On the relationship between dynamic Nash and instantaneous user equilibria

Networks

Volumn 32, Issue 2, 1998, Pages 141-163

  Wie, Byung Wook ^a   Tobin, Roger L ^b  

^a UNIVERSITY OF HAWAII   (United States)

^b VERIZON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001120201     PISSN: 00283045     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0037(199809)32:2<141::AID-NET7>3.0.CO;2-B     Document Type: Article

References (39)

1. T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory. Academic Press, New York (1982).
2. D. E. Boyce, B. Ran, and L. J. LeBlanc, Solving an instantaneous dynamic user-optimal route choice model. Trans. Sci. 29 (1995) 128-142.
3. B. M. Budak, E. M. Berkovich, and E. N. Solov'eva, Difference approximations in optimal control problems. SIAM J. Control 7 (1969) 18-31.
4. M. Carey, Optimal time-varying flows on congested networks. Oper. Res. 35 (1987) 58-69.
5. M. Carey and A. Srinivasan, Externalities, average and marginal costs, and tolls on congested networks with time-varying flows. Oper. Res. 41 (1993) 217-231.
6. J. Cullum, Discrete approximations to continuous optimal control problems. SIAM J. Control 7 (1969) 32-49.
7. S. Dafermos and A. Nagurney, Oligopolistic and competitive behavior of spatially separated markets. Region. Sci. Urban Econ. 17 (1987) 245-254.
8. G. Debreu and H. Scarf, A limit theorem on the core of an economy. Int. Econ. Rev. 4 (1963) 235-246.
9. A. A. Economides, Dynamic competitive resource sharing in multimedia networks. Proceedings of the Seventh International Symposium on Dynamic Games and Applications 1 (1996) 172-181.
10. T. L. Friesz, D. Bernstein, T. E. Smith, R. L. Tobin, and B. W. Wie, A variational inequality formulation of the dynamic network user equilibrium problem. Oper. Res. 41 (1993) 179-191.
11. T. L. Friesz, F. J. Luque, R. L. Tobin, and B. W. Wie, Dynamic network traffic assignment considered as a continuous time optimal control problem. Oper. Res. 37 (1989) 893-901.
12. S. T. Glad, A combination of penalty function and multiplier methods for solving optimal control problems. J. Optim. Theory Appl. 28 (1979) 303-329.
13. A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equilibria. Networks 15 (1985) 295-308.
14. M. R. Hestenes, Multiplier and gradient methods. J. Optim. Theory Appl. 4 (1969) 303-320.
15. S. Jorgensen, Sufficiency and game structure in Nash open-loop differential games. J. Optim. Theory Appl. 50 (1986) 189-193.
16. S. Lafortune, R. Sengupta, D. E. Kaufman, and R. L. Smith, Dynamic system-optimal traffic assignment using a state space model. Trans. Res. 27B (1993) 451-472.
17. L. S. Lasdon, S. K. Mitter, and A. D. Warren, The conjugate gradient method for optimal control problems. IEEE Trans. Automat. Control 12 (1967) 132-138.
18. H. S. Mahmassani and S. Peeta, Network performance under system optimal and user equilibrium dynamic assignments: Implications for AVIS. Trans. Res. Rec. 1408 (1993) 83-93.
19. D. K. Merchant and G. L. Nemhauser, A model and an algorithm for the dynamic traffic assignment problems. Trans. Sci. 12 (1976) 62-77.
20. D. K. Merchant and G. L. Nemhauser, Optimality conditions for a dynamic traffic assignment model. Trans. Sci. 12 (1976) 200-207.
21. B. Ran and D. E. Boyce, Modeling Dynamic Transportation Network: An Intelligent Transportation System Oriented Approach. Springer-Verlag, New York (1996).
22. B. Ran, D. E. Boyce, and L. J. LeBlanc, A new class of instantaneous dynamic user optimal traffic assignment models. Oper. Res. 41 (1993) 192-202.
23. J. F. Reinganum and N. L. Stokey, Oligopoly extraction of a common property natural resource: The importance of the period of commitment. Int. Econ. Rev. 26 (1985) 161-173.
24. A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications. North-Holland, New York (1987).
25. H. Stalford and G. Leitmann, Sufficiency conditions for Nash equilibria in N-person differential games. Topics in Differential Games (A. Blaquiere, Ed.). North-Holland (1973).
26. A. W. Starr and Y. C. Ho, Nonzero-sum differential games. J. Optim. Theory Appl. 3 (1969) 184-206.
27. J. M. Sussman, ITS: A short history and perspective on the future. Trans. Q. 50 (1996) 115-125.
28. B. Tolwinski, On the existence of Nash equilibrium points for differential games with linear and non-linear dynamics. Control Cybernet. 7 (1978) 57-69.
29. S. S. Tripathi and K. S. Narendra, Constrained optimization problems using multiplier methods. J. Optim. Theory Appl. 9 (1972) 59-69.
30. J. G. Wardrop, Some theoretical aspects of road traffic research. Proceedings, Institution of Civil Engineers II (1952) 235-378.
31. D. Watling and T. von Vuren, The modelling of dynamic route guidance systems. Trans. Res. 1C (1993) 159-182.
32. B. W. Wie, Dynamic models of network traffic assignment: A control theoretic approach. Ph.D. Dissertation, Department of City and Regional Planning. University of Pennsylvania (1988).
33. B. W. Wie, A differential game model of Nash equilibrium on a congested traffic network. Networks 23 (1993) 557-565.
34. B. W. Wie, A differential game approach to the dynamic mixed behavior traffic network equilibrium problem. Eur. J. Oper. Res. 83 (1995) 117-136.
35. B. W. Wie, A differential game model of departure time and route guidance on congested traffic networks. Presented at the 7th International Symposium on Dynamic Games and Applications, Japan (Dec. 16-18, 1996).
36. B. W. Wie, T. L. Friesz, and R. L. Tobin, Dynamic user optimal traffic assignment on congested multidestination networks. Trans. Res. 24B (1990) 431-442.
37. B. W. Wie, R. L. Tobin, and T. L. Friesz, The augmented Lagrangian method for solving dynamic network traffic assignment models in discrete time. Trans. Sci. 28 (1994) 204-220.
38. B. W. Wie, R. L. Tobin, D. Bernstein, and T. L. Friesz, A comparison of system optimum and user equilibrium traffic assignments with schedule delays. Trans. Res. 3C (1995) 389-411.
39. 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. Trans. Sci. 29 (1995) 79-92.