Optimization formulations and static equilibrium in congested transportation networks
AbstractIn 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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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1998061.
Date of creation: 01 Jul 1998
Date of revision:
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Other versions of this item:
- 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), Université de Cergy-Pontoise.
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- 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.
- 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.
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"Stable dynamics in transportation systems,"
CORE Discussion Papers
2000027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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- 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.
- 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.
- Erik T. Verhoef, 2000.
"Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demands,"
Tinbergen Institute Discussion Papers
00-078/3, Tinbergen Institute.
- 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.
- Erik T. Verhoef, 1998. "Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demand," Tinbergen Institute Discussion Papers 98-086/3, Tinbergen Institute.
- 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.
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