Stochastic Analysis of Cyclic Schedules

A cyclic schedule is a sequence of tasks on a set of machines that is repeated indefinitely. We model cyclic schedules as Markov chains and use ergodic theory to analyze and improve the performance of cyclic schedules in environments with machine breakdowns, yield losses, and other sources of variability. The concept of cyclic task criticality is developed as a natural extension of task criticalities in PERT networks. We show that cyclic task criticalities can and should be used to guide the management of cyclic schedules.