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
References
[1]
L. Li and D. S. Kim, “Least-cost path estimation in wireless ad hoc sensor networks using Petri nets,” in Proceedings of the 5th ACM International Conference on Ubiquitous Information Management and Communication (ICUIMC '11), Seoul, South Korea, February 2011.
[2]
C. N. Hadjicostis and G. C. Verghese, “Power system monitoring using Petri net embeddings,” IEE Proceedings C, vol. 147, no. 5, pp. 299–303, 2000.
[3]
N. Lu, Power system modeling using Petri nets [Ph.D. thesis], 2002, http://www.ima.umn.edu/~mali/thesis.pdf.
[4]
F. S. Hsieh and J. B. Lin, “Context-aware workflow management for virtual enterprises based on coordination of agents,” Journal of Intelligent Manufacturing, 2012.
[5]
F. S. Hsieh and C. Y. Chiang, “Collaborative composition of processes in holonic manufacturing systems,” Computers in Industry, vol. 62, no. 1, pp. 51–64, 2011.
[6]
F. S. Hsieh, “Design of reconfiguration mechanism for holonic manufacturing systems based on formal models,” Engineering Applications of Artificial Intelligence, vol. 23, no. 7, pp. 1187–1199, 2010.
[7]
L. Li, C. N. Hadjicostis, and R. S. Sreenivas, “Designs of bisimilar Petri net controllers with fault tolerance capabilities,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 38, no. 1, pp. 207–217, 2008.
[8]
A. di Febbraro and S. Sacone, “Hybrid modelling of transportation systems by means of Petri nets,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 131–135, October 1998.
[9]
A. di Febbraro, D. Giglio, and N. Sacco, “Modular representation of urban traffic systems based on hybrid petri nets,” in Proceedings of the IEEE International Conferences on Intelligent Transportation Systems, pp. 866–871, August 2001.
[10]
C. R. Vázquez, H. Y. Sutarto, R. Boel, and M. Silva, “Hybrid Petri net model of a traffic intersection in an urban network,” in Proceedings of the IEEE International Conference on Control Applications (CCA '10), pp. 658–664, Yokohama, Japan, September 2010.
[11]
A. di Febbraro, D. Giglio, and N. Sacco, “Urban traffic control structure based on hybrid petri nets,” IEEE Transactions on Intelligent Transportation Systems, vol. 5, no. 4, pp. 224–237, 2004.
[12]
G. F. List and M. Cetin, “Modeling traffic signal control using Petri nets,” IEEE Transactions on Intelligent Transportation Systems, vol. 5, no. 3, pp. 177–187, 2004.
[13]
Y. Qu, L. Li, Y. Liu, Y. Chen, and Y. Dai, “Travel routes estimation in transportation systems modeled by Petri nets,” in Proceedings of the IEEE International Conference on Vehicular Electronics and Safety, pp. 73–77, Qingdao, China, July 2010.
[14]
Y. S. Huang and T. H. Chung, “Modeling and analysis of urban traffic lights control systems using timed CP-nets,” Journal of Information Science and Engineering, vol. 24, no. 3, pp. 875–890, 2008.
[15]
Y. S. Huang and P. J. Su, “Modelling and analysis of traffic light control systems,” IET Control Theory and Applications, vol. 3, no. 3, pp. 340–350, 2009.
[16]
Y. S. Huang, Y. S. Weng, and M. Zhou, “Critical scenarios and their identification in parallel railroad level crossing traffic control systems,” IEEE Transactions on Intelligent Transportation Systems, vol. 11, no. 4, pp. 968–977, 2010.
[17]
C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Systems, Springer, New York, NY, USA, 2008.
[18]
T. Murata, “Petri nets: properties, analysis and applications,” Proceedings of the IEEE, vol. 77, no. 4, pp. 541–580, 1989.
[19]
R. David and H. Alla, Discrete, Continuous, and Hybrid Petri Nets, Springer, New York, NY, USA, 2005.
[20]
Y. S. Huang, “Design of traffic light control systems using statecharts,” The Computer Journal, vol. 49, no. 6, pp. 634–649, 2006.
[21]
J. Moody, K. Yamalidou, M. Lemmon, and P. J. Antsaklis, “Feedback control of petri nets based on place invariants,” Automatica, vol. 32, no. 1, pp. 15–28, 1996.