Sensitivity analysis of an M/G/1 retrial queueing system with disaster under working vacations and working breakdowns

Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA University, Kumbakonam 612001, Thanjavur, Tamil Nadu, India

^* Corresponding author: psdurai17@gmail.com

Received: 24 December 2016
Accepted: 19 December 2017

Abstract

This paper deals with the new type of retrial queueing system with working vacations and working breakdowns. The system may become defective by disasters at any point of time when the regular busy server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair and the repair period immediately begins. As soon as the orbit becomes empty at regular service completion instant or disaster occurs in the regular busy server, the server goes for a working vacation and working breakdown (called lower speed service period). During this period, the server works at a lower service rate to arriving customers. Using the supplementary variable technique, we analyze the steady state probability generating function of system size. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.