A Note on M/M/1 Queues with Gamma-Distributed Vacations

Walter Böhm

doi:10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1

A Note on M/M/1 Queues with Gamma-Distributed Vacations

Walter Böhm

Institute for Statistics and Mathematics

Publication: Working/Discussion Paper › WU Working Paper

22 Downloads (Pure)

Abstract

In this note we derive a simple formula for the density of Sn = i=1n Ti, where Ti is the duration of the i-th busy cycle in an M/M/1 queueing model with gamma distributed server vacations. Using this result we find the distribution of the queue length by standard renewal arguments. (author's abstract)

Original language	English
Place of Publication	Vienna
Publisher	Department of Statistics and Mathematics, WU Vienna University of Economics and Business
DOIs	https://doi.org/10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1
Publication status	Published - 1991

Publication series

Series	Forschungsberichte / Institut für Statistik
Number	22

WU Working Paper Series

Forschungsberichte / Institut für Statistik

Access to Document

10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1Licence: Unspecified

DocumentFinal published version, 173 KBLicence: Unspecified

Check availability

University Library Catalogue

Cite this

@techreport{ae2dd305dbd04fc4b4c64505655942c1,

title = "A Note on M/M/1 Queues with Gamma-Distributed Vacations",

abstract = "In this note we derive a simple formula for the density of Sn = i=1n Ti, where Ti is the duration of the i-th busy cycle in an M/M/1 queueing model with gamma distributed server vacations. Using this result we find the distribution of the queue length by standard renewal arguments. (author's abstract)",

author = "Walter B{\"o}hm",

year = "1991",

doi = "10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1",

language = "English",

series = "Forschungsberichte / Institut f{\"u}r Statistik",

number = "22",

publisher = "Department of Statistics and Mathematics, WU Vienna University of Economics and Business",

type = "WorkingPaper",

institution = "Department of Statistics and Mathematics, WU Vienna University of Economics and Business",

}

TY - UNPB

T1 - A Note on M/M/1 Queues with Gamma-Distributed Vacations

AU - Böhm, Walter

PY - 1991

Y1 - 1991

N2 - In this note we derive a simple formula for the density of Sn = i=1n Ti, where Ti is the duration of the i-th busy cycle in an M/M/1 queueing model with gamma distributed server vacations. Using this result we find the distribution of the queue length by standard renewal arguments. (author's abstract)

AB - In this note we derive a simple formula for the density of Sn = i=1n Ti, where Ti is the duration of the i-th busy cycle in an M/M/1 queueing model with gamma distributed server vacations. Using this result we find the distribution of the queue length by standard renewal arguments. (author's abstract)

U2 - 10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1

DO - 10.57938/ae2dd305-dbd0-4fc4-b4c6-4505655942c1

M3 - WU Working Paper

T3 - Forschungsberichte / Institut für Statistik

BT - A Note on M/M/1 Queues with Gamma-Distributed Vacations

PB - Department of Statistics and Mathematics, WU Vienna University of Economics and Business

CY - Vienna

ER -