Performance analysis of a GI/D- $$MSP/1/\infty$$ M S P / 1 / ∞ queueing system under different service phase initiations

Abstract

The main objective of this paper is to derive some analytic results concerning GI/D- $$MSP/1/\infty$$ queueing model in which customers arrive according to a discrete-time renewal process. We assume that the service process is correlated and its configuration is designed through discrete-time Markovian service process under different service phase initiations to start a busy period. The system-length distributions at various time epochs have been obtained by employing the matrix-geometric approach. An explicit closed form expression for the waiting-time distribution in the queue measured in slots has also been derived. Computational experiences with a variety of numerical results are discussed to show the effect of system parameters on the performance measures. This queueing model has potential applications in the domain of computer networks, telecommunication systems, and wireless local communication networks for evaluating the various system performances. An application of this type of queueing model in the domain of network coding in wireless communications is also discussed. This provides relevant information to the system analysts, researchers, and industry people who are interested to investigate congestion problems using queueing theory.