Simulating vehicular traffic in a network using dynamic routing

F. Siebel and W. Mauser

Mathematical and Computer Modelling of Dynamical Systems, 2007, vol. 13, issue 1, 83-97

Abstract: We present a new numerical code which solves the Lighthill -- Whitham model, the classic macroscopic model for vehicular traffic flow, in a network with multi-destinations. We use a high-resolution shock-capturing scheme with approximate Riemann solver to solve the partial differential equations of the Lighthill -- Whitham theory. These schemes are very efficient, robust and moreover well adapted to simulations of traffic flows. We develop a theory of dynamic routing including a procedure for traffic flow assignment at junctions which reproduces the correct propagation of irregularities and ensures at the same time conservation of the number of vehicles.

Date: 2007
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DOI: 10.1080/09687630500103713

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