On the existence of solutions to the dynamic user equilibrium problem

Transportation Science

Volumn 34, Issue 4, 2000, Pages 402-414

  Zhu, Daoli ^a   Marcotte, Patrice ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DYNAMIC PROGRAMMING; PROBLEM SOLVING;

DYNAMIC NETWORK EQUILIBRIUM PROBLEM (DNEP);

AIR TRAFFIC CONTROL;

EID: 0034314162     PISSN: 00411655     EISSN: None     Source Type: Journal    
DOI: 10.1287/trsc.34.4.402.12322     Document Type: Article

References (20)

1. V. ASTARITA, "A Continuous Time Link Model for Dynamic Network Loading Based on Travel Time Function," in Proceedings of the 13th International Symposium on Transportation and Traffic Theory, J.-B. Lesort (ed.), 1996.
2. M. BEN-AKIVA, M. CYNA, AND A. DE PALMA, "Dynamic Models of Peak Period Congestion," Transp. Res. B 18B, 339-355 (1984).
3. M. BEN-AKIVA, "Dynamic Network Equilibrium Research," Transp. Res. A 19A, 429-431 (1985).
4. C. DAGANZO, "Properties of Link Travel Time Functions under Dynamic Loads," Transp. Res. B 29B, 95-98 (1995).
5. O. DRISSI-KAÏTOUNI AND M. GENDREAU, "A New Dynamic Traffic Assignment Model," Publication 854, Centre de recherche sur les transports, Université de Montréal, Montréal, 1992.
6. T. L. FRIESZ, D. BERNSTEIN, T. E. SMITH, R. L. TOBIN, AND B. W. WEI, "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Opns. Res. 41, 179-191 (1993).
7. T. L. FRIESZ, F. J. LUQUE, R. L. TOBIN, AND B. W. WEI, "Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem," Opns. Res. 6, 893-901 (1989).
8. S. KARAMARDIAN AND S. SCHAIBLE, "Seven Kinds of Monotone Maps," J. Optim. Theory Appl. 66, 37-46 (1990).
9. A. N. KOLMOGOROV AND S. V. FOMIN, Introductory Real Analysis, Prentice-Hall, (1970).
10. J.-L. LIONS, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Paris (1969).
11. H. S. MAHMASSANI AND R. HERMAN, "Dynamic User Equilibrium Departure Time and Route Choice on Idealized Traffic Arterias," Transp. Sci. 18, 362-384 (1984).
12. P. MARCOTTE AND D. L. ZHU, "Equilibria with Infinitely Many Differentiated Classes of Customers," in Complementarity and Variational Problems, Proceedings of the 13th International Conference on Complementarity Problems: Engineering and Economics and Applications and Computational Methods, J.-S. Pang and M. Ferris (eds.), 234-258. SIAM, Philadelphia (1997).
13. D. K. MERCHANT AND G. L. NEMHAUSER, "A Model and Algorithm for the Dynamic Traffic Assignment Problem," Transp. Sci. 12, 182-199 (1978).
14. A. MUKHERJEA AND K. POTHOVEN, Real and Functional Analysis, Plenum Press, New York (1978).
15. B. RAN, R. W. HALL, AND D. E. BOYCE, "A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice," Transp. Res. B 30B, 31-46 (1996).
16. H. L. ROYDEN, Real Analysis, MacMillan, 1968.
17. M. J. SMITH, "A New Dynamic Traffic Model and the Existence and Calculation of Dynamic User Equilibria on Congested Capacity-Constrained Road Network," Transp. Res. B 27B, 49-63 (1993).
18. M. J. SMITH AND M. B. WISTEN, "Liapunov Methods for Dynamic Equilibrium Traffic Assignment," in Proceedings of the second Meeting of the EURO working group on Urban Traffic and Transportations, 223-245, INRETS, Paris, 1994.
19. B. W. WIE, R. L. TOBIN, T. L. FRIESZ, AND D. BERNSTEIN, "A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem," Transp. Res. B 29B, 79-92 (1995).
20. Y. W. XU, J. H. WU, M. FLORIAN, P. MARCOTTE, AND D. L. ZHU, "Advances in the Continuous Dynamic Network Loading Problem," Transp. Sci. 33, 341-353 (1999).