Analysis of an \(M / G / 1\) retrial queue with second optional service and customer feedback, under Bernoulli vacation schedule

Abstract

A single server retrial queueing system with second optional service under Bernoulli vacation schedule is investigated. The customer is permitted to balk if his service is not immediate upon arrival and allowed to join the orbit for repeating his service. Instead, if the server is free the customer's service is started immediately. Every customer is provided with a first phase of essential service followed by a second phase of optional service. After a service completion if the system is found to be empty then the server begins a vacation period. On the other hand if the system is not empty, the server chooses to either continue serving the customer with probability $(1-a)$ or goes on vacation with probability $a(0 \leq a \leq 1)$. After a service completion, a customer opts to either exit the system or chooses to join the orbit for repeating service. The joint generating functions of orbit size and server status are derived using supplementary variable technique. Some important performance measures have been derived and the effect of various parameters on the system performance has been analysed numerically. Stochastic decomposition law has been established in the absence of balking.