Bi-level threshold policy of \(M^{X}/(G_{1},G_{2})/1\) queue with early setup and single vacation
type: Item
instance of: scholarly article
title: Bi-level threshold policy of \(M^{X}/(G_{1},G_{2})/1\) queue with early setup and single vacation
zbMATH Open document ID: 1218.90060
DOI: 10.1504/IJOR.2011.039714
author: K. Julia Rose Mary
author: M. I. Afthab Begum
author: M. Jemila Parveen
published in: International Journal of Operational Research
publication date: 2011-08-04T00:00:00Z
review text: Summary: We analyse a queueing system with a second optional service channel under bi-level control policy and server's single vacation. There is a single server who provides the first essential service to all arriving customers. As soon as the first service of a customer is complete, then with probability \(r\), the customer may opt for the second service in which case the second service will immediately commence, or else with probability (\(1 - r\)) he may opt to leave the system, so that another customer at the head of the queue (if any) is taken up for his first essential service. The server operates an (\(m, N\)) policy with an early setup and takes a single vacation whenever the system becomes empty. For this model, the stationary probability generating function of the queue length distribution is obtained through supplementary variable technique and a decomposition property is discussed. The expected length of the cycle, various performance measures and the optimal values of thresholds \(m\) and \(N\) which minimise the total expected operating cost are also calculated.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5936131
zbMATH Keywords: bi-level threshold policy
zbMATH Keywords: first essential service
zbMATH Keywords: second optional service
zbMATH Keywords: early setup
zbMATH Keywords: single vacation policy
zbMATH Keywords: queueing systems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5936131