Production Networks with Stochastic Machinery Default
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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