An M/G/1 retrial queue with single working vacation under Bernoulli schedule

¹ School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
² Business School, Shandong University of Technology, Zibo 255049, China
³ School of Mathematics and Statistics, Fuyang Normal College, Fuyang 236037, China

^* Corresponding author: liltaot@126.com

Received: 15 February 2016
Accepted: 1 January 2019

Abstract

In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q, he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.