On the Existence of Solutions to the Dynamic User Equilibrium Problem

References

• Astarita V., Lesort J.-B. A Continuous Time Link Model for Dynamic Network Loading Based on Travel Time Function. Proceedings of the 13th International Symposium on Transportation and Traffic Theory (1996) Google Scholar
• Ben-Akiva M., Cyna M., De Palma A. Dynamic Models of Peak Period Congestion. Transp. Res. B (1984) 18B:339–355Crossref, Google Scholar
• Ben-Akiva M. Dynamic Network Equilibrium Research. Transp. Res. A (1985) 19A:429–431Crossref, Google Scholar
• Daganzo C. Properties of Link Travel Time Functions under Dynamic Loads. Transp. Res. B (1995) 29B:95–98Crossref, Google Scholar
• Drissi-KaÏtouni O., Gendreau M. A New Dynamic Traffic Assignment Model. (1992) . Publication 854, Centre de recherche sur les transports, Université de Montréal, MontréalGoogle Scholar
• Friesz T. L., Bernstein D., Smith T. E., Tobin R. L., Wei B. W. A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem. Opns. Res. (1993) 41:179–191Link, Google Scholar
• Friesz T. L., Luque F. J., Tobin R. L., Wei B. W. Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem. Opns. Res. (1989) 6:893–901Link, Google Scholar
• Karamardian S., Schaible S. Seven Kinds of Monotone Maps. J. Optim. Theory Appl. (1990) 66:37–46Crossref, Google Scholar
• Kolmogorov A. N., Fomin S. V.Introductory Real Analysis (1970) (Prentice-Hall)Google Scholar
• Lions J.-L.Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (1969) (Dunod, Paris) Google Scholar
• Mahmassani H. S., Herman R. Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterias. Transp. Sci. (1984) 18:362–384Link, Google Scholar
• Marcotte P., Zhu D. L., Pang J.-S., Ferris M. Equilibria with Infinitely Many Differentiated Classes of Customers. Complementarity and Variational Problems, Proceedings of the 13th International Conference on Complementarity Problems: Engineering and Economics and Applications and Computational Methods (1997) SIAM, Philadelphia:234–258Google Scholar
• Merchant D. K., Nemhauser G. L. A Model and Algorithm for the Dynamic Traffic Assignment Problem. Transp. Sci. (1978) 12:182–199Google Scholar
• Mukherjea A., Pothoven K.Real and Functional Analysis (1978) (Plenum Press, New York) Crossref, Google Scholar
• Ran B., Hall R. W., Boyce D. E. A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice. Transp. Res. B (1996) 30B:31–46Crossref, Google Scholar
• Royden H. L.Real Analysis (1968) (MacMillan)Google Scholar
• Smith M. J. A New Dynamic Traffic Model and the Existence and Calculation of Dynamic User Equilibria on Congested Capacity-Constrained Road Network. Transp. Res. B (1993) 27B:49–63Crossref, Google Scholar
• Smith M. J., Wisten M. B. Liapunov Methods for Dynamic Equilibrium Traffic Assignment. Proceedings of the second Meeting of the EURO working group on Urban Traffic and Transportations (1994) INRETS, Paris:223–245Google Scholar
• Wie B. W., Tobin R. L., Friesz T. L., Bernstein D. A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem. Transp. Res. B (1995) 29B:79–92Google Scholar
• Xu Y. W., Wu J. H., Florian M., Marcotte P., Zhu D. L. Advances in the Continuous Dynamic Network Loading Problem. Transp. Sci. (1999) 33:341–353Link, Google Scholar