An M/G/1 reneging queueing system with second optional service and with second optional vacation

Abstract

We study an M/G/1 queueing system where the arrival follows Poisson Process. The server provides service in two stages, the first stage service is essential and the second stage of service is optional. If the system is empty then the server goes for a vacation of random duration and after returning from vacation the server decides to take a second vacation which is optional. When the server is on vacation the customer may decide to renege. We treat reneging in this paper when the server is on vacation as the service is unavailable. Using supplementary variable technique we derive the probability generating function for the number of customers in the system. Some performance measures are derived. A Particular case is discussed. Numerical study is also presented.

Analysis of a non-Markovian single server batch arrival queueing system of compulsory three stages of services with fourth optional stage service, service interruptions and deterministic server vacations

“…Madan and Abu-Dayyeh (2004) and Madan (2015) have worked on deterministic vacations in their queueing models. Chodhury (2006), Manoharan and Sankara Sasi (2012) have studied the queueing model with a second optional vacation. A steady state analysis of a non-Markovian bulk queue with restricted vacation was studied by Jeyakumar and Arumuganathan (2011).…”