A dynamical system model of the traffic assignment problem

Transportation Research Part B: Methodological

Volumn 41, Issue 1, 2007, Pages 32-48

  Jin, Wen Long ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Dynamical system; Equilibrium; O D first in first out violation; Partial user equilibrium; The traffic assignment problem; User equilibrium

Indexed keywords

CONTROL SYSTEMS; DYNAMIC PROGRAMMING; PERTURBATION TECHNIQUES; TRANSPORTATION ROUTES;

DYNAMICAL SYSTEM MODEL; PARTIAL USER EQUILIBRIUM; TRANSPORTATION NETWORKS; USER EQUILIBRIUM;

TRAFFIC CONTROL;

NETWORK DESIGN; NUMERICAL MODEL; OPTIMIZATION; TRAFFIC MANAGEMENT; TRANSPORTATION PLANNING;

EID: 33746912041     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2006.02.010     Document Type: Article

References (25)

1. Beckmann M., McGuire C.B., and Winsten C.B. Studies in the Economics of Transportation (1956), Yale University Press, New Haven Connecticut, also published as Rand-RM-1488-PR, Rand Corporation, Santa Monica, CA, May 12, 1955
2. Dafermos S.C., and Sparrow F.T. The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards: Part B 73 (1969) 91-118
3. Daganzo C.F. The cell transmission model II: network traffic. Transportation Research Part B 29 2 (1995) 79-93
4. Daganzo C.F. Properties of link travel time functions under dynamic loads. Transportation Research Part B 29 2 (1995) 95-98
5. Horowitz J.L. The stability of stochastic equilibrium in a two-link transportation network. Transportation Research Part B 18 (1984) 13-28
6. Jin, W.-L., 2003. Kinematic wave models of network vehicular traffic. Ph.D. thesis, University of California, Davis. Available from: .
7. Jin W.-L., and Jayakrishnan R. First-in-first-out properties of a commodity-based kinematic wave simulation model. Transportation Research Record: Journal of the Transportation Research Board 1934 (2005) 197-297
8. Jin W.-L., and Zhang H.M. The inhomogeneous kinematic wave traffic flow model as a resonant nonlinear system. Transportation Science 37 3 (2003) 294-311
9. Jin, W.-L., Zhang, H.M., 2004. A multicommodity kinematic wave simulation model of network traffic flow. Transportation Research Record: Journal of the Transportation Research Board 1883, 59-67, presented at TRB 2004 Annual Meeting, Washington DC.
10. Jin, W.-L., Zhang, Y., Chu, L., 2006. Measuring first-in-first-out violation among vehicles. Presented at TRB 2006 Annual Meeting.
11. LaSalle J. Some extensions of Liapunov's second method. IRE Transactions on Circuit Theory 7 4 (1960) 520-527
12. Lebacque, J.P., 1996. The Godunov scheme and what it means for first order traffic flow models. In: The International Symposium on Transportation and Traffic Theory, Lyon, France.
13. Lighthill M.J., and Whitham G.B. On kinematic waves: II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London A 229 1178 (1955) 317-345
14. Moskowitz K., and Newman L. Note on freeway capacity. Highway Research Record 27 (1963) 44-68
15. Munjal P.K., Hsu Y.S., and Lawrence R.L. Analysis and validation of lane-drop effects of multilane freeways. Transportation Research 5 (1971) 257-266
16. Nagurney A., and Zhang D. Projected Dynamical Systems and Variational Inequalities with Applications (1996), Kluwer, Boston
17. Nagurney A., and Zhang D. Projected dynamical systems in the formulation, stability analysis, and computation of fixed-demand traffic network equilibria. Transportation Science 31 (1997) 147-158
18. Netter M. Affectations de trafic et tarification au coût marginal social: critique de quelques idées admises. Transportation Research 6 4 (1972) 411-429
19. Newell G.F. A simplified theory of kinematic waves in highway traffic I: general theory. II: queuing at freeway bottlenecks. III: multi-destination flows. Transportation Research Part B 27 4 (1993) 281-313
20. Patriksson M. The Traffic Assignment Problem-Models and Methods (1994), VSP, Utrecht, The Netherlands
21. Richards P.I. Shock waves on the highway. Operations Research 4 (1956) 42-51
22. Sheffi Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (1984), Prentice Hall, Englewood Cliffsm, NJ
23. Smith M.J. The stability of a dynamic model of traffic assignment-an application of a method of Lyapunov. Transportation Science 18 (1984) 245-252
24. Strogatz S.H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (1994), Addison-Wesley Publishing Company, Reading, Massachusetts
25. Wardrop J.G. Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers, Part II 1 (1952) 325-378