The queue M|G|1 with Markov modulated arrivals and services

G.J.K. Regterschot, J.H.A. de Smit

Research output: Contribution to journalArticleAcademic

36 Downloads (Pure)

Abstract

We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.
Original languageUndefined
Pages (from-to)465-483
JournalMathematics of operations research
Volume11
Issue number3
DOIs
Publication statusPublished - 1986

Keywords

  • IR-98505

Cite this

Regterschot, G.J.K. ; de Smit, J.H.A. / The queue M|G|1 with Markov modulated arrivals and services. In: Mathematics of operations research. 1986 ; Vol. 11, No. 3. pp. 465-483.
@article{413849a9397646088b107f19be2bce91,
title = "The queue M|G|1 with Markov modulated arrivals and services",
abstract = "We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.",
keywords = "IR-98505",
author = "G.J.K. Regterschot and {de Smit}, J.H.A.",
year = "1986",
doi = "10.1287/moor.11.3.465",
language = "Undefined",
volume = "11",
pages = "465--483",
journal = "Mathematics of operations research",
issn = "0364-765X",
publisher = "INFORMS Institute for Operations Research and the Management Sciences",
number = "3",

}

The queue M|G|1 with Markov modulated arrivals and services. / Regterschot, G.J.K.; de Smit, J.H.A.

In: Mathematics of operations research, Vol. 11, No. 3, 1986, p. 465-483.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - The queue M|G|1 with Markov modulated arrivals and services

AU - Regterschot, G.J.K.

AU - de Smit, J.H.A.

PY - 1986

Y1 - 1986

N2 - We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.

AB - We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.

KW - IR-98505

U2 - 10.1287/moor.11.3.465

DO - 10.1287/moor.11.3.465

M3 - Article

VL - 11

SP - 465

EP - 483

JO - Mathematics of operations research

JF - Mathematics of operations research

SN - 0364-765X

IS - 3

ER -