Sojourn time distributions for the M/M/1 queue in a Markovian environment
type: Item
instance of: scholarly article
title: Sojourn time distributions for the M/M/1 queue in a Markovian environment
zbMATH Open document ID: 0622.60111
DOI: 10.1016/0377-2217(87)90278-5
author: Bhaskar Sengupta
published in: European Journal of Operational Research
publication date: 1987-01-01T00:00:00Z
review text: In this paper, we study a single server queue in which both the arrival rate and service rate depend on the state of an external Markov process (called the environment) with a finite state space. Given that the environment is in state j, the mean arrival and service rates are \(\lambda_ j\) and \(\mu_ j\) respectively. For such a queue, the queue length distribution is known to be matrix geometric. In this paper, we characterize the Laplace-Stieltjes transform of the sojourn time distribution under four disciplines - last come first served preemptive resume, last come first served, processor sharing and round robin. We also discuss a potential application of this queue in the area of data communication.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 4009508
zbMATH Keywords: queue in a Markovian environment
zbMATH Keywords: single server queue
zbMATH Keywords: data communication
MaRDI profile type: Publication
full work available at URL: 0377-2217(87)90278-5
OpenAlex ID: W2080685583
cites work: Q4070096
cites work: Markov chain models - rarity and exponentiality
cites work: Q3938818
cites work: The M/M/1 queue with randomly varying arrival and service rates
cites work: Further results on the M/M/1 queue with randomly varying rates
cites work: Q3923308
cites work: The busy period of queues which have a matrix-geometric steady state probability vector
cites work: Stationary waiting time distribution in queues with phase type service and in quasi-birth-and-death processes
cites work: Q3713599
cites work: The M/M/1 Queue in a Markovian Environment
description: scientific article; zbMATH DE number 4009508