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Singularities in kinematic wave theory: Solution properties, extended methods and duality revisited

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  • Daganzo, Carlos F.

Abstract

According to Euler–Lagrange duality principle of kinematic wave (KW) theory any well-posed initial value traffic flow problem can be solved with the same methods either on the time–space (Euler) plane or the time vs vehicle number (Lagrange) plane. To achieve this symmetry the model parameters and the boundary data need to be expressed in a form appropriate for each plane. It turns out, however, that when boundary data that are bounded in one plane are transformed for the other, singular points with infinite density sometimes arise. Duality theory indicates that solutions to these problems must exist and be unique. Therefore, these solutions should be characterized.

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  • Daganzo, Carlos F., 2014. "Singularities in kinematic wave theory: Solution properties, extended methods and duality revisited," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 50-59.
    • Handle: RePEc:eee:transb:v:69:y:2014:i:c:p:50-59
    DOI: 10.1016/j.trb.2014.07.002
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    References listed on IDEAS

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    1. Daganzo, Carlos F, 2014. "Singularities in kinematic wave and variational theories: supershocks, solution properties and some exact solution methods," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1rw0p740, Institute of Transportation Studies, UC Berkeley.
    2. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    3. Daganzo, Carlos F., 2006. "On the Variational Theory of Traffic Flow: Well-Posedness, Duality and Applications," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt61v1r1qq, Institute of Transportation Studies, UC Berkeley.
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    1. Laval, Jorge A. & Costeseque, Guillaume & Chilukuri, Bargavarama, 2016. "The impact of source terms in the variational representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 204-216.

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