Time-continuous production networks with random breakdowns

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].

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