Stationary analysis of a single server retrial queue with priority and vacation
type: Item
instance of: scholarly article
title: Stationary analysis of a single server retrial queue with priority and vacation
zbMATH Open document ID: 1169.90332
DOI: 10.1504/IJOR.2009.024528
author: D. Arivudainambi
author: Igor Averbakh
author: Oded Berman
published in: International Journal of Operational Research
publication date: 2009-09-13T00:00:00Z
review text: Summary: We study a single server retrial queue with Bernoulli vacations and a priority queue. A customer who finds the server busy upon arrival either joins the priority queue with probability \(\alpha\) or leaves the service area and enters a retrial group (orbit) with probability \(\bar{\alpha}\) (\(= 1 - \alpha\)). Using the supplementary variable technique, we find the joint probability generating function of the number of customers in the priority queue and of the number of customers in the retrial group in a closed form. Also, we find explicit expressions for the mean queue length and the mean waiting time for both queues, and we derive steady-state performance measures for the system. We show that the general stochastic decomposition law for \(M\)/\(G\)/\(1\) vacation models holds for our system too. Some special cases and numerical results are also discussed.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5603386
zbMATH Keywords: priority queue
zbMATH Keywords: probability generating functions
zbMATH Keywords: retrial queues
zbMATH Keywords: Bernoulli vacations
zbMATH Keywords: steady-state performance measures
zbMATH Keywords: stochastic decomposition
zbMATH Keywords: single server queues
zbMATH Keywords: supplementary variable technique
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5603386