Steady State Analysis of Two MX/Ma,b/1 Queue Models with Random Breakdowns

We study two models of a single server bulk queueing system MX/Ma,b/1 in which the service facility suffers time homogeneous random breakdowns from time to time. In model A, the repair times are assumed to be exponential and in model B, the repair times are assumed to be detrministic. We obtain the probability generating functions of the queue size and the system size, the average queue size, the average system size and the average waiting time in the queue and the system. Some particular cases of interest are discussed and some known results are derived as special cases. A numerical example is also provided.