VLASOV-FOKKER-PLANCK MODELS FOR MULTILANE TRAFFIC FLOW

Communications in Mathematical Sciences

Volumn 1, Issue 1, 2003, Pages

  Illner, Reinhard ^a   Klar, Axel ^b   Materne, Thorsten ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Traffic flow; Vlasov fokker planck model

Indexed keywords

EID: 85128822610     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2003.v1.n1.a1     Document Type: Article

References (21)

1. [1] A. Aw, A. Klar, T. Materne, and M. Rascle, Derivation of continuum flow traffic models from microscopic follow-the-leader models, preprint.
2. [2] A. Aw and M. Rascle, Resurrection of second order models of traffic flow? SIAM J. Appl. Math., 60:916-938, 2000.
3. [3] C.F. Daganzo, Requiem for second order fluid approximations of traffic flow. Transportation Research B, 29B:277-286, 1995.
4. [4] M. Giinther, A. Klar, T. Materne, and R. Wegener, An explicitly solvable kinetic model for vehicular traffic and associated macroscopic equations, to appear in Math. Comp. Modelling.
5. [5] D. Helbing, Gas-kinetic derivation of Navier-Stokes-like traffic equation. Phys. Rev. E,53:2366-2381, 1996.
6. [6] R. Illner, A. Klar, H. Lange, A. Unterreiter, and R. Wegener, A kinetic model for vehicular traffic: Existence of stationary solutions. J. Math. Anal. Appl., 1999.
7. [7] R. Illner, A. Klar, C. Stoica, and R. Wegener, Kinetic equilibria in traffic flow models, preprint.
8. [8] R. Illner and J Wick, Statistical solutions of differential equations with non-uniquely solvable cauchy problems. Journal of Differential Equations, 41:289-300, 1981.
9. [9] B.S. Kerner, Experimental features of self-organization in traffic flow. Phys. Rev. Letters,81:3797-3800, 1998.
10. [10] B.S. Kerner, Congested traffic flow. Transp. Res. Rec., 1678:160-167, 1999.
11. [11] B.S. Kerner, Experimental features of the emergence of moving jams in free traffic flow. J.Phys. A, 33:221-228, 2000.
12. [12] B.S. Kerner and P. Konhauser, Structure and parameters of clusters in traffic flow. Phys. Rev.E, 50:5483, 1994.
13. [13] A. Klar, R.D. Kuehne, and R. Wegener, Mathematical models for vehicular traffic. Surv. Math.Ind., 6:215-239, 1996.
14. [14] A. Klar and R. Wegener, Enskog-like kinetic modelsfor vehicular traffic. J. Stat. Phys., 87:91-114, 1997.
15. [15] A. Klar and R. Wegener, A hierachy of models for multilane vehicular traffic I: Modeling.SIAM J. Appl. Math., 59:983-1001, 1998.
16. [16] A. Klar and R. Wegener, A hierachy of models for multilane vehicular traffic II: Numerical investigations. SIAM J. Appl. Math., 59:1002-1011, 1998.
17. [17] A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic. SIAM J. Appl. Math., 60:1749-1766, 2000.
18. [18] P. Nelson and A. Sopasakis, The Prigogine-Herman kinetic model predicts widely scattered traffic flow data at high concentrations. Transportation Research, to appear.
19. [19] S.L. Paveri-Fontana, On Boltzmann like treatments for traffic flow. Transportation Research,9:225-235, 1975.
20. [20] H.J. Payne and Whitham, FREFLO: A macroscopic simulation model offreeway traffic. Trans-portation Research Record, 722:68-75, 1979.
21. [21] I. Prigogine and R. Herman, Kinetic Theory of Vehicular Traffic. American Elsevier PublishingCo., New York, 1971.