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  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 19, Issue 4
  • December 1976, pp. 452-461

A Boltzmann-type equation in the kinetic theory of vehicular traffic

  • C. V. Pao (a1)
  • DOI: http://dx.doi.org/10.1017/S0334270000001314
  • Published online: 17 February 2009
Abstract
Abstract

In the theory of vehicular traffic flow on a highway the traffic interaction process is often considered as a collision similar to the particles' interaction in the kinetic theory of gases. This concept leads to a Boltzmann-type nonlinear intergro-differential equation which governs the traffic density function. The purpose of this paper is to present a constructive method for the determintation of a solution for this type of equation under certain boundary and initial conditions. Our method is by successive approximation which yields existence of both global and local solutions of the problem.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]A. Belleni-Morante and E. Barone , ‘Nonlinear kinetic theory of vehicular traffic’, J. Math. Anal. Appl. 47(1974), 443457.

[2]A. V. Gafarian , P. Munjal and J. Pahl , ‘An experimental validation of the Boltzmann-type statistical models for multi-lane traffic flow’, Transportation Res., 5 (1971), 211224.

[3]D. C. Gazis , ‘Mathematical theory of automobile traffic’, Science, 157 (1967), 273281.

[4]F. A. Haight , Mathematical Theory for Traffic Flow, Academic Press, New York, 1963.

[5]P. Munjal and J. Pahl , ‘An analysis of the Boltzmann-type statistical models for multi-lane traffic flow’, Transportation Res., 3 (1969), 151163.

[6]C. V. Pao , ‘Solution of a nonlinear Boltzmann equation for neutron transport in L' space’, Arch. Rat. Mech. Anal., 50 (1973), 290302.

[7]I. Prigogine and F. C. Andrews , ‘A Boltzmann-like approach for traffic flow’, Ops. Res., 8 (1960), 789797.

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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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