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Networks and Heterogeneous Media

2011, Volume 6, Issue 4: 695-714. doi: 10.3934/nhm.2011.6.695
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Time-continuous production networks with random breakdowns

  • 1.
    Department of Mathematics, University of Mannheim, D-68131 Mannheim
  • 2.
    Dept. of Mathematics, TU Kaiserslautern, 67663 Kaiserslautern
  • 3.
    Maxwell Institute and Heriot-Watt University, Dept. of Mathematics, Edinburgh, EH14 4AS, Scotland
  • Our main objective is the modelling and simulation of complex production networks originally introduced in [15, 16] with random breakdowns of individual processors. Similar to [10], the breakdowns of processors are exponentially distributed. The resulting network model consists 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 proposed in [10].

    Citation: Simone Göttlich, Stephan Martin, Thorsten Sickenberger. Time-continuous production networks with random breakdowns[J]. Networks and Heterogeneous Media, 2011, 6(4): 695-714. doi: 10.3934/nhm.2011.6.695

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