A weakly coupled model of differential equations for thief tracking | Zendy

Simone Göttlich | Zendy; Camill Harter | Zendy

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A weakly coupled model of differential equations for thief tracking

Author(s) -

Simone Göttlich,

Camill Harter

Publication year - 2016

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2016004

Subject(s) - ordinary differential equation , scalar (mathematics) , computer science , conservation law , tracking (education) , flow (mathematics) , partial differential equation , traffic flow (computer networking) , mathematics , differential equation , mathematical optimization , mathematical analysis , geometry , psychology , pedagogy , computer security

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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