Calculation of steady-state probabilities for repair facilities with multiple sources and dynamic return priorities

The authors develop iterative computational formulas for the steady-state probabilities of an exponential single-channel repair facility with multiple Poisson sources and a dynamic return policy. Such facilities occur as part of multi-echelon repairable item provisioning systems in which backorders are filed according to need instead of FIFO or SIRO policies. Some computational examples are given which show the difference in system performance. The present analysis is an example of the state-reduction computational method for Markov chains. The implementation makes use of taboo sets and taboo probabilities which have physically meaningful interpretations.