Objectives and benchmarks for kinetic theories of vehicular traffic

Criticisms and accomplishments of the Prigogine–Herman kinetic theory are reviewed. Two of the latter are identified as possible benchmarks against which proposed novel kinetic theories of vehicular traffic can be measured. Various kinetic theories that have been proposed to eliminate perceived deficiencies of the Prigogine–Herman theory are assessed in this light. None are found to have yet been shown to meet these benchmarks. Possible objectives and applications for kinetic theories of vehicular traffic are considered. Among these is the traditional application to the development of continuum models, with the resulting microscopically based coefficients. However, the focus is upon direct applications of the kinetic theory (e.g., the kinetic distribution function). It is concluded that the primary applications are likely to be found among situations in which variability between instances is an important consideration (e.g., travel times, or driving cycles). It is suggested that cellular automata can provide a useful framework for testing of proposed kinetic theories of vehicular traffic. This possibility is illustrated by the initial results from an ongoing project intended to illuminate the basis for the recent result that the equilibrium solutions of (a mild generalization of) the Prigogine–Herman kinetic model comprise a two-parameter family, at sufficiently high densities. (And thus the corresponding traffic stream model displays the observed scatter at such densities.) These studies are based on the simple cellular automaton CA-184-CC.