An M/G/1 retrial queue with second optional service and unreliable server under single exhaustive vacation

Abstract

A single server retrial queue with two phases of service of which the second phase is optional, where the server is subjected to starting failures and takes a single vacation when no customers are waiting in the orbit is discussed in this paper. A necessary and sufficient condition for the system to be stable is investigated.  The joint probability generating functions of the system size and server states are studied using supplementary variable technique.  Further, some important system performance measures like mean system size, mean orbit size, server utilization and probability that the orbit is empty are derived. The stochastic decomposition law is shown to hold good for this model. Some of the existing results are deduced as special cases. Finally, extensive numerical illustrations are provided to showcase the effect of the parameters on the system performance measures.