Heriot-Watt Mathematics Report Series
HWM10-9, 17 Mar 2010

Time-continuous production networks with random breakdowns

S Göttlich, S Martin and T Sickenberger


Our main objective is the modelling and simulation of complex production networks with random breakdowns of individual processors. The breakdowns of processors are exponentially distributed. The resulting network model is of coupled system of partial and ordinary differential equations with Markovian switching and its solution is a stochastic process. We show our model to fit into the framework of piecewise deterministic processes, which allows for a deterministic interpretation of dynamics between a multivariate two-state process. We develop an efficient algorithm with an emphasis on accurately tracing stochastic events. Numerical results are presented for three exemplary networks, including a comparison with the long-chain model.

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Full text: http://www.ma.hw.ac.uk/~ts117/publ/Goettlich_Martin_Sickenberger_Prod_Networks_With_Random_Breakdowns.pdf

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