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Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network

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  • Takamasa Iryo

Abstract

Uniqueness is an important characteristic of network user equilibrium. Uniqueness in dynamic user equilibrium (DUE) has been shown to exist under certain conditions, whereas a case with multiple Wardrop equilibria has been found in a twofold symmetric network with two bottlenecks. This setting is very special, and therefore, it is worthwhile to investigate the factors that are essential to obtain non-unique solutions in this case in order to discuss the implication of this special example for real network problems. The asymmetric structure of the network, stochastic user equilibrium (SUE), and whole-link model were employed to check whether these factors affect the existence of multiple equilibria. It was shown that placing bottlenecks with equivalent capacities causes the singularity of the linear equation system that describes Wardrop’s first principle in a particular network structure called as a loopy network. Then, it was shown that this singularity causes the existence of multiple equilibria. On the other hand, this singularity was not found in SUE or the whole-link cases, and therefore, non-unique solutions were not found in them. It was also shown that the singularity does not appear to be the only source of non-uniqueness by presenting another example in which at least three equilibrium solutions exists when either the bottleneck model or the whole-link model is employed. Copyright Springer Science+Business Media New York 2015

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  • Takamasa Iryo, 2015. "Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network," Networks and Spatial Economics, Springer, vol. 15(3), pages 599-616, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:599-616
    DOI: 10.1007/s11067-013-9206-6
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    References listed on IDEAS

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    1. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    2. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    3. 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.
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    Cited by:

    1. Zhiyuan Liu & Wen Yi & Shuaian Wang & Jun Chen, 2017. "On the Uniqueness of User Equilibrium Flow with Speed Limit," Networks and Spatial Economics, Springer, vol. 17(3), pages 763-775, September.
    2. 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.
    3. Iryo, Takamasa, 2016. "Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 88-103.
    4. Iryo, Takamasa & Smith, Michael J., 2018. "On the uniqueness of equilibrated dynamic traffic flow patterns in unidirectional networks," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 757-773.
    5. Yasushi Masuda & Akira Tsuji, 2019. "Congestion Control for a System with Parallel Stations and Homogeneous Customers Using Priority Passes," Networks and Spatial Economics, Springer, vol. 19(1), pages 293-318, March.

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