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Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions

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  • Lie Han

    (Wuhan Textile University)

Abstract

This paper proposes a dynamic process to formulate the day-to-day evolution process of traffic flows, which is called “proportional-switch adjustment process with elastic demand (PSAP-ED)”. PSAP-ED extends Smith’s process (Smith in Transp Sci 18:259–304, 1984) from the case of fixed demand to the case of elastic demand and characterizes the process of approaching equilibrium states from non-equilibrium states in traffic networks. Several desirable properties of PSAP-ED are provided, such as the equivalence between user equilibrium and the stationary state of PSAP-ED, the existence and uniqueness of the stationary flow state, and the convergence of PSAP-ED. We also show that a proper fixed toll scheme can drive PSAP-ED to evolve towards system optimum states. When the demand functions are unknown, the trial-and-error procedure presented by Yang et al. (Transp Res B 38:477–493, 2004) can be modified and applied in the context of PSAP-ED. Furthermore, we develop a more efficient dynamic congestion toll scheme for PSAP-ED in the absence of demand functions. The properties of PSAP-ED and the effectiveness of toll schemes are demonstrated by a numerical example.

Suggested Citation

  • Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:4:d:10.1007_s11067-022-09565-w
    DOI: 10.1007/s11067-022-09565-w
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    1. Ye, Hongbo & Yang, Hai & Tan, Zhijia, 2015. "Learning marginal-cost pricing via a trial-and-error procedure with day-to-day flow dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 794-807.
    2. Guo, Ren-Yong & Szeto, W.Y. & Long, Jiancheng, 2020. "Trial-and-error operation schemes for bimodal transport systems," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 106-123.
    3. Terry L. Friesz & David Bernstein & Nihal J. Mehta & Roger L. Tobin & Saiid Ganjalizadeh, 1994. "Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems," Operations Research, INFORMS, vol. 42(6), pages 1120-1136, December.
    4. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    5. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    6. Feng Xiao & Minyu Shen & Zhengtian Xu & Ruijie Li & Hai Yang & Yafeng Yin, 2019. "Day-to-Day Flow Dynamics for Stochastic User Equilibrium and a General Lyapunov Function," Transportation Science, INFORMS, vol. 53(3), pages 683-694, May.
    7. Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
    8. William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 667-689.
    9. Wang, Xiaolei & Yang, Hai, 2012. "Bisection-based trial-and-error implementation of marginal cost pricing and tradable credit scheme," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1085-1096.
    10. Terry L. Friesz & David Bernstein & Roger Stough, 1996. "Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows," Transportation Science, INFORMS, vol. 30(1), pages 14-31, February.
    11. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.
    12. Watling, David, 1999. "Stability of the stochastic equilibrium assignment problem: a dynamical systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 281-312, May.
    13. Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    14. Hazelton, Martin L., 2002. "Day-to-day variation in Markovian traffic assignment models," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 637-648, August.
    15. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
    16. 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.
    17. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    18. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    19. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    20. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    21. Yang, Hai & Meng, Qiang & Lee, Der-Horng, 2004. "Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 477-493, July.
    22. Mounce, Richard & Carey, Malachy, 2011. "Route swapping in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 102-111, January.
    23. Iryo, Takamasa & Smith, Michael J. & Watling, David, 2020. "Stabilisation strategy for unstable transport systems under general evolutionary dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 136-151.
    24. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    25. Guo, Xiaolei, 2013. "Toll sequence operation to realize target flow pattern under bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 203-216.
    26. 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.
    27. Han, Deren & Yang, Hai, 2009. "Congestion pricing in the absence of demand functions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(1), pages 159-171, January.
    28. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    29. Zhong, R.X. & Xie, X.X. & Luo, J.C. & Pan, T.L. & Lam, W.H.K. & Sumalee, A., 2020. "Modeling double time-scale travel time processes with application to assessing the resilience of transportation systems," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 228-248.
    30. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    31. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    32. Zhou, Bojian & Bliemer, Michiel & Yang, Hai & He, Jie, 2015. "A trial-and-error congestion pricing scheme for networks with elastic demand and link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 77-92.
    33. 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.
    34. Mounce, Richard, 2006. "Convergence in a continuous dynamic queueing model for traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 779-791, November.
    35. Richard Mounce, 2007. "Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone," Transportation Science, INFORMS, vol. 41(3), pages 409-504, August.
    36. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    37. Wang, Shuaian & Zhang, Wei & Qu, Xiaobo, 2018. "Trial-and-error train fare design scheme for addressing boarding/alighting congestion at CBD stations," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 318-335.
    38. Richard Mounce & Malachy Carey, 2015. "On the Convergence of the Method of Successive Averages for Calculating Equilibrium in Traffic Networks," Transportation Science, INFORMS, vol. 49(3), pages 535-542, August.
    39. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
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