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

Shane Velan () and Michael Florian ()
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Shane Velan: Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7
Michael Florian: Centre for Research on Transportation, Université de Montréal, C.P. 6128 succursale Centre-ville, Montréal, Québec H3C 3J7

Transportation Science, 2002, vol. 36, issue 4, 435-446

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:36:y:2002:i:4:p:435-446

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