## 1 Introduction  
In urban transportation networks, arterial roads serve as the main arteries of city streets and often bear a substantial transportation burden. In practice, traffic flow is constantly changing, and factors such as \"commuter traffic\", \"tidal traffic\", road construction, local speed limits, pedestrian crossings, and driver behavior can significantly impact traffic volume. This results in high vehicle dispersion, which disrupts traffic flow stability and causes traffic congestion and accidents on urban arterial roads and at key intersections. Multiple studies have shown that traffic congestion and complex driving environments significantly increase driver stress and anxiety, which in turn affects their decision-making and driving behavior, potentially leading to more severe consequences [1]. Therefore, effective solutions are urgently needed [2]. Coordinated traffic signal control methods are often adopted to alleviate the above-mentioned issues by linking multiple consecutive intersections on urban arterials as an integrated control subarea [3; 4; 5]. The intersections within the subarea are controlled using a unified system cycle length or half of the system cycle length. This method can achieve relatively ideal optimization and control effects when the number of intersections is small and traffic flows on the sections are similar. However, it is not very applicable and can easily lead to more severe congestion when the incoming straight traffic accounts for a relatively small percentage of the coordinated direction, while left and right turns account for a relatively large percentage, or when dispersibility of vehicles passing through intersections is high with substantial interference. Therefore, unequal cycle lengths are often used to control adjacent intersections with large fluctuations in traffic demand and high dispersibility of passing vehicles to ensure traffic demand and throughput efficiency between adjacent intersections. Researchers have conducted in-depth studies on coordinated control methods for unequal cycle lengths based on these issues. The bidirectional design approach for green wave signal coordination was first proposed by [PERSON] et al. [6]. As research continued, [PERSON] et al. [7] proposed the multi-band coordination control model for road sections with different capacities. [PERSON] and [PERSON] [8] presented a data-driven cycle offset (or simply offset) optimization model solved by genetic algorithms, significantly reducing travel delays. [PERSON] et al. [9] used an unbalanced dual cycle control scheme and established the maxband model based on an unequal dual cycle, aiming to maximize bidirectional constant green bandwidth and minimize delay at dual cycle intersections. [PERSON] et al. [10] constructed mathematical equations to predict average delay and queue length and verified through case studies that using dual-cycle control can reduce delay and queue length to some extent. [PERSON] et al. [11] combined genetic algorithms to achieve global optimization of mixed cycle lengths at intersections. However, the above research was mainly based on graphical [12; 13], analytical [14; 15], and modeling [16] methods for control in conventional environments. They often assume fixed speeds for optimization, making fine-grained control of individual vehicles difficult. Additionally, road and vehicle information perceptibility and predictability are poor and unable to dynamically adapt to traffic flow changes [17; 18]. Thus, improving the travel efficiency of intersections with unequal cycles is challenging. In recent years, with the continuous development of intelligent information technology, applying vehicle-road collaboration techniques to related research has gradually become a hot topic [19; 20]. [PERSON] et al. [21] proposed single-vehicle speed and multi-vehicle coordinated guidance methods based on bidirectional communication between vehicles and traffic control systems in a VANET environment.