On the fundamental diagram of traffic flow

SIAM Journal on Applied Mathematics

Volumn 66, Issue 4, 2006, Pages 1150-1162

  Siebel, Florian ^a   Mauser, Wolfram ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

High resolution shock capturing schemes; Instability; Macroscopic traffic model; System of balance laws

Indexed keywords

DATA REDUCTION; MATHEMATICAL MODELS; RELAXATION PROCESSES; STABILITY;

HIGH-RESOLUTION SHOCK-CAPTURING SCHEMES; MACROSCOPIC TRAFFIC MODELS; NUMERICAL CODES; SYSTEM OF BALANCE LAWS;

TRAFFIC CONTROL;

EID: 33744952332     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050627113     Document Type: Article

References (26)

1. A. Aw, A. KLAR, T. MATERNE, AND M. RASCLE, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), pp. 259-278.
2. A. Aw AND M. RASCLE, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916-938.
3. M. BANDO, K. HASEBE, A. NAKAYAMA, A. SHIBATA, AND Y. SUGIYAMA, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E (3), 51 (1995), pp. 1035-1042.
4. M. CREMER, Der Verkehrsfluß auf Schnellstraßen (Traffic Flow on Freeways), Springer, Berlin, 1979.
5. C.F. DAGANZO, Requiem for second-order fluid approximations of traffic flow, Transportation Res. B, 29 (1995), pp. 277-286.
6. L.C. DAVIS, Multilane simulations of traffic phases, Phys. Rev. E (3), 69 (2004), p. 016108.
7. R. DONAT AND A. MARQUINA, Capturing shock reflections: An improved flux formula, J. Comput. Phys., 146 (1996), pp. 42-58.
8. J.M. GREENBERG, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math., 62 (2001), pp. 729-745.
9. J.M. GREENBERG, A. KLAR, AND M. RASCLE, Congestion on multilane highways, SIAM J. Appl. Math., 63 (2003), pp. 818-833.
10. D. HELBING, Traffic and related self-driven many-particle systems, Rev. Modern Phys., 73 (2001), pp. 1067-1141.
11. R. JIANG, Q.-S. Wu, AND Q.-S. ZHU, A new continuum model for traffic flow and numerical tests, Transportation Res. B, 36 (2002), pp. 405-419.
12. B.S. KERNER, The Physics of Traffic, Springer, Berlin, 2004.
13. R. J. KOPPA, Human factors, in Monograph on Traffic Flow Theory, U.S. Department of Transportation, Federal Highway Administration, Washington, DC, 1997, pp. (3)1-32; available online at http://www.tfhrc.gov/its/tft/tft.htm.
14. R. KÜHNE AND P. MICHALOPOULOS, Continuum flow models, in Monograph on Traffic Flow Theory, U.S. Department of Transportation, Federal Highway Administration, Washington, DC, 1997, pp. (5)1-51; available online at http://www.tfhrc.gov/its/tft/tft.htm.
15. R.J. LEVEQUE, Numerical Methods for Conservation Laws, 2nd ed., Birkhäuser-Verlag, Basel, 1992.
16. M.J. LIGHTHILL AND G.B. WHITHAM, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London Ser. A, 229 (1955), pp. 317-345.
17. P. NELSON, Synchronized traffic flow from a modified Lighthill-Whitman model, Phys. Rev. E (3), 61 (2000), p. R6052.
18. G. OROSZ, R.E. WILSON, AND B. KRAUSKOPF, Global bifurcation investigation of an optimal velocity traffic model with driver reaction time, Phys. Rev. E (3), 70 (2004), p. 026207.
19. P.I. RICHARDS, Shock waves on the highway, Oper. Res., 4 (1956), pp. 42-51.
20. M. SCHÖNHOF AND D. HELBING, Empirical Features of Congested Traffic States and Their Implications for Traffic Modelling, http://arxiv.org/pdf/cond-mat/0408138 (6 August 2004).
21. C.-W. SHU AND S. OSHER, Efficient implementation of essentially nonoscillatory shock-capturing schemes. II, J. Comput. Phys., 83 (1989), pp. 32-78.
22. F. SIEBEL AND W. MAUSER, Simulating vehicular traffic in a network using dynamic routing, Math. Comput. Model. Dynam. Syst., to appear.
23. M. TREIBER, A. HENNECKE, AND D. HELBING, Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model, Phys. Rev. E (3), 59 (1999), pp. 239-253.
24. B.J. VAN LEER, Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, J. Comput. Phys., 23 (1977), pp. 276-299.
25. G.B. WHITHAM, Linear and Nonlinear Waves, John Wiley & Sons, New York, 1974.
26. H.M. ZHANG, A theory of noneguilibrium traffic flow, Transportation Res. B, 32 (1998), pp. 485-498.