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Networks and Heterogeneous Media

2016, Volume 11, Issue 3: 447-469. doi: 10.3934/nhm.2016004
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A weakly coupled model of differential equations for thief tracking

  • 1.
    Department of Mathematics, University of Mannheim, D-68131 Mannheim
  • Received: 01 April 2015 Revised: 01 November 2015

  • Primary: 90B20; Secondary: 65M06.

  • In this work we introduce a novel model for the tracking of a thief moving through a road network. The modeling equations are given by a strongly coupled system of scalar conservation laws for the road traffic and ordinary differential equations for the thief evolution. A crucial point is the characterization at intersections, where the thief has to take a routing decision depending on the available local information. We develop a numerical approach to solve the thief tracking problem by combining a time-dependent shortest path algorithm with the numerical solution of the traffic flow equations. Various computational experiments are presented to describe different behavior patterns.

    Citation: Simone Göttlich, Camill Harter. A weakly coupled model of differential equations for thief tracking[J]. Networks and Heterogeneous Media, 2016, 11(3): 447-469. doi: 10.3934/nhm.2016004

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  • In this work we introduce a novel model for the tracking of a thief moving through a road network. The modeling equations are given by a strongly coupled system of scalar conservation laws for the road traffic and ordinary differential equations for the thief evolution. A crucial point is the characterization at intersections, where the thief has to take a routing decision depending on the available local information. We develop a numerical approach to solve the thief tracking problem by combining a time-dependent shortest path algorithm with the numerical solution of the traffic flow equations. Various computational experiments are presented to describe different behavior patterns.


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  • This article has been cited by:

    1. Raluca Eftimie, 2018, Chapter 3, 978-3-030-02585-4, 55, 10.1007/978-3-030-02586-1_3
    2. Theresa Dambach, Simone Göttlich, Stephan Knapp, Car path tracking in traffic flow networks with bounded buffers at junctions, 2020, 43, 0170-4214, 3331, 10.1002/mma.6121
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