Reliability analysis of a M-1(X1), M-2(X2)/G(1), G(2)/1 queueing system with a repairable service station

A queueing situation often encountered in practice is that in which the service station may fail and can be repaired. This paper considers a priority queueing system with a repairable service station, where two types of customers arrive in batches according to two homogeneous independent Poisson processes, their service time distributions are general and only one customer can be served at a time. Assume that the service station has a constant failure rate and arbitrary repair time distribution. The focus of this paper is on the reliability. Using the supplementary variable method, we obtain the Laplace transform of the pointwise availability, the pointwise failure frequency and the reliability of the service station. Furthermore, we obtain the mean steady-state availability, steady-state failure frequency and mean time to first failure of the service station. (C) 1997 Elsevier Science Ltd.