Markov-modulated PH/G/1 queueing systems
type: Item
instance of: scholarly article
title: Markov-modulated PH/G/1 queueing systems
zbMATH Open document ID: 0734.60095
DOI: 10.1007/BF01158469
author: Yixin Zhu
author: N. U. Prabhu
published in: Queueing Systems
publication date: 1991-01-01T00:00:00Z
review text: The authors study a queue in which the arrival process and the service times depend on the state of an underlying Markov chain on a countable state space. The interarrival time has a phase type distribution, the service time is general, and, given the states of the Markov chain, independent of the arrival process. By using properties of Markov- additive processes, the authors derive the busy period process, waiting time and idle time, and then study the special case of a Markov-modulated \(E_ K/G/1\). All the proofs and techniques draw from a previous paper [Queueing Syst. 5, No.1-3, 215-245 (1989; Zbl 0694.60087)] and from \textit{G. J. K. Regterschot} and \textit{J. H. A. de Smit} [Math. Oper. Res. 11, 465-483 (1986; Zbl 0619.60093)].
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 4215118
zbMATH Keywords: queue in which the arrival process and the service times depend on the state
zbMATH Keywords: Markov-additive processes
zbMATH Keywords: waiting time
zbMATH Keywords: idle time
reviewed by: Patrick Jaillet
MaRDI profile type: Publication
cites work: Q3900799
cites work: Markov-modulated queueing systems
cites work: From the matrix-geometric to the matrix-exponential
cites work: The Queue M|G|1 with Markov Modulated Arrivals and Services
full work available at URL: https://doi.org/10.1007/bf01158469
OpenAlex ID: W2041738260
description: scientific article; zbMATH DE number 4215118