Approximations for the Repairman Problem with Two Repair Facilities. II. Spares

摘要

The report considers a generalization of the repairman models treated in a previous report. Here the system studied consists of n operating units, m(n) spare units, and two repair facilities. The operating units are subject to failures of two types: minor and major. Minor failures are sent to a local repair facility and major failures to a central repair facility. Once a unit is repaired it is returned to the spare pool is n units are operating, otherwise it goes directly into operation. The stochastic processes representing the number of units waiting or undergoing repair at each of the two repair facilities is a finite state, continuous-parameter Markov chain, which attains a stationary or steady-state distribution after a long time has elapsed. The method developed in this paper provides a readily calculated approximation when n is large, along with results which allow for reliable prediction of system performance. The principal concern in this paper is to understand how system performance is effected by the many system parameters.