Stochastic dynamics of long supply chains with random breakdowns

We analyze the stochastic large time behavior of long supply chains via a traffic flow random particle model. As items travel on a virtual road from one production stage to the next, random breakdowns of the processors at each stage are modeled via a Markov process. The result is a conservation law for the expectation of the part density which holds on time scales which are large compared to the mean up and down times of the processors.