Work and Sojourn Time in an M/G/1 Retrial Queue with Breakdowns

A single-server subject to random breakdowns (or preemptive interruptions) insure the service of customers who arrive in the system according to a homogeneous Poisson process. The customer who arrive when the server is blocked (out of order or busy) is admitted to repeat his call until the server can provide his service. The purpose of this paper is to provide a simple approach to compute the stationary probability distribution of the customer´s sojourn time in the system. We also obtain the probability distribution of the work which is different from the sojourn time contrary to the classical FIFO discipline. We show how mean performance measures such as mean waiting time and mean sojourn time can be obtained. Finally, we obtain asymptotic distributions of the waiting and sojourn times in heavy traffic and in the case of low retrial rate.