Modelling and Analysis of Oversaturated Intersections Using Jointly Hybrid Petri net and Hybrid Automata


The Urban traffic network is a typical example of a complex system called hybrid dynamic system. It is also a multivariable and multi-scale system having the interaction of two dynamics kinds. The difficulties encountered in the study of traffic and especially in the traffic signal control problem is how to model the traffic flow, how to define its variables and how to analyze their behavior. In this paper, we propose a modeling of oversaturated intersections traffic a view to designing a traffic control approach. This concept is based on the joint use of the two well-known hybrid representation tools: hybrid Petri networks and hybrid automata. The interest of this combination is to profit from the both models advantages while avoiding their disadvantages. A formal verification property is performed to refine this model. This technique is based on the computation of the reachable state spaces. Indeed, the new model captures important aspects of the traffic flow dynamics. Its favorable structure can be used in order to provide an efficient signal-timing plan to avoid oversaturation and to ease congestion. The numerical results show that the coordination traffic signal obtained by the proposed control approach outperforms those obtained using the widely utilized signal timing optimization software SYNCHRO under various demand scenarios from unsaturated to oversaturated.

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  1. 1.

    Webster, F.V.: “Traffic Signal Settings,” Road Research Technique Paper No. 39. Road Research Laboratory, London (1958)

  2. 2.

    Little, J.D.C.: The synchronization of traffic signals by mixed-integer linear programming. Oper Res. 14(4), 568–594 (Jul. 1966)

    Article  MATH  Google Scholar 

  3. 3.

    Robertson, D.: TRANSYT: a traffic network study tool. Traffic Eng Control. 11(04), 276–281 (1969)

    Google Scholar 

  4. 4.

    TRB: HCM 2010 Highway capacity manual. Transportation Research Board. National Research Council, Washington, D.C (2010)

    Google Scholar 

  5. 5.

    H. P. et al: The SCOOT on-line traffic signal optimization technique. Traffic Eng Control. 23, 190–192 (1982)

    Google Scholar 

  6. 6.

    Gartner, N.: OPAC: a demand responsive strategy for traffic signal control. Transp Res Rec. 906(1983), 75–81 (1983)

    Google Scholar 

  7. 7.

    Gartner, C.M., Tarnoff, N.H., Andrews, P.J.: Evaluation of optimized policies for adaptive control strategy. Transp. Res. Rec. 1324, 105–114 (1991)

  8. 8.

    Gazis, D.C.: Optimum control of a system of oversaturated intersections. Oper Res. 12(6), 815–831 (1964)

    Article  MATH  Google Scholar 

  9. 9.

    Michalopoulos, P.G., Stephanopoulos, G.: Oversaturated signal systems with queue length constraints—I. Transp Res. 11(6), 413–421 (1977)

    Article  Google Scholar 

  10. 10.

    Chang, T.-H., Lin, J.-T.: Optimal signal timing for an oversaturated intersection. Transp Res Part B Methodol. 34(6), 471–491 (2000)

    Article  Google Scholar 

  11. 11.

    Chang, T.H., Sun, G.Y.: Modeling and optimization of an oversaturated signalized network. Transp Res Part B Methodol. 38(8), 687–707 (2004)

    Article  Google Scholar 

  12. 12.

    Aboudolas, K., Papageorgiou, M., Kosmatopoulos, E.: Store-and-forward based methods for the signal control problem in large-scale congested urban road networks. Transp Res Part C Emerg Technol. 17(2), 163–174 (2009)

    Article  Google Scholar 

  13. 13.

    U. States and B. Early, “Development of Traffic Control and,” no. 970707.

  14. 14.

    Abu-Lebdeh, G., Benekohal, R.F.: Development of traffic control and queue management procedures for oversaturated arterials. Transp. Res. Rec.: J Transp Res Board. 1603, 119–127 (1997)

  15. 15.

    Girianna, M., Benekohal, R.: Dynamic signal coordination for networks with oversaturated intersections. Transp Res Rec J Transp Res Board. 1811, 122–130 (2002)

    Article  MATH  Google Scholar 

  16. 16.

    Abu-Lebdeh, G., Benekohal, R.F.: Genetic algorithms for traffic signal control and queue management of oversaturated two-way arterials. Transp Res Rec J Transp Res Board. 1727(1), 61–67 (2000)

    Article  Google Scholar 

  17. 17.

    Lieberman, E., Chang, J., Prassas, E.: Formulation of real-time control policy for oversaturated arterials. Transp Res Rec J Transp Res Board. 1727, 77–88 (2000)

    Article  Google Scholar 

  18. 18.

    Lertworawanich, P., Kuwahara, M., Miska, M.: A new Multiobjective signal optimization for oversaturated networks. IEEE Trans Intell Transp Syst. 12(4), 967–976 (2011)

    Article  Google Scholar 

  19. 19.

    Hajbabaie, A., Benekohal R.F.: A Program for Simultaneous Network Signal Timing Optimization and Traffic Assignment. IEEE Trans Intell Transp Syst. 16(5), 2573–2586 (2015)

  20. 20.

    Daganzo, C.F.: The cell transmission model, part II: network traffic. Transp Res Part B Methodol. 29(2), 79–93 (1995)

    Article  Google Scholar 

  21. 21.

    Lo, H.K.: A novel tra • c signal control formulation. Transp Res. 33, 433–448 (1999)

    Article  Google Scholar 

  22. 22.

    Wang, P., Jones, L.S., Yang, Q.: A novel conditional cell transmission model for oversaturated arterials. J Cent South Univ. 19(5), 1466–1474 (2012)

    Article  Google Scholar 

  23. 23.

    Rohde, J., Friedrich, B.: Offset optimizing with CTM and genetic algorithms: results from field studies in Hannover. Procedia - Soc Behav Sci. 20, 437–444 (2011)

    Article  Google Scholar 

  24. 24.

    Han, K., Gayah, V.V.: Continuum signalized junction model for dynamic traffic networks: offset, spillback, and multiple signal phases. Transp Res Part B Methodol. 77, 213–239 (2015)

    Article  Google Scholar 

  25. 25.

    Jang, K., Kim, H., Jang, I.G.: Traffic signal optimization for oversaturated urban networks: queue growth equalization. IEEE Trans Intell Transp Syst. 16(4), 2121–2128 (2015)

  26. 26.

    Li, P., Mirchandani, P., Zhou, X.: Solving simultaneous route guidance and traffic signal optimization problem using space-phase-time hypernetwork. Transp Res Part B Methodol. 81, 103–130 (2015)

    Article  Google Scholar 

  27. 27.

    Xiang, W., Xiao, J., Jiang, Y.: Real-time signalization for an oversaturated intersection via static state feedback control: a switched system approach. J Franklin Inst. 352(8), 3304–3324 (2015)

  28. 28.

    Motawej, F., Bouyekhf, R., El Moudni, A.: A dissipativity-based approach to traffic signal control for an over-saturated intersection. J Frankl Inst. 348(4), 703–717 (2011)

    Article  MATH  Google Scholar 

  29. 29.

    Murata, T.: Petri nets: properties, analysis and applications. Proc IEEE. 77(4), 541–580 (1989)

    Article  Google Scholar 

  30. 30.

    Hrúz, B., Zhou, M.: Modeling and control of discrete-event dynamic systems: with petri nets and other tools. Springer Science & Business Media, London (2007)

  31. 31.

    Liu, D., Li, Z., Zhou, M.: Hybrid liveness-enforcing policy for generalized petri net models of flexible manufacturing systems. IEEE Trans Syst Man, Cybern Part ASystems Humans. 43(1), 85–97 (2013)

    Article  Google Scholar 

  32. 32.

    Ng, K.M., Bin, M., Reaz, I., Alauddin, M., Ali, M.: A Review on the Applications of Petri Nets in Modeling. Analysis , and Control of Urban Traffic. 14(2), 858–870 (2013)

    Google Scholar 

  33. 33.

    G. F. List and M. Cetin, “Modeling Traffic Signal Control Using Petri Nets,” vol. 5, no. 3, pp. 177–187, 2004.

  34. 34.

    Badamchizadeh, M.A., Joroughi, M.: Deterministic and stochastic Petri Net for urban traffic systems. 2010 2nd Int Conf Comput Autom Eng. 5, 364–368 (2010)

    Google Scholar 

  35. 35.

    Di Febbraro, A., Giglio, D., Sacco, N.: A deterministic and stochastic petri net model for traffic-responsive signaling control in urban areas. IEEE Trans Intell Transp Syst. 17(2), 510–524 (2016)

    Article  Google Scholar 

  36. 36.

    Huang, Y.-S., Weng, Y.-S., Zhou M.: Modular design of urban traffic-light control systems based on synchronized timed Petri nets. IEEE Trans Intell Transp Syst. 15(2), 530–539 (2014)

  37. 37.

    Alla, H., David, R.: A modelling and analysis tool for discrete events systems: continuous petri net. Perform Eval. 33, 175–199 (1998)

    Article  Google Scholar 

  38. 38.

    Júlvez, J., Boel, R.: Modelling and controlling traffic behaviour with continuous Petri nets. IFAC Proceedings. 38(1), 43–48 (2005)

  39. 39.

    Júlvez, J., Boel, R.: A continuous petri net approach for model predictive control of traffic systems. Ieee Trans Syst Cybern. 40(4), 686–697 (2010)

    Article  Google Scholar 

  40. 40.

    David, R., Alla H.: Discrete, continuous, and hybrid Petri nets. Springer Science & Business Media, Heidelberg (2010)

  41. 41.

    Di Febbraro, A., Sacco, N.: On modelling urban transportation networks via hybrid petri nets. Control Eng Pract. 12(10), 1225–1239 (2004)

    Article  Google Scholar 

  42. 42.

    M. K. Jbira and M. Ahmed, “Computer Simulation: A Hybrid Model for Traffic Signal Optimisation,” vol. 7, no. 1, pp. 1–16, 2011.

  43. 43.

    Chen, F., Wang, L., Jiang, B., Wen, C.: A novel hybrid petri net model for urban intersection and its application in signal control strategy. J Frankl Inst. 351(8), 4357–4380 (2014)

    MathSciNet  Article  MATH  Google Scholar 

  44. 44.

    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theor Comput Sci. 138(1), 3–34 (Feb. 1995)

    MathSciNet  Article  MATH  Google Scholar 

  45. 45.

    Zhao, X., Chen, Y.: Traffic light control method for a single intersection based on hybrid systems. Proc 2003 I.E. Int Conf Intell Transp Syst. 2, 1105–1109 (2003)

    Google Scholar 

  46. 46.

    Herman Sutarto and René Boel, “Hybrid Automata Model Approach for Coordinating Traffic Signal Control Herman Sutarto and René Boel SYSTeMS Research Group , Department of EESA , University of Ghent Intersection-1 Intersection-2 References: 1 . E . Lefeber and J. E Rooda, Controller d,” vol. 363, p. 01, 2010.

  47. 47.

    Chen, Y., Li, W., Guo, Y., Wu, Y.: Dynamic Graph Hybrid Automata: A Modeling Method for Traffic Network. 2015 I.E. 18th Int Conf Intell Transp Syst. 1396–1401 (2015)

  48. 48.

    A. T. Sava and H. Alla, “Combining Hybrid Petri Nets and Hybrid Automata,” vol. 17, no. 5, pp. 670–678, 2001.

  49. 49.

    H. Motallebi and M. A. Azgomi, “Translation from Multisingular Hybrid Petri Nets to Multisingular Hybrid Automata *,” Fundam. Informaticae, vol. 130, no. October 2012, pp. 275–315, 2014.

  50. 50.

    Ghomri, L., Alla, H., Sari, Z.: Structural and hierarchical translation of hybrid Petri nets in hybrid automata. IMACS05 (2005)

  51. 51.

    Zhang, M., Jia, L., Zhu, W.: A cell-based robust optimal coordinated control on urban arterial road. J Control Theory Appl. 10(4), 543–548 (2012)

    MathSciNet  Article  Google Scholar 

  52. 52.

    Tolba, C., et al.: Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modelling. Simul Model Pract Theory. 13(5), 407–436 (2005)

  53. 53.

    Ghomri, L., Alla, H.: Modeling and analysis using hybrid petri nets. Nonlinear Anal Hybrid Syst. 1(2), 141–153 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  54. 54.

    Henzinger, T.a., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? J Comput Syst Sci. 57(1), 94–124 (1998)

    MathSciNet  Article  MATH  Google Scholar 

  55. 55.

    Ghomri, L., Alla, H.: Continuous flow systems and control methodology using hybrid petri nets. Control Eng Appl Inf 15(4), 106–116 (2013)

  56. 56.

    G. Frehse, “PHAVer: Algorithmic Verification of Hybrid Systems past HyTech,” no. Hscc 2005, pp. 258–273, 2006.

  57. 57.

    Bouriachi, F., Kechida, S.: Hybrid petri nets and hybrid automata for modeling and control of two adjacent oversaturated intersections. Journal of Control, Automation and Electrical Systems. 27(6), 646–657 (Sep. 2016)

    Article  Google Scholar 

  58. 58.

    Bouriachi, F., Kechida, S.: “Control of large-scale urban traffic networks using hierarchical hybrid automata,” 2016 8th International Conference on Modelling, Identification and Control (ICMIC), Algiers. 751–756 (2016). doi:10.1109/ICMIC.2016.7804212

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This work was performed as part of a Tassili project in cooperation between Gipsa-Lab Grenoble, France and LAIG laboratory, Guelma, Algeria. This research is funded by LAIG laboratory. The authors would like to thank Pr H. Alla and Pr H. Tebbikh for their valuable advices and their assistance. The authors are grateful to the anonymous referee for a careful checking of the details and for helpful comments that improve this paper.

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Bouriachi, F., Kechida, S. Modelling and Analysis of Oversaturated Intersections Using Jointly Hybrid Petri net and Hybrid Automata. Int. J. ITS Res. 16, 138–150 (2018).

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  • Modelling
  • Hybrid petri net
  • Hybrid automata
  • Reachability analysis
  • Oversaturated intersections
  • Signal timing coordination
  • Traffic control