Fluid-stochastic-event graphs for evaluation and optimization of discrete-event systems with failures

This paper addresses the performance evaluation and optimization of failure-prone discrete-event systems. We propose a fluid-stochastic-event graph model that is a decision-free Petri net. Tokens are considered as continuous flows. A transition can be in operating state or in failure state. Jumps between failure and operating states do not depend on the firing conditions, and the sojourn time in each state is a random variable of general distribution. For performance evaluation, a set of evolution equations that determines continuous-state variables at epochs of failure/repair events is established. The cumulative firing quantity of each transition is proven to be concave in system parameters, including firing rates and initial marking. Gradient estimators are derived. Finally, an optimization problem of maximizing a concave function of throughput rate and system parameters is addressed.