Single Channel Queues with Breakdowns and Delayed or Two-Phase Repairs

Abstract

ABSTRACT : We study a queueing system wherein the service channel is subject to breakdowns occurring randomly in time. Immediately on a failure the service of units is suspended and the service channel waits for repairs to start. This waiting time is termed as delay time which has been assumed to have exponential distribution whereas the repair times are also exponential. A time-dependent solution in terms of the probability generating functions has been obtained. Finally, the dependence of the average number in the system on the delay parameter has been shown graphically. The above problem has been generalised in the sense that instead of exponential delay times, we have considered them to have a general (arbitrary) distribution. Next, we study a queueing system with bulk arrivals wherein the service channel is subject to random failures and the repairs are performed in two phases. Units wait until both phases of repairs of the service channel are complete. First, the service times have been considered to be exponentially distributed. A time-dependent solution in terms of the probability generating functions has been obtained and steady state results have been derived. Later we have generalised this model by considering the service times to have general (arbitrary) distribution.