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A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow

Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7
Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7
shane{at}crt.umontreal.ca
mike{at}crt.umontreal.ca

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.

History: Received: September 2000; revised: April 2001; accepted: September 2001.