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Optimization formulations and static equilibrium in congested transportation networks

Author

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  • A. de Palma
  • Y. Nesterov

Abstract

In this paper we study the concepts of equilibrium and optimum in static transportation networks with elastic and non-elastic demands. The main mathematical tool of our paper is the theory of variational inequalities. We demonstrate that this theory is useful for proving the existence theorems. It also can justify Beckmann's formulation of the equilibrium problem.The main contribution of this paper is to propose a new definition of equilibrium, the normal equilibrium, which exists under very general assumptions. This concept can be used, in particular, when the travel costs are discontinuous and unbounded. As examples we consider the models of signalized intersections, traffic lights and unbounded travel-time relationships. For some of those cases, the standard concepts of user and Wardrop equilibria cannot be used.
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Suggested Citation

  • A. de Palma & Y. Nesterov, 1997. "Optimization formulations and static equilibrium in congested transportation networks," Thema Working Papers 97-17, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:97-17
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    Cited by:

    1. NESTEROV, Yu & de PALMA, André, 2000. "Stable dynamics in transportation systems," LIDAM Discussion Papers CORE 2000027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mahdi Takalloo & Changhyun Kwon, 2019. "On the Price of Satisficing in Network User Equilibria," Papers 1911.07914, arXiv.org.
    3. Erik T. Verhoef, 2000. "Second-Best Congestion Pricing in General Networks - Algorithms for Finding Second-Best Optimal Toll Levels and Toll Points," Tinbergen Institute Discussion Papers 00-084/3, Tinbergen Institute.
    4. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500068 is not listed on IDEAS
    5. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    6. Correa, Jose R. & Schulz, Andreas S. & Stier Moses, Nicolas E., 2003. "Selfish Routing in Capacitated Networks," Working papers 4319-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Fernando Ordóñez & Nicolás E. Stier-Moses, 2010. "Wardrop Equilibria with Risk-Averse Users," Transportation Science, INFORMS, vol. 44(1), pages 63-86, February.
    8. Verhoef, Erik T., 2002. "Second-best congestion pricing in general static transportation networks with elastic demands," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 281-310, May.
    9. Correa, José R. & Schulz, Andreas S. & Stier-Moses, Nicolás E., 2008. "A geometric approach to the price of anarchy in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 457-469, November.
    10. Bliemer, Michiel C.J. & Raadsen, Mark P.H. & Smits, Erik-Sander & Zhou, Bojian & Bell, Michael G.H., 2014. "Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 363-384.
    11. Verhoef, Erik T., 2002. "Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 707-729, September.
    12. Chai, Huajun, 2019. "Dynamic Traffic Routing and Adaptive Signal Control in a Connected Vehicles Environment," Institute of Transportation Studies, Working Paper Series qt9ng3z8vn, Institute of Transportation Studies, UC Davis.
    13. Verhoef, Erik Teodoor, 2000. "The Generalized Second-Best Network Congestion Pricing Problem," ERSA conference papers ersa00p336, European Regional Science Association.

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