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Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System

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  • Wenyi Zhang
  • Wei Guan
  • Jihui Ma
  • Tao Wang

Abstract

This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors.

Suggested Citation

  • Wenyi Zhang & Wei Guan & Jihui Ma & Tao Wang, 2013. "Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, May.
    • Handle: RePEc:hin:jnddns:162128
    DOI: 10.1155/2013/162128
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    1. 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.
    2. Zhang, Ding & Nagurney, Anna & Wu, Jiahao, 2001. "On the equivalence between stationary link flow patterns and traffic network equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 731-748, September.
    3. 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.
    4. 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.
    5. 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.
    6. Mounce, Richard & Carey, Malachy, 2011. "Route swapping in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 102-111, January.
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