Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule

Abstract

An M/G/1 retrial queueing system with two phases of service of which the second phase is optional and the server operating under Bernoulli vacation schedule is investigated. Further, the customer is allowed to balk upon arrival if he finds the server unavailable to serve his request immediately. The joint generating functions of orbit size and server status are derived using supplementary variable technique. Some important performance measures like the orbit size, the system size, the server utilisation and the probability that the system is empty are found. Stochastic decomposition law is established when there is no balking permitted. Some existing results are derived as special cases of our model under study. Interestingly, these performance measures are compared for various vacation schedules namely exhaustive service, 1-limited service, Bernoulli vacation and modified Bernoulli vacation schedules. Extensive numerical analysis is carried out to exhibit the effect of the system parameters on the performance measures.