Modeling and Analysis of Connected Traffic Intersections Based on Modified Binary Petri Nets

We propose an approach for the modeling and analysis of two connected traffic intersections based on Petri nets (PNs). We first use a PN to model an isolated four-way signalized intersection; then we extend it to model two successive signalized intersections. We find that this model has unbounded places, which in turn results in some confliction problems. Hence, we introduce the concept of modified binary petri nets (MBPNs) to overcome the limitation and resolve the confliction problem when we design our model and its controller. This MBPN model is a powerful tool and can be useful for the modeling and analysis of many other traffic applications. 1. Introduction As a powerful tool that consists of a combined graphical and mathematical representation, Petri nets have been used for the modeling, control, and analysis in different applications including sensor networks [1], power systems [2, 3], manufacturing systems [4–7], and many other practical systems. In traffic management problems, Petri nets have been used to model the traffic network in different ways for a variety of purposes. It can be concluded that when vehicle flow has been studied, hybrid Petri nets (HPNs) are a suitable modeling tool because they consist of both continuous and discrete nodes that work together to reflect the dynamics of the overall traffic system. Continuous nodes are suitable for modeling continuous events such as vehicle flow while discrete nodes are used to represent discrete events such as phase change in traffic signal and enabling/disabling vehicle movement because of occurrences of emergent events such as accidents and the blocking of the road. In [8], a general HPN model for transportation system was developed. Traffic flow was described by continuous nodes and the events that affect the traffic dynamics were modeled through discrete nodes. In [9], a simple HPN was used to model the intersection of two one-way streets, while in [10] a continuous Petri net was used to model a nonsignalized intersection, and then were added discrete nodes that are essential to represent a four-way intersection with two-phase traffic light through an HPN. In [11], the authors developed an HPN model to improve the performance of special and emergency vehicles. In the aforementioned works on traffic network modeling and management, HPN models were adopted because they are more accurate to reflect the dynamics of the entire traffic network for certain applications. On the other hand, however, in some traffic network applications such as control and monitoring, only events are critical to