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

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.Mathematics Subject Classification. 60k25, 90B22.

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

“…Li et al [15] analyzed the retrial queue with Bernoulli working vacation interruption. A retrial queue with general retrial times and single working vacation was studied by Li et al [16] by utilizing the supplementary variable method. Gupta and Kumar [17] studied a retrial queue with a single waiting server subject to breakdown and repair under working vacation and interruption.…”

Analysis of a bulk arrival N-policy queue with two-service genre, breakdown, delayed repair under Bernoulli vacation and repeated service policy

“…Further, Choudhury and Deka [14] generalized their earlier model [13] by addendum of multiple vacation policy to it. Li et al [46] discussed an M/G/1 retrial queue where the retrial times follows general distribution and the server undergoes a working vacation following the bernoulli schedule.…”