Queues with semi-Markovian arrivals

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue s...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied probability 1967-08, Vol.4 (2), p.365-379
Main Author: Çinlar, Erhan
Format: Article
Language:English
Subjects:
Absolute value
Adjoints
Eigenvalues
Eigenvectors
Ergodic theory
Markov chains
Matrices
Network servers
Polynomials
Research Papers
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203
cites cdi_FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203
container_end_page 379
container_issue 2
container_start_page 365
container_title Journal of applied probability
container_volume 4
creator Çinlar, Erhan
description A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.
doi_str_mv 10.2307/3212030
format article
fullrecord <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_2307_3212030</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_2307_3212030</cupid><jstor_id>3212030</jstor_id><sourcerecordid>3212030</sourcerecordid><originalsourceid>FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203</originalsourceid><addsrcrecordid>eNp9j01LxDAURYMoWEfxLxQUxEU0eXltmqUMfsGICLouaZNoqp1K0o74741Md4KbdzeHe98h5JizCxBMXgrgwATbIRlHWdCSSdglGWPAqUp3nxzE2DHGsVAyIydPk51szL_8-JZH23v6oMP7sPF6nesQ_EZ_xEOy51LYozkX5OXm-nl5R1ePt_fLqxVtAeVIW9GoUgiFhTTC6MZgZUCnmYqDLbByJWpojQFZiqplyJ2SDSA6o9A16ecFOdv2tmGIMVhXfwbf6_Bdc1b_utWzWyJPt2QXxyH8g53Phbpvgjevtu6GKayTxB_2B-fHVxE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Queues with semi-Markovian arrivals</title><source>JSTOR Archival Journals and Primary Sources Collection</source><creator>Çinlar, Erhan</creator><creatorcontrib>Çinlar, Erhan</creatorcontrib><description>A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.2307/3212030</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Absolute value ; Adjoints ; Eigenvalues ; Eigenvectors ; Ergodic theory ; Markov chains ; Matrices ; Network servers ; Polynomials ; Research Papers</subject><ispartof>Journal of applied probability, 1967-08, Vol.4 (2), p.365-379</ispartof><rights>Copyright © Sheffield: Applied Probability Trust</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203</citedby><cites>FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3212030$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/3212030$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,27898,27899,58210,58443</link.rule.ids></links><search><creatorcontrib>Çinlar, Erhan</creatorcontrib><title>Queues with semi-Markovian arrivals</title><title>Journal of applied probability</title><addtitle>Journal of Applied Probability</addtitle><description>A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.</description><subject>Absolute value</subject><subject>Adjoints</subject><subject>Eigenvalues</subject><subject>Eigenvectors</subject><subject>Ergodic theory</subject><subject>Markov chains</subject><subject>Matrices</subject><subject>Network servers</subject><subject>Polynomials</subject><subject>Research Papers</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1967</creationdate><recordtype>article</recordtype><recordid>eNp9j01LxDAURYMoWEfxLxQUxEU0eXltmqUMfsGICLouaZNoqp1K0o74741Md4KbdzeHe98h5JizCxBMXgrgwATbIRlHWdCSSdglGWPAqUp3nxzE2DHGsVAyIydPk51szL_8-JZH23v6oMP7sPF6nesQ_EZ_xEOy51LYozkX5OXm-nl5R1ePt_fLqxVtAeVIW9GoUgiFhTTC6MZgZUCnmYqDLbByJWpojQFZiqplyJ2SDSA6o9A16ecFOdv2tmGIMVhXfwbf6_Bdc1b_utWzWyJPt2QXxyH8g53Phbpvgjevtu6GKayTxB_2B-fHVxE</recordid><startdate>19670801</startdate><enddate>19670801</enddate><creator>Çinlar, Erhan</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19670801</creationdate><title>Queues with semi-Markovian arrivals</title><author>Çinlar, Erhan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1967</creationdate><topic>Absolute value</topic><topic>Adjoints</topic><topic>Eigenvalues</topic><topic>Eigenvectors</topic><topic>Ergodic theory</topic><topic>Markov chains</topic><topic>Matrices</topic><topic>Network servers</topic><topic>Polynomials</topic><topic>Research Papers</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Çinlar, Erhan</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Çinlar, Erhan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Queues with semi-Markovian arrivals</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>1967-08-01</date><risdate>1967</risdate><volume>4</volume><issue>2</issue><spage>365</spage><epage>379</epage><pages>365-379</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><abstract>A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.2307/3212030</doi><tpages>15</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0021-9002
ispartof Journal of applied probability, 1967-08, Vol.4 (2), p.365-379
issn 0021-9002
1475-6072
language eng
recordid cdi_crossref_primary_10_2307_3212030
source JSTOR Archival Journals and Primary Sources Collection
subjects Absolute value
Adjoints
Eigenvalues
Eigenvectors
Ergodic theory
Markov chains
Matrices
Network servers
Polynomials
Research Papers
title Queues with semi-Markovian arrivals
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-03-04T11%3A59%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Queues%20with%20semi-Markovian%20arrivals&rft.jtitle=Journal%20of%20applied%20probability&rft.au=%C3%87inlar,%20Erhan&rft.date=1967-08-01&rft.volume=4&rft.issue=2&rft.spage=365&rft.epage=379&rft.pages=365-379&rft.issn=0021-9002&rft.eissn=1475-6072&rft_id=info:doi/10.2307/3212030&rft_dat=%3Cjstor_cross%3E3212030%3C/jstor_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c247t-c3b96339457d3dabd48d2a459812e548f64a2cdd27638c041f97b244fd94fb203%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cupid=10_2307_3212030&rft_jstor_id=3212030&rfr_iscdi=true