A kinetic model for vehicular traffic derived from a stochastic microscopic model

References

• Wiedemann , R. 1974 . Simulation des Strasenverkehrsflusses. , Schriftenreihe des Instituts für Verkehrswesen der Universität Karlruhe .
   Google Scholar
• Gerlough , D. L. and Huber , M. J. 1975, 1965 . “ Transportation Research Board Special Report ” . In Traffic Flow Theory. , Washington D.C. .
   Google Scholar
• Gazis , D. C. , Herman , R. and Rothery , R. 1961 . Nonlinear follow-the-leader models for traffic flow. . Opns. Res. , 9 : 545
   Web of Science ®Google Scholar
• Anstett , N. 1992 . “ Entwicklung eines ereignisorientierten Fahrzeug-Folge-Modells zur mikroskopischen Verkehrssimulation. ” . Diplomarbeit Universität Stuttgart/Daimler Benz AG .
   Google Scholar
• Helbing , D. An improved fluid dynamic model for vehicular traffic. . to appear in Physical Review E. ,
   Google Scholar
• Kerner , B. S. and Konhäuser , P. 1994 . Physical Review E , 50 : 54
   PubMed Web of Science ®Google Scholar
• Kühne , B. D. and Rödiger . 1991, 1991 . “ Proceedings of the Winter Simulation Conference ” . Phoenix, Arizona .
   Google Scholar
• Kühne , R. D. 1991 . Verkehrsablauf auf Fernstrasen. . Phys. Bl. , 47/3 : 201
   Google Scholar
• Payne , H. J. 1979 . Transportation Research Record , 722 : 68
   Google Scholar
• Witham , G. B. 1974 . Linear and Nonlinear Waves. , New York : Wiley .
   Google Scholar
• Prigogine , I. and Herman , R. 1971 . “ Kinetic Theory of Vehicular Traffic. ” . In American Elsevier Publishing Co. New York 1st edition
   Google Scholar
• Phillips , W. F. 1977 . “ National Technical Information Service ” . In Kinetic Model for Traffic Flow. , Virginia : Springfield .
   Google Scholar
• Paveri-Fontana , S. L. 1979 . On Boltzmann like treatments for traffic flow. . Transportation Research , 9 : 225
   Google Scholar
• Nagel , K. and Schleicher , A. 1994 . Parallel Computing , 20 : 125
   Web of Science ®Google Scholar
• Schreckenberg , M. , Schadschneider , A. , Nagel , K. and Ito , N. 1995 . Physical Review E , 51 : 2939
   PubMed Web of Science ®Google Scholar
• Prigogine , I. and Andrews , F. C. 1960 . A Boltzmann like approach for traffic flow. . Oper. Res. , 8 : 789
   Web of Science ®Google Scholar
• Prigogine , I. 1961 . “ A Boltzmann like approach to the statistical theory of traffic flow. In ” . In Theory of traffic flow Edited by: Herman , R. 158
   Google Scholar
• Lampis , M. 1978 . Transportation Science , 12 : 16
   Google Scholar
• Nelson , P. 1994 . A kinetic model of vehicular traffic and its associated bimodal equilibrium solutions. . to appear in Transp. Theory and Stat. Phys. ,
   Google Scholar
• Cercignani , C. 1988 . The Boltzmann Equation and its Applications. , New York : Springer . 1st edition
   Google Scholar
• Keitzer , J. 1987 . Statistical Thermodynamics of Nonequilibrium Processes. , New York : Springer .
   Google Scholar
• Klar , A. , Kühne , R. D. and Wegener , R. 1996 . Mathematical models for vehicular traffic. . to appear in Surv. Math. Ind. ,
   Google Scholar