Production Networks with Stochastic Machinery Default

  • Simone Göttlich
  • Stephan Martin
  • Thorsten Sickenberger
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


We present a model of production networks that includes random breakdowns of individual processors. The defaults of processors are exponentially distributed and the time-continuous formulation of network dynamics yields a coupled PDE-ODE system with Markovian switching. Its solution is a piecewise deterministic process, which allows us to use a modified stochastic simulation algorithm to trace stochastic events and to simulate the deterministic behavior of the network between them. The impact of stochastic default is illustrated with an exemplary Monte-Carlo simulation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Simone Göttlich
    • 1
  • Stephan Martin
    • 2
  • Thorsten Sickenberger
    • 3
  1. 1.School of Business Informatics and MathematicsUniversity of MannheimMannheimGermany
  2. 2.Department of MathematicsTU KaiserslauternKaiserslauternGermany
  3. 3.Department of MathematicsMaxwell Institute and Heriot-Watt UniversityEdinburghUK

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