On a multilevel controlled bulk queueing system \(M^ X /G^{r,R} /1\)
type: Item
instance of: scholarly article
title: On a multilevel controlled bulk queueing system \(M^ X /G^{r,R} /1\)
zbMATH Open document ID: 0762.60084
DOI: 10.1155/S1048953392000200
author: Jewgeni H. Dshalalow
author: Lev Abolnikov
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1993-01-19T00:00:00Z
full work available at URL: https://eudml.org/doc/46797
review text: The authors study a general bulk queueing system with a multilevel control and a queue length dependent service delay discipline. Earlier works on queueing system with service delay discipline deals with the case that bulk input on the service times depends on the group sizes. In this work, interval times of the input stream, the sizes of arriving batches of customers, and service time distributions of groups of customers taken for service, all depend upon the queue length. Necessary and sufficient conditions for the ergodicity of the queueing process with discrete and continuous time parameters are established. Techniques of the analysis of a class of general Markov chains is used. The stationary distribution of the continuous time queueing process is obtained by using semi-regenerative techniques.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 98945
zbMATH Keywords: bulk queueing system
zbMATH Keywords: multilevel control
zbMATH Keywords: ergodicity of the queueing process
zbMATH Keywords: stationary distribution
zbMATH Keywords: semi-regenerative techniques
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 98945