Performance optimization of discrete event systems with failures using fluid Petri nets

Performance evaluation and optimization of failure-prone discrete event systems are addressed. Our analysis is based on a fluid stochastic event graph model that is a decision-free Petri net. In fluid Petri nets, each place holds a continuous flow instead of discrete tokens of conventional Petri nets. A transition can be in operating state or in failure state. A transition in operating state can fire at its maximal speed and a transition in failure state cannot fire. Jumps between failure and operating states are independent of 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 discrete events is established. Based on the evolution equations, we prove that the cumulative firing of transitions are Lipschitz continuous, non-decreasing and concave functions of system parameters including maximal firing rates and the initial marking. Gradient estimators are derived and their properties established. Finally, an optimization problem that maximizes a concave function of throughput rate and the system parameters is addressed