On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow
type: Item
instance of: scholarly article
title: On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow
zbMATH Open document ID: 0753.60090
DOI: 10.1155/S0161171292000759
author: Jewgeni H. Dshalalow
author: Gary Russell
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/46732
review text: Summary: The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi- Markov process embedded in the queueing process. It is also assumed that the server capacity is \(r\geq 1\) and that any service act will not begin until the queue accumulates at least \(r\) units. In this model, therefore, idle periods also depend upon the queue length. The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity of the input stream, distribution of the idle period, and the mean busy period. Various special cases are treated.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 89252
zbMATH Keywords: single-server queueing system
zbMATH Keywords: ergodicity criterion
zbMATH Keywords: stationary distribution
zbMATH Keywords: intensity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 89252