Time-continuous production networks with random breakdowns

Abstract

Our main objective is the modelling and simulation of complex production networks originallyintroduced in [15, 16] with random breakdowns of individual processors. Similar to[10], the breakdowns of processors are exponentially distributed. The resulting networkmodel consists of coupled system of partial and ordinary differential equations with Markovian switchingand its solution is a stochastic process. We show our model to fit into the framework of piecewisedeterministic processes, which allows for a deterministic interpretation of dynamics between amultivariate two-state process. We develop an efficient algorithm with an emphasis on accuratelytracing stochastic events. Numerical results are presented for three exemplary networks, includinga comparison with the long-chain model proposed in [10].