$, starting from the lead vehicle in the priority lane, is designated a priority platoon. Conversely, a platoon of vehicles with headway not exceeding $H_{t0}$, starting from the lead vehicle in the conflict direction, is defined as a conflict platoon. Vehicles in the conflict platoon can utilize gaps within the priority platoon to proceed through the intersection.

In the event of a collision between two vehicles, severity is primarily influenced by the type of collision. Notably, the collision angle plays a significant role in determining the extent of the damage and injury severity. Assuming a collision between two vehicles with masses $m_1$ and $m_2$, the respective velocities of the vehicles before the collision are ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$, and the angle of collision between them is θ. This kind of collision process is considered to be inelastic. After the collision, the combined weight of the two vehicles is $m_3$, and the speed is ${\overrightarrow{v}}_3^{\prime }$. The energy loss in a collision is defined as the difference between the pre-collision kinetic energy and the post-collision kinetic energy of the system. The inelastic collision process is depicted in Figure 1.

By applying the law of conservation of momentum, Equation (1) is derived. Subsequently, Equation (2) can be used to determine the combined speed of the two vehicles post-collision.

$$m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2=(m_1+m_2){\overrightarrow{v}}_3$$

(1)

$$v_3=\sqrt{{\displaystyle \frac{m_1^2{v}_1^2+m_2^2{v}_2^2+2m_1{m}_2{v}_1{v}_2\cos \theta }{{(m_1+m_2)}^2}}}$$

(2)

Furthermore, energy loss $∆E$ can be computed by the law of conservation of kinetic energy:

$$∆E={\displaystyle \frac{1}{2}}{m}_1{v}_1^2+{\displaystyle \frac{1}{2}}{m}_2{v}_2^2-{\displaystyle \frac{1}{2}}\left(m_1+m_2\right)v_3^2$$

(3)

By substituting Equation (2) into Equation (3), the relationship between energy loss and collision angle can be determined as follows:

$$∆E={\displaystyle \frac{m_1{m}_2\left(v_1^2+v_2^2-2v_1{v}_2\cos \theta \right)}{2(m_1+m_2)}}$$

(4)

Please note that the vehicle collision angle $\theta$ lies within the range $[0,\pi ]$. According to Equation (4), it can be concluded that a larger collision angle corresponds to greater energy loss, indicating a higher severity of the accident.

Apart from the energy loss resulting from collisions between two vehicles, the conflict probability between different vehicle platoons is also a crucial metric for assessing crossing risks. This research utilizes the distribution of headways to calculate the probability of conflicts occurring between platoons from different entrance lanes at an intersection. The distribution of headways within a platoon represents the variation in the time required for vehicles within the platoon to pass through the stop line, reflecting the spacing between adjacent vehicles in the platoon. As illustrated in Figure 2, assume that Vehicle 1 is the lead vehicle of the priority platoon and Vehicle 2 is the lead vehicle of a conflict platoon. The time for Vehicle 1 to travel from the stop line to the conflict point is defined as $t_1$, and the time for Vehicle 2 to travel from the stop line to the conflict point is defined as $t_2$. We are assuming a fully autonomous driving environment where real-time intersection data can be received and processed by a cloud control center [51] and use V2V and V2I technologies dynamically adjust vehicle movements and aggregate them into platoons. Based on the actual traffic conditions, the cloud control center can then select appropriate distribution functions to fit the headway distribution patterns of vehicle platoons from different entrance lanes.

The time interval during which two vehicles narrowly avoid a collision is referred to as the critical acceptable gap, defined as $∆t$. Thus, the condition for Vehicles 1 and Vehicles 2 to avoid collision is shown in Equation (5).

$$t_1+∆t\ge t_2$$

(5)

Assuming that the probability density function (pdf) of the headway time distribution for the priority vehicle platoon is represented by $f_1\left(t\right)$, and the pdf of the headway time distribution for the conflicting vehicle platoon is represented by $f_2\left(t\right)$, then the probability of Vehicles 1 and Vehicle 2 colliding can be determined as follows:

$$p={\int }_0^{t_1+∆t}{f}_1\left(t\right)dt\ast {\int }_0^{+\infty }{f}_2\left(t\right)dt$$

(6)

From Equation (6), the probability of an individual vehicle from the priority platoon colliding with an individual vehicle from the conflict platoon at an intersection can be determined, denoted as $p$. Therefore, if the conflict platoon consists of $n$ vehicles, the probability of it conflicting with the priority platoon is defined as $P_n$.

$$P_n=p_1+\left(1-p_1\right)p_2+\left(1-p_1\right)\left(1-p_2\right)p_3+\cdots +\left(1-p_1\right)\left(1-p_2\right)\cdots \left(1-p_{n-1}\right)p_n$$

(7)

To describe the risk level of a conflicting platoon passing through an intersection, this paper introduces the Crossing Risk Degree (CRD) indicator. The CRD is defined as the product of the energy loss resulting from a collision between vehicles in the priority platoon and vehicles in the conflicting platoon and the probability of such a conflict occurring. Therefore, CRD can be determined based on Equations (4) and (7), which is shown in Equation (8):

$$CRD=∆E\ast P_n$$

(8)

While our proposed Crossing Risk Degree (CRD) indicator shares similarities with the risk degree metric introduced by Liu et al. [27], which uses PET and CPOT to assess conflict severity at signalized intersections, our approach is tailored for unsignalized intersections in a fully autonomous environment. Unlike Liu et al. [27], who focus on the linear control of AV acceleration and speed, our CRD integrates kinetic energy loss from potential collisions and conflict probability to prioritize vehicle passage, ensuring both safety and efficiency without reliance on signal control. The CRD indicator can be employed to determine the sequence in which vehicles proceed through an unsignalized intersection by utilizing gaps in an autonomous driving environment. By calculating the CRD values of various conflicting platoons, the risk level associated with releasing each platoon is quantified. A higher CRD value indicates a greater risk for the conflicting platoon when crossing the intersection, while a lower CRD value suggests a safer passage. To balance intersection efficiency and safety, the CRD value should not exceed a specified upper limit, denoted as CRD₀. Conflicting platoons with CRD values not exceeding CRD₀ can utilize gaps in the priority platoon to proceed through the intersection. The vehicles in the conflicting platoons should be released in order based on the estimated CRD values, with the platoon with the smallest CRD value given priority to pass, followed by the others in sequence. By assessing the CRD values of different conflicting platoons and determining their corresponding passage priorities, a safer and more reliable theoretical foundation is established for developing vehicle passage strategies at intersections in autonomous driving environments.

In summary, to determine the vehicle passage sequence at unsignalized intersections in a fully autonomous driving environment based on the crossing risk indicator, the priority platoon entering the intersection should be identified first. Subsequently, the passage priority of conflict platoons should be determined in ascending order of their CRD values, with conflict platoons exceeding the upper limit value, CRD₀, being prohibited from passing. By utilizing acceptable gaps for vehicle passage, this method can enhance intersection safety and improve traffic efficiency. The flowchart of the proposed optimization method for the safe passage of autonomous vehicles at unsignalized intersections is shown in Figure 3.

To validate the feasibility and effectiveness of the proposed optimization method, the next section will conduct simulation experiments. By comparing the vehicle delays and emissions under the CRD-based unsignalized control scheme with those under the traditional fixed signal control scheme, this study aims to provide quantitative data. These results will demonstrate the advantages of the optimization method for improving traffic efficiency and reducing environmental impact, thereby highlighting its potential for practical application.

4. Simulation Modeling

This section begins by detailing the testbed setup utilizing SUMO microsimulation software, version 1.22. Subsequently, it presents the simulation results, providing a comparative analysis between fixed signal control and the proposed optimization method. Finally, it discusses the findings, highlighting their implications for real-world applications.

4.1. Testbed

This study utilizes the urban traffic microsimulation software SUMO to model a four-leg intersection [52] and employs Python 3.12 programming to implement the proposed intersection passage method (please refer to the Supplementary Material file for the programming code), achieving real-time vehicle control via the TraCI interface. Considering that unsignalized intersections typically experience lower traffic volumes and that right-turning vehicles have minimal impact on intersection operations, we configured each approach with one dedicated left-turn lane and one through lane to accommodate for low to moderate traffic flows, as illustrated in Figure 4. All vehicles in the simulation are CAVs, and the CACC (Cooperative Adaptive Cruise Control) model is used in SUMO to simulate vehicle-following behavior. Unlike traditional car-following models, CACC incorporates vehicle-to-vehicle communication, allowing vehicles to cooperate with each other, which makes the calculation of safe speeds and inter-vehicle distances more precise and better reflects the interaction behaviors of CAVs [53].

Fixed signal control is a widely adopted method at intersections, renowned for its simplicity, low cost, and high predictability. However, due to its lack of flexibility, the control method proposed in this paper may offer greater benefits in a fully autonomous driving environment. To validate this hypothesis, this section introduces two simulation experiments: the first (Experiment 1) simulates traffic flow at an intersection with fixed signal control, while the second (Experiment 2) simulates traffic flow at an unsignalized intersection based on a crossing risk indicator. Assuming a cross-shaped intersection, the fixed signal control scheme consists of four phases, effectively reducing vehicle conflicts within the intersection. Signal timing is typically designed based on historical traffic flow data and may not adapt to real-time changes in traffic volume. Given that the Webster method is a standard approach for optimizing signal timing at urban intersections to minimize delay [54], this study adopts a four-phase fixed-time signal control scheme for Experiment 1 using the Webster method, in combination with traffic flow information obtained from the simulation. The specific parameters are as follows: Phases 1 and 3 correspond to north–south and east–west straight-through movements, with each phase having a green light duration of 25 s; Phases 2 and 4 correspond to north–south and east–west left-turn movements, with each phase having a green light duration of 15 s. The total signal cycle length is 92 s.

In Experiment 2 without signal control, vehicle passage rules were formulated based on the optimization method proposed in this paper. Specifically, vehicles are allowed to proceed based on the magnitude of their CRD values. Given that unsignalized control is more suitable for intersections with lower traffic volumes, the traffic parameters for both simulation experiments were set to 1200 vehicles per hour, with vehicle arrivals following a random normal distribution. The CACC model was selected to simulate vehicle-following behavior, as it better suits the autonomous driving environment. The simulation time step was set to 1 s, and the total simulation duration was 1800 s. Vehicle characteristics (e.g., length, acceleration) and road parameters (e.g., lane widths) use SUMO’s default values, which are calibrated to reflect typical vehicle dynamics and urban road geometries [52].

Table 2. Parameters for simulation modeling.

Modeling Parameter	Parameter Description (Unit)	Parameter Value
$l$	$\mathrm{Vehicle} \mathrm{length} (\mathrm{m}$)	5
$minGap$	$\mathrm{Minimum} \mathrm{headway} (\mathrm{m}$)	2.5
$maxspeed$	$\mathrm{Maximum} \mathrm{speed} (\mathrm{m}·{\mathrm{s}}^{-1}$)	13.89
$accel$	$\mathrm{Acceleration} \mathrm{rate} (\mathrm{m}·{\mathrm{s}}^{-2}$)	2
$decel$	$\mathrm{Deceleration} \mathrm{rate} (\mathrm{m}·{\mathrm{s}}^{-2}$)	2
$emergencyDecel$	$\mathrm{Emergency} \mathrm{deceleration} \mathrm{rate} (\mathrm{m}·{\mathrm{s}}^{-2}$)	4
$tau$	$\mathrm{Simulation} \mathrm{step} (\mathrm{s}$)	1
$C$	$\mathrm{Cycle} \mathrm{length} (\mathrm{s}$)	92
$t_{NL},t_{SL},t_{EL},t_{WL}$	$\mathrm{Through} \mathrm{phase} \mathrm{green} \mathrm{signal} (\mathrm{s}$)	25
$t_{NT},t_{ST},t_{ET},t_{WT}$	$\mathrm{Left-turn} \mathrm{phase} \mathrm{green} \mathrm{signal} (\mathrm{s}$)	15
$vehicles per hour$	$\mathrm{Traffic} \mathrm{volume} \mathrm{per} \mathrm{hour} (\mathrm{v}\mathrm{e}\mathrm{h}/\mathrm{h}$)	1200
$end$	$\mathrm{Simulation} \mathrm{duration} (\mathrm{s}$)	1800

summarizes the main parameters used in the simulation experiments.

To comprehensively evaluate the effectiveness of the proposed optimization method, vehicle trajectory data were collected during the simulation from 50 m upstream to 50 m downstream of the intersection. This section uses average vehicle delay, average fuel consumption, average carbon dioxide emissions, and average carbon monoxide emissions as evaluation metrics. The vehicle delay refers to the difference between the time required for a vehicle to pass through the intersection at free-flow speed and the actual travel time, which is used to measure traffic smoothness and vehicle throughput efficiency. Indicators such as fuel consumption and emissions reflect the environmental impact of traffic flow. The indicators selected in this section effectively assess the improvement effects of the optimization method in enhancing traffic flow efficiency, reducing energy consumption, and minimizing environmental impact. The fuel consumption and emission outputs in SUMO are calculated using built-in models, particularly the HBEFA-based (Handbook Emission Factors for Road Transport) emission model, which estimates fuel usage and various pollutants (e.g., CO, NOx) based on vehicle speed, acceleration, and type. After completing the simulation, the values of these metrics were recorded in a spreadsheet for subsequent data visualization, analysis, and comparison.

To illustrate the implementation of the CRD-based control algorithm and its integration with SUMO via the TraCI interface, we provide the pseudocode in Algorithm 1: CRD-Based Intersection Control for Autonomous Vehicles. The algorithm dynamically retrieves real-time vehicle data from SUMO (such as position, speed, and vehicle mass), forms priority and conflict queues based on headway thresholds, and calculates CRD values by combining collision energy loss with conflict probability. Vehicles with the lowest CRD are prioritized for release to optimize intersection throughput. The TraCI interface enables precise control over vehicle movements, ensuring that the simulation accurately reflects the theoretical framework described in Section 3.

Algorithm 1: CRD-Based Intersection Control for Autonomous Vehicles

Input:$\mathrm{SUMO} \mathrm{simulation} \mathrm{environment} V$$, \mathrm{traffic} \mathrm{volume} C$ (1200 veh/h), headway

$\mathrm{threshold} H$$(10 \mathrm{s}). \mathrm{CRD} \mathrm{threshold} D\left({CRD}_0\right)$

Output:$\mathrm{Vehicle} \mathrm{release} \mathrm{sequence} \mathrm{and} \mathrm{performance} \mathrm{metrics} \pi$ (delay, fuel consumption,

emissions)

Initialize SUMO simulation via TraCI interface;

$\mathrm{sim} \leftarrow$ StartSUMO (V);

for simulation time step t from 1 to 1800 do

vehicles $\leftarrow$ TraCI.getVehicleState (sim);

for$each vehicle v_i$ in vehicles do

$\mathrm{Retrieve} \mathrm{position} p_i$$, \mathrm{speed} s_i$$, \mathrm{mass} m_i$$\mathrm{via} \mathbf{TraCI.getPosition} (v_i$),

TraCI.getSpeed$(v_i$$), \mathbf{TraCI.getVehicleClass}(v_i$);

if $startdistance<p_i<enddistance$ then

Record delay, fuel consumption, CO2, CO emissions via

$\mathbf{TraCI.getWaitingTime}(v_i$$), \mathbf{TraCl.getFuelConsumption} (v_i$),

$\mathbf{TraCI.getC02Emission} (v_i$$), \mathbf{TraCI.getCOEmission} (v_i$);

$\mathrm{Identify} \mathrm{priority} \mathrm{lane} L_p\leftarrow$ lane with vehicle closest to stop line;

$\mathrm{Form} \mathrm{priority} \mathrm{platoon} P_p\leftarrow \{v_i\in L_p|headway\le H\}$;

for $each lane L_c\ne L_p$ do

$\mathrm{Form} \mathrm{conflict} \mathrm{platoon} P_c\leftarrow \{v_j\in L_c|headway\le H\}$;

conflict platoons $\leftarrow$conflict platoons$\cup P_c$;

for each conflict platoon $P_c$ in conflict platoons do

$\mathrm{Compute} \mathrm{collision} \mathrm{angle} \theta$ based on intersection geometry;

$\mathrm{Calculate} \mathrm{kinetic} \mathrm{energy} \mathrm{loss} E_{loss}\leftarrow$CalculateCollisionLoss $(P_p$$,P_c$$,\theta$) using

Equation (4);

$\mathrm{Estimate} \mathrm{conflict} \mathrm{probability} P_{conflict}\leftarrow$CalculateConfictProbability $(P_p$$,{ P}_c$)

using Equation (7);

$\mathrm{Compute} \mathrm{CRD}\leftarrow E_{loss}\times P_{conflict}$;

$\mathrm{Store} \mathrm{CRD} (P_c$);

Sort conflict platoons by CRD in ascending order;

for each conflict platoon $P_c$$\mathrm{with} CRD\le D$ do

$\mathrm{Release} \mathrm{vehicles} \mathrm{in} P_c$$\mathrm{via} \mathbf{TraCI.setSpeed} (v_j$$,s_j$);

$\mathrm{Update} \mathrm{vehicle} \mathrm{routes} \mathrm{via} \mathbf{TraCI.changeTarget} (v_j$);

TraCI.simulationStep (sim);

Compute average delay, fuel consumption, emissions per approach;

$\pi \leftarrow$AnalyzeMetrics (vehicles);

return $\pi$;

4.2. Simulation Results

Section 4.1 outlined the simulation setup used to evaluate the CRD-based optimization approach at a four-leg intersection using the SUMO platform. To facilitate a more intuitive understanding, Figure 5 presents the visualized implementation scenarios of the two experiments. Experiment 1 employs a fixed-time control strategy with a four-phase signal cycle, while Experiment 2 adopts the proposed CRD-based unsignalized control method, which dynamically prioritizes vehicle platoons in real time. Figure 5 offers a direct comparison between these two control strategies. In Figure 5a, taken from Experiment 1, the green signal permits through movements from the north and south approaches, while vehicles in the other directions are stopped at red lights. In contrast, Figure 5b shows the CRD-based scenario from Experiment 2, where the northbound left-turn platoon is currently granted priority. Since the CRD value for the conflicting northbound through platoon is calculated as zero, both movements are allowed to proceed simultaneously, demonstrating improved traffic efficiency through conflict-aware coordination.

In the two simulation experiments, it was observed that both fixed signal control and the optimization method proposed in this paper effectively coordinated the passage of autonomous vehicles through intersections. However, the fixed signal control strategy failed to fully capitalize on the advantages offered by autonomous vehicles, leading to lower intersection passage efficiency. In contrast, the optimization method proposed in this paper takes into consideration the characteristics of autonomous driving technology, resulting in a significant improvement in intersection passage efficiency through intelligent regulation. The specific results and comparison of the two experiments are presented below.

Figure 6 illustrates the average delay of vehicles at each approach of the intersection. In Experiment 1, the average delay time is relatively high, whereas in Experiment 2, the average delay time is significantly reduced. Specifically, in Experiment 1, the average delay for each entry approach was approximately 20 s, whereas in Experiment 2, the average delay for each entry approach decreased significantly to around 0.22 s. Notably, the average delay for the east entry approach was 22 s in Experiment 1, but it dramatically reduced to only 0.15 s in Experiment 2. This indicates that the optimization method implemented in Experiment 2 is effective at substantially reducing the intersection’s delay time. Moreover, this validates the limitations of fixed signal control. Due to its fixed signal timing, it leads to higher average vehicle delays in low traffic flow conditions.

Figure 7 illustrates the average fuel consumption of vehicles at each approach of the intersection. For instance, in Experiment 1, the average fuel consumption for the east, north, south, and west entry approach was 785,000 mL, 875,000 mL, 873,000 mL, and 782,000 mL, respectively. In Experiment 2, the average fuel consumption for these entry approaches decreased to 442,000 mL, 426,000 mL, 440,000 mL, and 418,000 mL, respectively, corresponding to reductions of approximately 43.7%, 51.3%, 49.6%, and 46.5%. In Experiment 1, the average fuel consumption at each approach is higher compared to Experiment 2. This difference can be attributed to the signal control utilized in Experiment 1, which necessitates the frequent stopping and starting of vehicles at the intersection, thereby increasing fuel consumption. In contrast, in Experiment 2, the average fuel consumption at each approach is more uniform, indicating improved traffic flow. With fewer instances of stopping and starting as vehicles pass through the intersection, driving speeds become more consistent. This not only reduces fuel consumption but also enhances the efficiency of intersection passage.

Figure 8 presents the average carbon dioxide and carbon monoxide emissions of vehicles at each approach of the intersection. As shown in Figure 8a, carbon dioxide emissions in Experiment 2 are approximately 50% of those in Experiment 1. Simultaneously, Figure 8b indicates that the average carbon monoxide emissions for the four entry lanes in Experiment 1 were approximately 132,000 mg, while in Experiment 2, the emissions dropped to around 12,000 mg, representing a reduction of over 90%. These results suggest that the optimization method proposed in this study significantly reduces vehicle emissions, particularly in terms of reducing carbon monoxide emissions.

4.3. Discussion and Analysis

According to the simulation results and subsequent comparison, it is evident that all of the evaluation metrics in Experiment 2 are significantly better than those in Experiment 1. This clearly indicates that the unsignalized intersection model based on a crossing risk indicator is more effective at optimizing traffic flow and reducing both fuel consumption and emissions compared to the fixed signal control intersection. This notable improvement can be attributed to the adoption of the optimization strategy proposed in this paper, which significantly enhances the efficiency of vehicle passage. Furthermore, the lower traffic volume set in the simulation experiments likely contributed to the superior performance of the signal-free control strategy. This strategy demonstrates greater efficiency and environmental friendliness when compared to the fixed signal control approach.

The simulation results in Section 4.2 demonstrate that the proposed Crossing Risk Degree (CRD)-based method significantly outperforms fixed signal control, reducing the average delay per approach by approximately 20 s and fuel consumption by about 50% under a traffic volume of 1200 vehicles per hour. These results are competitive when compared to similar studies on unsignalized intersection management for Connected and Autonomous Vehicles (CAVs). For instance, Mirheli et al. [55] reported the development of a signal-head-free intersection control logic for CAVs, achieving travel time reductions of 59.4–83.7% compared to fixed-time and fully actuated control case studies. The substantial delay reduction achieved by our CRD-based method highlights the effectiveness of integrating risk-based prioritization, which balances safety and efficiency by dynamically adjusting vehicle passage based on conflict probability and energy loss. Similarly, Luo et al. [56] proposed a machine-vision-based collision risk warning method for unsignalized intersections on arterial roads, utilizing real-time visual data to predict conflict risks and enhance safety. Their approach complements our CRD-based method by reinforcing the critical role of risk-driven strategies in improving both safety and operational performance at unsignalized intersections. Together, these findings underscore the potential of the CRD-based method to advance intelligent transportation systems by significantly enhancing efficiency and sustainability.

The research results indicate that, in a fully autonomous driving environment, fixed signal control strategies, due to their lack of dynamic responsiveness, struggle to meet the high-precision path planning requirements of autonomous vehicles. This leads to frequent vehicle stagnation due to signal waiting, significantly reducing throughput efficiency. Autonomous vehicles rely on real-time Vehicle-to-Everything (V2X) communication, while the rigid rules of fixed signals limit the full utilization of these capabilities, preventing the system performance from reaching optimal levels. In contrast, the signal-free control strategy based on the CRD indicator dynamically adjusts vehicle priorities and passage strategies, more flexibly allocating road resources, effectively avoiding congestion and unnecessary waiting. Moreover, traditional signal-free control strategies often necessitate additional safety constraints to ensure feasibility. The optimization method proposed in this paper addresses these shortcomings by incorporating comprehensive safety considerations, thereby making it applicable to a wide range of traffic conditions.

The CRD-based model, while effective in controlled simulations, has several limitations that warrant further improvement. Firstly, it assumes a fully autonomous environment, limiting its applicability to mixed traffic scenarios with human-driven vehicles, which require additional coordination strategies. Considering the time and technological limitations in the development of autonomous driving technology, there is an inevitable transitional period between manual and autonomous driving. Future roads will feature mixed traffic conditions with both autonomous and manually driven vehicles. In this mixed traffic environment, intersection management becomes more complex and challenging. Future research should focus on more complex traffic scenarios and develop intersection passage strategies that accommodate mixed traffic flow conditions to optimize intersection efficiency. This includes studying how to effectively coordinate and manage the passage priorities of different types of vehicles, exploring the application of intelligent transportation systems, and developing new traffic signal control algorithms to adapt to ever-changing traffic demands and conditions. For instance, one potential approach would be to implement dedicated signal phases for CAVs, thereby separating them from human-driven vehicles. During the CAV-exclusive phases, the CRD-based control strategy proposed in this study could be applied to fully utilize the autonomous system’s coordination capabilities.

Secondly, the model was tested on a simplified four-leg intersection with fixed traffic volume (1200 vehicles per hour), potentially overlooking the complexities of diverse intersection geometries (e.g., roundabouts) or fluctuating volumes. The innovative method proposed in this paper has been simulated and tested at low-traffic four-way intersections. However, in real-world scenarios, intersections vary significantly in terms of geometric characteristics, traffic flow, and road conditions, all of which are crucial for the safe passage of vehicles. As the geometric conditions of intersections change, the angles of vehicle conflicts vary within the interval [0, π], with larger collision angles resulting in greater energy loss. Furthermore, different intersection designs, such as those with skewed angles or roundabouts, may further affect conflict angles and frequencies. For example, in roundabouts, conflict points are more continuous and circular in nature, requiring the CRD model to account for angular vehicle trajectories and merging dynamics. Similarly, variations in traffic volume affect the distribution of headways between vehicles, thereby influencing the probability of conflicts. In high-traffic situations, shorter headways increase the likelihood of conflicts, whereas in low-traffic situations, longer headways reduce this likelihood. Therefore, CRD values should be calculated based on the specific intersection type and traffic flow, with the priority of vehicle passage evaluated and adjusted according to actual traffic conditions. More specifically, real-world traffic management needs to account for various vehicle attributes, such as vehicle type, vehicle length, and whether the vehicle is an emergency vehicle. Additionally, road conditions, such as road width, surface quality, signage, and weather conditions, also impact traffic flow and safety at intersections. These factors must be considered when applying the innovative method to ensure its effectiveness and feasibility under various real-world conditions. Thus, the proposed method requires not only theoretical refinement but also extensive field testing and validation across different types of intersections and traffic conditions to ensure its general applicability and reliability.

Thirdly, the reliance on idealized sensor data in SUMO may not account for real-world inaccuracies or delays in V2X communication. To address these, future work should extend the model to mixed traffic by incorporating human driver behavior models, testing it across varied intersection types and dynamic traffic volumes, and validating it with real-world data to ensure robustness against sensor noise and communication latencies. Overall, through comprehensive optimization and adjustment, more efficient and safer traffic management can be achieved, enhancing road capacity, reducing the incidence of traffic accidents, and ultimately realizing intelligent and modern traffic system management.

5. Concluding Remarks

This paper presents an optimization method for the safe passage of autonomous vehicles at unsignalized intersections based on the Crossing Risk Degree (CRD) indicator. The CRD metric effectively quantifies the risk level of autonomous vehicles using acceptable gaps at intersections, making a significant contribution to the research on assessing crossing risks for autonomous vehicles. The effectiveness of this optimization method was validated through SUMO simulations, which demonstrated substantial reductions in vehicle delays, fuel consumption, and tailpipe emissions. Specifically, the average delay per entry approach decreased by approximately 20 s, and fuel consumption was reduced by about 50%.

The CRD value, as a quantitative indicator for measuring crossing risk, plays a crucial role in traffic management. Based on the CRD value, the passage priority of different conflict platoons can be determined. Lower CRD values indicate higher passage priority for conflict platoons, thereby improving intersection efficiency. It is also essential to ensure that the CRD values of all released platoons do not exceed a set upper limit to guarantee traffic safety. Setting a reasonable upper limit for CRD serves as a control measure in traffic management to ensure the safety of traffic flow. Additionally, adjusting the headway distribution can effectively reduce CRD values. The CRD value can be integrated into urban intelligent transportation systems, enabling real-time calculation through cameras, sensors, and V2X communication technologies, thereby dynamically adjusting traffic signals or optimizing traffic flow. In practical applications, CRD thresholds can be preset based on the geometric conditions and traffic volume of different intersections, and stricter control strategies can be applied to high-risk traffic scenarios, such as peak-hour congestion, intersections with skewed angles, or adverse weather conditions. Infrastructure upgrades are key to implementing this method, and policy support is also needed to promote the widespread application of these technologies in urban traffic management.

In conclusion, this study enhances traffic safety at unsignalized intersections by reducing conflict risks and developing efficient intersection passage strategies tailored to autonomous vehicles. The findings demonstrate that by effectively utilizing the CRD indicator, it is possible to significantly improve traffic flow and energy efficiency while ensuring traffic safety. These insights provide a valuable theoretical foundation for further research and practical applications. Policymakers should leverage these findings to design adaptive and dynamic intersection management policies, integrating the CRD indicator into regulatory frameworks. By incorporating real-world data, real-time data monitoring, and analytics, these policies can ensure timely adjustments to traffic flow based on current conditions. Additionally, investing in infrastructure upgrades to support autonomous vehicle technologies will further augment the benefits of CRD-based management. Based on practical considerations, deploying V2V and V2X communication infrastructure is more urgent as it forms the foundation for data acquisition and vehicle control. Long-term efforts should focus on establishing regulatory frameworks and policy support. These combined efforts will not only improve traffic efficiency and safety but also contribute to environmental sustainability by reducing vehicle emissions and fuel consumption. Future research can build on these results, incorporating different traffic scenarios to further optimize and validate these strategies, ultimately aiming for comprehensive autonomous driving traffic management solutions. Collaboration between government agencies, private sector stakeholders, and research institutions will be essential to successfully implement these advanced traffic management strategies across diverse urban environments.