## 1 Introduction  
Traffic congestion in urban networks has increased significantly, becoming a major challenge in many large cities due to the rising number of vehicles. It is marked by slower speeds, longer travel times, and increased vehicle queueing. Congestion occurs when traffic demand exceeds road capacity, causing vehicle interactions to disrupt smooth traffic flow. This article focuses on analyzing and addressing vehicle congestion in urban traffic networks. An intelligent transportation system (ITS) is essential for improving the effectiveness and security of transport networks [1]. The concept of the ITS emerged nearly thirty years ago as part of efforts to address long-term traffic congestion. ITS technologies have been extensively utilized to address traffic congestion challenges, encompassing aspects such as accident detection and validation [2, 3, 4], emergency response coordination [5], accident-related wireless communications [6], and freeway traffic simulation [7]. Traffic congestion is a complex factor that influences various aspects of traffic accidents. [PERSON] et al. [8] suggested that if the correlation between congestion and fatal or serious injury accidents is negative, congestion may, in some cases, contribute to improved road safety. This poses a challenge for traffic management, as reducing congestion does not always lead to fewer accidents. To address this issue, it is crucial to lower accident rates while gaining a deeper understanding of how congestion impacts traffic incidents. Despite extensive research on the relationship between congestion and accidents, no clear consensus has been reached. Traffic accidents not only cause congestion but also contribute to its spread across urban networks. Therefore, studying the formation and propagation of traffic congestion is essential for developing effective traffic management strategies. Traffic congestion can arise from one of three primary causes [9]: temporary obstructions, permanent capacity constraints, or stochastic fluctuations in demand. Accidents are a type of temporary obstruction, often leading to congestion. In this research, we concentrate on traffic congestion resulting from accidents within two-way grid networks. [PERSON] et al. [10] classified accident-induced congestion as a distinct type of traffic jam, emphasizing that if accidents are not cleared promptly, they can trigger large-scale upstream congestion. In recent years, considerable research has been dedicated to understanding accident-induced traffic jams, leading to the development of both analytical models [11] and accident simulation models that examine congestion formation and growth [12]. Additionally, [PERSON] et al. [13] classified traffic control strategies for accidents into static and dynamic methods. Static strategies emphasize roadway design elements to minimize congestion spread, whereas dynamic approaches focus on real-time interventions to control and alleviate congestion propagation. By integrating these strategies, traffic management systems can more effectively address congestion resulting from accidents. Moreover, various methodologies [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] have been proposed to mitigate traffic congestion. Nevertheless, the majority of existing control strategies prove most effective under low-to-moderate traffic flow and stable conditions, restricting their suitability for more intricate and dynamic traffic environments. To alleviate urban traffic congestion caused by accidents, various rerouting strategies have been implemented with the support of traffic authorities. Notably, several studies [14; 15; 16; 17] focus on dispersing incident-induced traffic jams in urban networks. Typically, red lights are used to prevent vehicles from entering congested areas [17; 18; 19; 20]. [PERSON] et al. [14] introduced a diamond control strategy that prevents all vehicles from entering a specifically designated diamond-shaped area. [PERSON] et al.