Analysis of a single server queue with semi-Markovian service interruption

In this paper we analyze a discrete time single server queue where the service time equals one slot The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables The service process is interrupted by a semi Markov process namely in certain states the server is available for service while the server is not available in other states We analyze both the transient and steady state models We study the generating function of the joint probability of queue length the state and the residual sojourn time of the semi Markov process We derive a system of Hilbert boundary value problems for the generating functions The system of Hilbert boundary value problems is converted to a system of Fredholm integral equations We show that the system of Fredholm integral equations has a unique solution