## 1 Introduction  
Public transit systems have been extensively studied in the literature [1; 2; 3] to improve the safety and efficiency of transportation in urban traffic networks. The quality of the transit service depends heavily on how punctually the transit arrives at each bus stop and picks up passengers. Especially, transit signal priority control and signal switching behaviors are becoming necessary functions for any transit system to improve the safety and efficiency of public transportation. Transit signal priority (TSP) control operates under the logic explained as follows. It extends the originally planned green light phase or starts the phase early to make the green light time longer if some conditions are met such that some transit vehicles can go through an intersection without waiting there. To decide which logic should be used, a quick calculation is performed on site using a bus arrival time prediction model based on historical data [4; 5; 6]. There are many classical TSP methods being employed, including offset modification [7], green wave [8], cycle extension [9], and phase recall [10]. [PERSON] [11] presented a simulation-based model for analyzing partial dynamic signal timings as well as fully adaptive signal control systems. [PERSON] et al. [12] developed a logic-based adaptive TSP control system with double detection and they make comparison with full priority for mixed lane conditions. [PERSON] et al. [13] presented a traffic control system that can work standalone to handle various boundary conditions of the recurrent, non-recurrent congestion, TSP and downstream blockage conditions to improve the overall traffic network vehicular productivity and efficiency. In addition,there are some studies, such as [11; 14], based on adaptive traffic signal control such as SCOOT and PRIBUSS to explore new priority strategies. Although these approaches promoted the transit signal priority control research to some extent, it is worth noting that all these approaches are mainly based on analytical methods and many strict mathematical assumptions. Furthermore, the correctness and reliability of the TSP control systems are unproven, and potential design errors can lead to conflicting traffic at the intersection, which in turn affects the actual control effect. Petri nets (PN) have shown to be powerful in modeling, analyzing, scheduling, and controlling for various kinds of information and production systems that are characterized as being concurrent, asynchronous, distributed and stochastic [15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Their graphical representation provides a friendly man-machine interface for simulation and logic control. To the best of the authors' knowledge, the work in [25] may be the earliest attempt to apply PNs for the modeling and analysis of urban traffic networks. Since then, a lot of researchers have focused their attention on this specific area. [PERSON] et al. [26] presented a comprehensive review on the applications of PNs in modeling, analysis, and control of traffic networks. A variety of high-level PNs such as continuous PNs with variable speed, first-order Hybrid PNs and Synchronized Timed PNs have been used for modeling and analysis of traffic flow [27; 28], and urban traffic networks [29; 30]. Unlike the continuous characteristics of vehicle flow, the behavior of a signal control system at the intersection shows a discrete feature. [PERSON] et al. [31] used P-invariant and a reachability tree to confirm that a PN-based eight-phase traffic signal control model is conflict- and deadlock-free, respectively. [PERSON] et al. [29] developed modularized eight-phase, six-phase, and two-phase traffic-light control systems, respectively. The advantage of these models is that the size of the urban traffic network control systems can be easily extended with their proposed modular technique. It is worth noting that the common feature of the abovementioned research is that PNs are used for regular adjustment of phase and timing of traffic signal systems.