Hybrid Petri Nets and Hybrid Automata for Modeling and Control of Two Adjacent Oversaturated Intersections


The problem of avoiding oversaturated phenomena between two adjacent intersections by intelligent traffic control strategy is addressed in this paper. The complex traffic behavior in this urban area is viewed as a dynamical hybrid system that can be modeled by hybrid Petri nets (HPNs). The property analysis of HPN model that gives an evaluation of the system performance is very limited. The translation of this model into hybrid automata (HA) can avoid this drawback. The interest of this translation is to profit from the both models advantages while avoiding their disadvantages that associate the modeling power of HPN with the analysis capacities of HA. The resulting model can capture an important aspect of the traffic flow dynamics where the oversaturated traffic conditions are presented by forbidden locations. A reachability analysis is performed to check this model. An optimal supervised controller synthesis algorithm is elaborated to get an optimal plan with coordinated traffic signals that satisfy the imposed constraints where the forbidden locations are suppressed. The experiment results show that the coordination traffic signal obtained by the proposed control approach outperforms those obtained using the widely used signal timing optimization software SYNCHRO under various demand scenarios from unsaturated to oversaturated.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. Aboudolas, K., Papageorgiou, M., & Kosmatopoulos, E. (2009). Store-and-forward based methods for the signal control problem in large-scale congested urban road networks. Transportation Research Part C: Emerging Technologies, 17(2), 163–174.

    Article  Google Scholar 

  2. Alla, H., & David, R. (1998a). A modelling and analysis tool for discrete events systems: continuous Petri net. Performance Evaluation, 33, 175–199.

    Article  Google Scholar 

  3. Alla, H., & David, R. (1998b). Continuous and hybrid Petri nets. Journal of Circuits, Systems and Computers, 8(1), 159–188.

    MathSciNet  Article  Google Scholar 

  4. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T. A., Ho, P.-H., Nicollin, X., et al. (1995). The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138(1), 3–34.

    MathSciNet  Article  MATH  Google Scholar 

  5. Badamchizadeh, M. A, & Joroughi, M. (2010). Deterministic and stochastic Petri Net for urban traffic systems. In 2010 The 2nd international conference on computer and automation engineering (ICCAE) (Vol. 5, pp. 364–368).

  6. Branislav Hrúz, M. Z. (2007). Modeling and control of discrete-event dynamic systems. (A. T. in C. and S. Processing, Ed.). Advanced textbooks in control and signal processing.

  7. Chang, T. H., & Sun, G. Y. (2004). Modeling and optimization of an oversaturated signalized network. Transportation Research Part B: Methodological, 38(8), 687–707.

    Article  Google Scholar 

  8. Chen, Y., Li, W., Guo, Y., & Wu, Y. (2015). Dynamic graph hybrid automata: A modeling method for traffic network. In 2015 IEEE 18th international conference on intelligent transportation systems (pp. 1396–1401).

  9. Chen, F., Wang, L., Jiang, B., & Wen, C. (2014). A novel hybrid petri net model for urban intersection and its application in signal control strategy. Journal of the Franklin Institute, 351(8), 4357–4380.

    MathSciNet  Article  MATH  Google Scholar 

  10. Daganzo, C. F. (1995). The cell transmission model, part II: Network traffic. Transportation Research Part B: Methodological, 29(2), 79–93.

    Article  Google Scholar 

  11. David, R., & Alla, H. (2004). Discrete, continuous, and hybrid Petri nets (2nd ed.). Berlin: Springer.

    Google Scholar 

  12. Di Febbraro, A., Giglio, D., & Sacco, N. (2016). A deterministic and Stochastic Petri net model for traffic-responsive signaling control in urban areas. IEEE Transactions on Intelligent Transportation Systems, 17(2), 510–524.

    Article  Google Scholar 

  13. Di Febbraro, A., & Sacco, N. (2004). On modelling urban transportation networks via hybrid Petri nets. Control Engineering Practice, 12(10), 1225–1239.

    Article  Google Scholar 

  14. Frehse, G. (2006). PHAVer: Algorithmic verification of hybrid systems past HyTech, no. Hscc, 2005 (pp. 258–273).

  15. Gazis, D. C. (1964). Optimum control of a system of oversaturated intersections. Operations Research, 12(6), 815–831.

    Article  MATH  Google Scholar 

  16. Ghomri, L., Alla, H., & Zaki, S. (2005). Structural and hierarchical translation of hybrid Petri nets in hybrid automata. In Proceedings of IMACS 2005, Paris.

  17. Ghomri, L., & Alla, H. (2007). Modeling and analysis using hybrid Petri nets. Nonlinear Analysis: Hybrid Systems, 1(2), 141–153.

    MathSciNet  MATH  Google Scholar 

  18. Ghomri, L., & Alla, H. (2013). Continuous flow systems and control methodology using hybrid Petri nets. Journal of Control Engineering and Applied Informatics, 15(4), 106–116.

    Google Scholar 

  19. Grandinetti, P., de Wit, C., & Garin. F. (2015b). An efficient one-step-ahead optimal control for urban signalized traffic networks based on an averaged celltransmission model. In European Control Conference (ECC) (pp. 3478–3483).

  20. Grandinetti, P., Garin, F., Canudas de Wit, C. (2015a). Towards scalable optimal traffic control. In 54th IEEE conference on decision and control, 2015, Osaka.

  21. Hajbabaie, A., & Benekohal, R. F. (2015). A program for simultaneous network signal timing optimization and traffic assignment. IEEE Transactions on Intelligent Transportation Systemsntelligent Transportation Systems, 16(5), 2573–2586.

    Article  Google Scholar 

  22. Henzinger, T. A., Kopke, P. W., Puri, A., & Varaiya, P. (1998). What’s decidable about hybrid automata? Journal of Computer and System Sciences, 57(1), 94–124. doi:10.1006/jcss.1998.1581.

    MathSciNet  Article  MATH  Google Scholar 

  23. Huang, Y., Weng, S., & Zhou, M. (2014). Modular design of urban traffic-light control systems based on synchronized timed Petri nets. IEEE Transactions on Intelligent Transportation Systems, 15(2), 530–539.

    Article  Google Scholar 

  24. Jbira, M. K., & Ahmed, M. (2011). Computer simulation: A hybrid model for traffic signal optimisation. Journal of Information Processing Systems, 7(1), 1–16.

    Article  Google Scholar 

  25. Júlvez, J., & Boel, R. (2005). Modelling and controlling traffic behaviour with continuous Petri nets. In Proceedings of the 16th IFAC world congress, 2005 (Vol. 16).

  26. Júlvez, J., & Boel, R. (2010). A continuous Petri net approach for model predictive control of traffic systems. IEEE Transactions on Systems, Man, and Cybernetics, 40(4), 686–697.

    Article  Google Scholar 

  27. Jang, K., Kim, H., & Jang, I. G. (2015). Traffic signal optimization for oversaturated urban networks: Queue growth equalization. IEEE Transactions on Intelligent Transportation Systems, 16(4), 2121–2128.

  28. List, G. F., & Cetin, M. (2004). Modeling traffic signal control using Petri nets. IEEE Transactions on Intelligent Transportation Systems, 5(3), 177–187.

    Article  Google Scholar 

  29. Little, J. D. C. (1966). The synchronization of traffic signals by mixed-integer linear programming. Operations Research, 14(4), 568–594.

    Article  MATH  Google Scholar 

  30. Michalopoulos, P. G., & Stephanopoulos, G. (1977). Oversaturated signal systems with queue length constraints–I. Transportation Research, 11(6), 413–421.

    Article  Google Scholar 

  31. Ng, K. M., Bin, M., Reaz, I., Alauddin, M., & Ali, M. (2013). A review on the applications of Petri nets in modeling, analysis, and control of urban traffic. IEEE Transactions on Intelligent Transportation Systems, 14(2), 858–870.

    Article  Google Scholar 

  32. Robertson, D. I. (1969). TRANSYT: A traffic network study tool. RRL Report LR 253, Road Research Laboratory, England.

  33. Transportation Research Board. (2010). Highway capacity manual (5th ed.). Washington: National Academy of Sciences.

  34. Wang, P., Jones, L. S., & Yang, Q. (2012). A novel conditional cell transmission model for oversaturated arterials. Journal of Central South University, 19(5), 1466–1474.

    Article  Google Scholar 

  35. Webster, F. (1958). Traffic signal settings, Road resea. H.M. Stationery Office: Richmond.

    Google Scholar 

  36. Zhang, M., Jia, L., & Zhu, W. (2012). A cell-based robust optimal coordinated control on urban arterial road. Journal of Control Theory and Applications, 10(4), 543–548.

    MathSciNet  Article  Google Scholar 

  37. Zhao, X., & Chen, Y. (2003). Traffic light control method for a single intersection based on hybrid systems. In Proceedings of the 2003 IEEE international conference on intelligent transportation systems (Vol. 2, pp. 1105–1109).

Download references


This work was performed as part of a Tassili project in cooperation between Gipsa-Lab Grenoble, France, and LAIG laboratory, Guelma, Algeria. This research work is funded by LAIG laboratory. The authors would like to thank Dr. Nadir Farhi of IFSTTAR for their support and guidance in this paper, and we thank Pr H. Alla and Pr H. Tebbikh for their valuables advice and their assistance.

Author information



Corresponding author

Correspondence to Fares Bouriachi.

Appendix 1: Control Algorithm Synthesis

Appendix 1: Control Algorithm Synthesis

The control algorithm synthesis of this work presented in Sect. 3.2.1 is detailed in the following algorithm:


Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bouriachi, F., Kechida, S. Hybrid Petri Nets and Hybrid Automata for Modeling and Control of Two Adjacent Oversaturated Intersections. J Control Autom Electr Syst 27, 646–657 (2016). https://doi.org/10.1007/s40313-016-0275-x

Download citation


  • Arterial network
  • Hybrid Petri net
  • Hybrid automata
  • Traffic control
  • Oversaturated traffic condition