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Traffic Equilibrium with Responsive Traffic Control

Author

Listed:
  • M. J. Smith

    (University of York, Heslington, York YO1 5DD, U.K.)

  • T. van Vuren

    (Institute for Transport Studies, University of Leeds, Leeds LS2 9JT, U.K.)

Abstract

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on “day” 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on “day 2” the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on “day” 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern…. We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of (flow, control) pairs such that (i) the flow is a user equilibrium and (ii) the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions—we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way from satisfying our conditions; and seeking to satisfy them with this delay formula leads us to two novel control policies. We assume throughout that demand is determined by a fixed OD matrix, giving the steady total flow rates for each OD pair. We also suppose that network characteristics do not change; so that incidents are not considered and saturation flows, for example, are constant.

Suggested Citation

  • M. J. Smith & T. van Vuren, 1993. "Traffic Equilibrium with Responsive Traffic Control," Transportation Science, INFORMS, vol. 27(2), pages 118-132, May.
    • Handle: RePEc:inm:ortrsc:v:27:y:1993:i:2:p:118-132
    DOI: 10.1287/trsc.27.2.118
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    Citations

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    Cited by:

    1. D’Acierno, Luca & Gallo, Mariano & Montella, Bruno, 2012. "An Ant Colony Optimisation algorithm for solving the asymmetric traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 217(2), pages 459-469.
    2. Liu, Ronghui & Smith, Mike, 2015. "Route choice and traffic signal control: A study of the stability and instability of a new dynamical model of route choice and traffic signal control," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 123-145.
    3. Cipriani, Ernesto & Fusco, Gaetano, 2004. "Combined signal setting design and traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 155(3), pages 569-583, June.
    4. Castillo González, Rodrigo & Clempner, Julio B. & Poznyak, Alexander S., 2019. "Solving traffic queues at controlled-signalized intersections in continuous-time Markov games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 283-297.
    5. Yu, Hao & Ma, Rui & Zhang, H. Michael, 2018. "Optimal traffic signal control under dynamic user equilibrium and link constraints in a general network," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 302-325.
    6. Smith, M.J. & Liu, R. & Mounce, R., 2015. "Traffic control and route choice: Capacity maximisation and stability," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 863-885.
    7. Smith, Mike & Mounce, Richard, 2011. "A splitting rate model of traffic re-routeing and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1389-1409.
    8. Michael Patriksson & R. Tyrrell Rockafellar, 2002. "A Mathematical Model and Descent Algorithm for Bilevel Traffic Management," Transportation Science, INFORMS, vol. 36(3), pages 271-291, August.
    9. Smith, Michael J & Viti, Francesco & Huang, Wei & Mounce, Richard, 2023. "With spatial queueing, the P0 responsive traffic signal control policy may fail to maximise network capacity even if queue storage capacities are very large," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    10. Lee, Seunghyeon & Wong, S.C. & Varaiya, Pravin, 2017. "Group-based hierarchical adaptive traffic-signal control part I: Formulation," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 1-18.
    11. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    12. Claudio Meneguzzer, 1998. "Stochastic user equilibrium assignment with traffic-responsive signal control," ERSA conference papers ersa98p337, European Regional Science Association.
    13. Evers, Ruth & Proost, Stef, 2015. "Optimizing intersections," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 100-119.
    14. Maher, Michael J. & Zhang, Xiaoyan & Vliet, Dirck Van, 2001. "A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 23-40, January.
    15. Wang, Guangmin & Xu, Meng & Grant-Muller, Susan & Gao, Zaihan, 2020. "Combination of tradable credit scheme and link capacity improvement to balance economic growth and environmental management in sustainable-oriented transport development: A bi-objective bi-level progr," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 459-471.
    16. Guo, Jianhua & Kong, Ye & Li, Zongzhi & Huang, Wei & Cao, Jinde & Wei, Yun, 2019. "A model and genetic algorithm for area-wide intersection signal optimization under user equilibrium traffic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 92-104.
    17. Ennio Cascetta & Mariano Gallo & Bruno Montella, 2006. "Models and algorithms for the optimization of signal settings on urban networks with stochastic assignment models," Annals of Operations Research, Springer, vol. 144(1), pages 301-328, April.
    18. Lin Xiao & Hong Lo, 2015. "Combined Route Choice and Adaptive Traffic Control in a Day-to-day Dynamical System," Networks and Spatial Economics, Springer, vol. 15(3), pages 697-717, September.
    19. Lee, Seunghyeon & Wong, S.C., 2017. "Group-based approach to predictive delay model based on incremental queue accumulations for adaptive traffic control systems," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 1-20.
    20. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    21. Wang, Guangmin & Gao, Ziyou & Xu, Meng & Sun, Huijun, 2014. "Joint link-based credit charging and road capacity improvement in continuous network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 67(C), pages 1-14.

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