A weakly coupled model of differential equations for thief tracking

Simone Göttlich; Camill  Harter; Simone Göttlich; Camill  Harter

doi:10.3934/nhm.2016004

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

Simone Göttlich ^{1
,},
Camill Harter ^{1
,}

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.
- Traffic flow networks,
- thief trajectories,
- numerical simulations
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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Abstract

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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