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Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks

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  • Takashi Akamatsu

    (Graduate School of Information Sciences, Tohoku University, Aoba, Sendai, Miyagi 980-8579, Japan)

  • Benjamin Heydecker

    (Centre for Transport Studies, University College London, Gower Street, London, WC1E 6BT, England)

Abstract

Creation of a new link or increase in capacity of an existing link can reduce the efficiency of a congested network as measured by the total travel cost. This phenomenon, of which an extreme example is given by Braess paradox, has been examined in conventional studies within the framework of static assignment. For dynamic traffic assignment, which makes account of the effect of congestion through explicit representation of queues, Akamatsu (2000) gave a simple example of the occurrence of this paradox. The present paper extends that result to a more general network. We first present a necessary and sufficient condition for the paradox to occur in a general network in which there is a queue on each link. We then give a graph-theoretic interpretation of the condition, which gives us a convenient method to test whether or not the paradox will occur by performing certain tests on information that describes the network structure. Finally, as an application of this theory, we examine several example networks and queueing patterns where occurrence of this paradox is inevitable.

Suggested Citation

  • Takashi Akamatsu & Benjamin Heydecker, 2003. "Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks," Transportation Science, INFORMS, vol. 37(2), pages 123-138, May.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:2:p:123-138
    DOI: 10.1287/trsc.37.2.123.15245
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    References listed on IDEAS

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    Cited by:

    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. Wei-Hua Lin & Hong K. Lo, 2009. "Investigating Braess' Paradox with Time-Dependent Queues," Transportation Science, INFORMS, vol. 43(1), pages 117-126, February.
    3. 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.
    4. Wada, Kentaro & Satsukawa, Koki & Smith, Mike & Akamatsu, Takashi, 2019. "Network throughput under dynamic user equilibrium: Queue spillback, paradox and traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 391-413.
    5. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.
    6. Zhao, Chunxue & Fu, Baibai & Wang, Tianming, 2014. "Braess paradox and robustness of traffic networks under stochastic user equilibrium," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 135-141.
    7. Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.

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