A class of multi-server queueing system with server failures

A multi-server queueing system with identical unreliable servers with phase type distributed service times is considered. The servers are subject to random breakdowns and repairs when a repair person is available. We consider both the cases of infinite and finite buffers. Job arrivals are Poisson and server inter-failure and repair times follow exponential distributions. The infinitesimal generator matrix has a block tri-diagonal structure. The stability condition for the infinite case and the loss probability for the finite buffer case are obtained. We use a matrix-geometric approach to analyze the infinite buffer problem. Numerical examples are presented for both cases.