Analysis of a Batch Arrival Single Service Retrial Queueing System with Threshold Policy for Modified Vacations

Five different classical bulk queueing models with variations are considered from chapter II to chapter VI. This chapter and chapter VIII are devoted for the analysis of two different retrial queueing models. Retrial queueing system is characterized by the feature that the arriving customers, who encounter the server busy, join a virtual pool called orbit. An arbitrary customer in the orbit generates a stream of repeated requests that is independent of the rest of customers in the orbit. Such queueing systems play important roles in the analysis of many telephone switching systems, telecommunications networks and computer systems. The first result on M/G/1 retrial queues is due to Keilson et al (1968) who used the method of supplementary variable technique to investigate the join distribution of the channel state and the number of customers in orbit in the steady state. Later, Aleksandrov (1974) considered the case of arbitrarily distributed service times. A variant of the M/G/1 retrial queue was considered by Neuts and Ramalhoto (1984). Artalejo (1998) studied some results on M/G/1 queue with N – policy.