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Advances in Dynamic Traffic Assgmnt: TAC

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  • Wen-Long Jin

Abstract

Traditionally traffic assignment problems (TAPs) have been formulated as non-cooperative games (NCGs), and Wardrop’s user equilibrium (UE) of a TAP as Nash equilibrium (NE) of the corresponding NCG. In this study, in contrast, we propose a mapping from finite NCGs (F-NCGs) to asymmetric TAPs (A-TAPs) on a two-way or urban network, in which the travel cost of one link depends on flows on other links. With the help of three route-based formulations of UE, we show that NE of an F-NCG is equivalent to UE of the corresponding A-TAP. Based on the new relationship, we extend Nash’s fixed point formulation of NE to prove the existence of static UE. This study provides a more complete picture of the relationships between NCGs and TAPs. In the future we will be interested in studying Nash’s fixed point formulation for dynamic UE. Copyright Springer Science+Business Media New York 2015

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  • Wen-Long Jin, 2015. "Advances in Dynamic Traffic Assgmnt: TAC," Networks and Spatial Economics, Springer, vol. 15(3), pages 617-634, September.
    • Handle: RePEc:kap:netspa:v:15:y:2015:i:3:p:617-634
    DOI: 10.1007/s11067-014-9250-x
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    1. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    2. Carlos F. Daganzo, 1998. "Queue Spillovers in Transportation Networks with a Route Choice," Transportation Science, INFORMS, vol. 32(1), pages 3-11, February.
    3. Heydecker, B. G., 1986. "On the definition of traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 20(6), pages 435-440, December.
    4. Robert Gibbons, 1997. "An Introduction to Applicable Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 127-149, Winter.
    5. Smith, M. J., 1984. "Two alternative definitions of traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 63-65, February.
    6. Iryo, Takamasa, 2011. "Multiple equilibria in a dynamic traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 45(6), pages 867-879, July.
    7. Devarajan, Shantayanan, 1981. "A note of network equilibrium and noncooperative games," Transportation Research Part B: Methodological, Elsevier, vol. 15(6), pages 421-426, December.
    8. Jin, Wen-Long, 2007. "A dynamical system model of the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 32-48, January.
    9. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    10. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    11. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "A model and an algorithm for the dynamic traffic assignment problems," LIDAM Reprints CORE 346, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. 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.
    13. Stella C. Dafermos, 1971. "An Extended Traffic Assignment Model with Applications to Two-Way Traffic," Transportation Science, INFORMS, vol. 5(4), pages 366-389, November.
    14. Milchtaich, Igal, 2004. "Social optimality and cooperation in nonatomic congestion games," Journal of Economic Theory, Elsevier, vol. 114(1), pages 56-87, January.
    15. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    16. David E. Boyce & Hani S. Mahmassani & Anna Nagurney, 2005. "A retrospective on Beckmann, McGuire and Winsten's Studies in the Economics of Transportation," Papers in Regional Science, Wiley Blackwell, vol. 84(1), pages 85-103, March.
    17. Stella C. Dafermos, 1972. "The Traffic Assignment Problem for Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 6(1), pages 73-87, February.
    18. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    19. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Patrice Marcotte & Laura Wynter, 2004. "A New Look at the Multiclass Network Equilibrium Problem," Transportation Science, INFORMS, vol. 38(3), pages 282-292, August.
    21. David Bernstein & Tony E. Smith, 1994. "Equilibria for Networks with Lower Semicontinuous Costs: With an Application to Congestion Pricing," Transportation Science, INFORMS, vol. 28(3), pages 221-235, August.
    22. Deepak K. Merchant & George L. Nemhauser, 1978. "A Model and an Algorithm for the Dynamic Traffic Assignment Problems," Transportation Science, INFORMS, vol. 12(3), pages 183-199, August.
    23. Han, Ke & Friesz, Terry L. & Yao, Tao, 2013. "Existence of simultaneous route and departure choice dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 17-30.
    24. Smith, M. J., 1979. "Traffic control and route-choice; a simple example," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 289-294, December.
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    Cited by:

    1. 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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