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A theoretical analysis of congestion in a two-lane freeway

Published online by Cambridge University Press:  14 July 2016

Donald R. Mcneil
Donald R. Mcneil*
Affiliation:
The Johns Hopkins University
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Extract

To current workers in the mathematical theory of road traffic, one of the most challenging and important problems is to describe and analyze the congestion suffered by motorists on freeways. While there is, as yet, no satisfactory unified theory, several different models have been suggested, each of which is reasonable for a limited class of situations. These approaches fall largely into two categories. The first may be described as looking at traffic “in the large” and its principal exponents were Lighthill and Whitham (1955) and Prigogine (1961). The theory of Lighthill and Whitham involves treating the system of vehicles as a fluid subject to a rule of conservation of mass (that is, vehicles) and an assumed relation between the flow and concentration at each point. This theory is completely deterministic. Prigogine's approach is to regard the system of vehicles as behaving like the particles in a gas and subject to the laws of statistical mechanics.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 304 - 315
Copyright
Copyright © Applied Probability Trust 1970 

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