A Hierarchy of Models for Multilane Vehicular Traffic I: Modeling

In the present paper multilane models for vehicular traffic are considered. A microscopic multilane model based on reaction thresholds is developed. Based on this model an Enskog- like kinetic model is developed. In particular, care is taken to incorporate the correlations between the vehicles. From the kinetic model a fluid dynamic model is derived. The macroscopic coefficients are deduced from the underlying kinetic model. Numerical simulations are presented for all three levels of description in [A. Klar and R. Wegener, SIAM J. Appl. Math., 59 (1999), pp. 1002--1011]. Moreover, a comparison of the results is given there.

[1]  J. Ferziger,et al.  Mathematical theory of transport processes in gases , 1972 .

[2]  Axel Klar,et al.  A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model , 1996 .

[3]  J. Kingman.  A FIRST COURSE IN STOCHASTIC PROCESSES , 1967 .

[4]  Helbing.  Gas-kinetic derivation of Navier-Stokes-like traffic equations. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Axel Klar,et al.  A Hierarchy of Models for Multilane Vehicular Traffic II: Numerical Investigations , 1998, SIAM J. Appl. Math..

[6]  Dirk Helbing.  Modeling and simulation of multilane traffic flow , 1997 .

[7]  Takashi Nagatani,et al.  Kinetics of Clustering and Acceleration in 1D Traffic Flow , 1996 .

[8]  Robert Herman,et al.  Kinetic theory of vehicular traffic , 1971 .

[9]  Axel Klar,et al.  Enskog-like kinetic models for vehicular traffic , 1997 .

[10]  S. L. Paveri-Fontana,et al.  On Boltzmann-like treatments for traffic flow: A critical review of the basic model and an alternative proposal for dilute traffic analysis , 1975 .

[11]  Axel Klar,et al.  Mathematical Models for Vehicular Traffic , 1995 .

[12]  Harold J Payne,et al.  FREFLO: A MACROSCOPIC SIMULATION MODEL OF FREEWAY TRAFFIC , 1979 .

[13]  D. Gazis,et al.  Nonlinear Follow-the-Leader Models of Traffic Flow , 1961 .

[14]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[15]  Helbing.  Improved fluid-dynamic model for vehicular traffic. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  D. L. Gerlough,et al.  Traffic flow theory : a monograph , 1975 .

[17]  I. Prigogine,et al.  A Boltzmann-Like Approach for Traffic Flow , 1960 .

[18]  Maria Lampis,et al.  On the Kinetic Theory of Traffic Flow in the Case of a Nonnegligible Number of Queueing Vehicles , 1978 .

[19]  KlarFachbereich Mathematik.  Enskog-like Kinetic Models for Vehicular Traffic , 1997 .

[20]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[21]  P. Nelson.  A kinetic model of vehicular traffic and its associated bimodal equilibrium solutions , 1995 .

[22]  Schürmann,et al.  Second-order continuum traffic flow model. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.