A note on losses in M/GI/1/n queues
Let L n be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L n and L n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL n = 1 for all n. We also show that L n i...
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| Veröffentlicht in: | Journal of applied probability 1999-12, Vol.36 (4), p.1240-1243 |
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| Format: | Artikel |
| Sprache: | eng |
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| container_end_page | 1243 |
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| container_issue | 4 |
| container_start_page | 1240 |
| container_title | Journal of applied probability |
| container_volume | 36 |
| creator | Righter, Rhonda |
| description | Let L
n
be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L
n
and L
n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL
n
= 1 for all n. We also show that L
n
is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time. |
| doi_str_mv | 10.1239/jap/1032374770 |
| format | Article |
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n
be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L
n
and L
n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL
n
= 1 for all n. We also show that L
n
is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.1239/jap/1032374770</identifier><identifier>CODEN: JPRBAM</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>60K25 ; Applied sciences ; Customers ; Exact sciences and technology ; Loss systems ; M/GI/1/n queues ; Mathematics ; Operational research and scientific management ; Operational research. Management science ; Probability and statistics ; Probability theory and stochastic processes ; Queuing theory. Traffic theory ; Sciences and techniques of general use ; Short Communications ; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) ; stochastic coupling</subject><ispartof>Journal of applied probability, 1999-12, Vol.36 (4), p.1240-1243</ispartof><rights>Copyright © Applied Probability Trust 1999</rights><rights>Copyright 1999 Applied Probability Trust</rights><rights>2000 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c385t-b3336771fb997fd0ba7b8120065838bd10b471bd2c7c1ab9a750faf9a9dc90453</citedby><cites>FETCH-LOGICAL-c385t-b3336771fb997fd0ba7b8120065838bd10b471bd2c7c1ab9a750faf9a9dc90453</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3215593$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/3215593$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,885,27923,27924,58016,58020,58249,58253</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1323156$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Righter, Rhonda</creatorcontrib><title>A note on losses in M/GI/1/n queues</title><title>Journal of applied probability</title><addtitle>Journal of Applied Probability</addtitle><description>Let L
n
be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L
n
and L
n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL
n
= 1 for all n. We also show that L
n
is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time.</description><subject>60K25</subject><subject>Applied sciences</subject><subject>Customers</subject><subject>Exact sciences and technology</subject><subject>Loss systems</subject><subject>M/GI/1/n queues</subject><subject>Mathematics</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Queuing theory. Traffic theory</subject><subject>Sciences and techniques of general use</subject><subject>Short Communications</subject><subject>Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)</subject><subject>stochastic coupling</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1UD1PwzAQtRBIlMLKxBAJ1pC7OI7jjaqCUqmIhc6R7TgoURoXOxn49xg1agfEcifd-9I7Qm4RHjGlImnlPkGgKeUZ53BGZphxFufA03MyA0gxFmFekivvWwDMmOAzcr-IejuYyPZRZ703Pmr66C1ZrRNM-uhrNKPx1-Silp03N9Oek-3L88fyNd68r9bLxSbWtGBDrCilOedYKyF4XYGSXBWYAuSsoIWqEFTGUVWp5hqlEpIzqGUtpKi0gIzROXk6-O6dbY0ezKi7pir3rtlJ911a2ZTL7Wa6TiuULk-lg8XjwUK70MaZ-qhGKH-_9FfwMGVKr2VXO9nrxp9UgYgsD7S7A631g3VHmKbImKABhilW7pRrqk9TtnZ0ffjWf8E_9vN92Q</recordid><startdate>19991201</startdate><enddate>19991201</enddate><creator>Righter, Rhonda</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19991201</creationdate><title>A note on losses in M/GI/1/n queues</title><author>Righter, Rhonda</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c385t-b3336771fb997fd0ba7b8120065838bd10b471bd2c7c1ab9a750faf9a9dc90453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>60K25</topic><topic>Applied sciences</topic><topic>Customers</topic><topic>Exact sciences and technology</topic><topic>Loss systems</topic><topic>M/GI/1/n queues</topic><topic>Mathematics</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Queuing theory. Traffic theory</topic><topic>Sciences and techniques of general use</topic><topic>Short Communications</topic><topic>Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)</topic><topic>stochastic coupling</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Righter, Rhonda</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Righter, Rhonda</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on losses in M/GI/1/n queues</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>1999-12-01</date><risdate>1999</risdate><volume>36</volume><issue>4</issue><spage>1240</spage><epage>1243</epage><pages>1240-1243</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><abstract>Let L
n
be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L
n
and L
n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL
n
= 1 for all n. We also show that L
n
is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1239/jap/1032374770</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 1999-12, Vol.36 (4), p.1240-1243 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_jap_1032374770 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | 60K25 Applied sciences Customers Exact sciences and technology Loss systems M/GI/1/n queues Mathematics Operational research and scientific management Operational research. Management science Probability and statistics Probability theory and stochastic processes Queuing theory. Traffic theory Sciences and techniques of general use Short Communications Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) stochastic coupling |
| title | A note on losses in M/GI/1/n queues |
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