Queues with Markovian Arrivals, Phase type Services, Breakdowns, and Repairs

In service sectors, the server interruptions occur naturally and are studied using queueing models with interruptions. Such models have been studied extensively in the literature. The server interruptions may occur due to external events such as shocks and negative customers, or due to internal events which are dictated by a timer or a clock which when expired may result in an interruption. In this paper, we analyze models of $MAP/PH/1$-type with phase type breakdowns and phase type repairs analytically. The breakdowns are modeled using internal clocks. The study of such breakdowns in the context of $MAP/PH/c$-type models is carried out via simulation. Some illustrative examples are discussed.