The GI/M/1 queue in a multi-phase service environment with disasters and working breakdowns

Abstract

ABSTRACTIn this paper, we consider a GI/M/1 queue in a multi-phase service environment with disasters and working breakdowns. When the server is working in any normal service phases, it may suffer disastrous interruptions, causing all present customers to leave the system. At an exponential failure instant, the system becomes defective, and goes directly to repair phase. During the repair period, instead of stopping service completely, the system is equipped with a substitute server which continues to provide service to the arriving customers. After an exponential repair time, the substitute server stops service and the system moves to normal operative phase i with probability . Using the matrix analytic approach and semi-Markov process, we obtain the stationary queue length distribution at both arrival and arbitrary epochs. We also provide the elaborate analysis of some performance measures and sojourn time distribution of an arbitrary customer. In addition, some numerical examples are presented.