Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A continuum model for two-directional traffic flow

Authors: J. H. Bick and G. F. Newell
Journal: Quart. Appl. Math. 18 (1960), 191-204
DOI: https://doi.org/10.1090/qam/99969
MathSciNet review: QAM99969
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Abstract | References | Additional Information

Abstract: The flow of traffic in two directions of an undivided highway is investigated using the equations of continuity and assumed empirical relations between the average velocities and densities in both lanes. These lead to a pair of quasi-linear partial differential equations. Even if the velocity in one lane depends only very weakly on the density in the other lane, it is found that for a certain small range of densities the equations are of elliptic rather than the expected hyperbolic type. For densities outside this range, solutions of the equations can be found for various special types of initial conditions.

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Additional Information

DOI: https://doi.org/10.1090/qam/99969
Article copyright: © Copyright 1960 American Mathematical Society

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