A note on the entropy solutions of the hydrodynamic model of traffic flow

A note on the entropy solutions of the hydrodynamic model of traffic flow

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Article ID: iaor20032901
Country: United States
Volume: 36
Issue: 4
Start Page Number: 435
End Page Number: 446
Publication Date: Nov 2002
Journal: Transportation Science
Authors: ,
Keywords: entropy, traffic flow
Abstract:

This paper describes the hydrodynamic model of traffic flow, which is used to derive the future density and flow along a roadway with known initial density. The complete model is a first-order partial differential equation, complemented by the entropy condition. The contributions from fluid dynamics and traffic flow theory are integrated. The entropy condition is proven to be equivalent to driver's ride impulse. It is shown that multiple weak solutions are possible for initial value problems with certain density discontinuities. In addition, the implications of nonsmooth equilibrium flow-density relationships are explored.

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