Abstract
We consider the existence, characterization, and calculation of equilibria in transportation networks, when the route capacities and demand requirements depend on time. The problem is situated in a Banach space setting and formulated in terms of a variational inequality.
Similar content being viewed by others
References
Maugeri, A., Optimization Problems with Side Constraints and Generalized Equilibrium Principles, Le Matematiche, Vol. 49, pp. 305–312, 1994.
Maugeri, A., Monotone and Nonmonotone Variational Inequalities, Rendiconti del Circolo Matematico di Palermo, Serie 2, Supplemento, Vol. 48, pp. 179–184, 1997.
Maugeri, A., Dynamic Models and Generalized Equilibrium Problems, New Trends in Mathematical Programming, Edited by F. Giannessi et al., Kluwer, Dordrecht, Holland, pp. 191–202, 1998.
Maugeri, A., Oettli, W., and SchlÄger, D., A Flexible Form of Wardrop's Principle for Traffic Equilibria with Side Constraints, Rendiconti del Circolo Matematico di Palermo, Serie 2, Supplemento, Vol. 48, pp. 185–193, 1997.
Smith, M. J., A New Dynamic Traffic Model and the Existence and Calculation of Dynamic User Equilibria on Congested Capacity-Constrained Road Networks, Transportation Research, Vol. 27B, pp. 49–63, 1993.
Schaefer, H. H., Topological Vector Spaces, Springer, New York, New York, 1971.
Ferrari, P., Equilibrium in Asymmetric Multimodal Transport Networks with Capacity Constraints, Le Matematiche, Vol. 49, pp. 223–241, 1994.
Larsson, T., and Patriksson, M., Equilibrium Characterizations of Solutions to Side-Constrained Asymmetric Traffic Assignment Models, Le Matematiche Vol. 49, pp. 249–280, 1994.
Oettli, W., and SchlÄger, D., Generalized Vectorial Equilibria and Generalized Monotonicity, Functional Analysis with Current Applications, Edited by M. Brokate and A. H. Siddiqi, Longman, Harlow, England, pp. 145–154, 1998.
Conway, J. B., A Course in Functional Analysis, 2nd Edition, Springer, New York, New York, 1990.
Auslender, A., Optimisation: Méthodes Numériques, Masson, Paris, France, 1976.
Oettli, W., An Iterative Method, Having Linear Rate of Convergence, for Solving a Pair of Dual Linear Programs, Mathematical Programming, Vol. 3, pp. 302–311, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Daniele, P., Maugeri, A. & Oettli, W. Time-Dependent Traffic Equilibria. Journal of Optimization Theory and Applications 103, 543–555 (1999). https://doi.org/10.1023/A:1021779823196
Issue Date:
DOI: https://doi.org/10.1023/A:1021779823196