Control Policies for the MX/G/1 Queueing System
The M X / G /1 queueing system is studied under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server...
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| Veröffentlicht in: | Management science 1989-06, Vol.35 (6), p.708-721 |
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| container_title | Management science |
| container_volume | 35 |
| creator | Lee, Hyo-Seong Srinivasan, Mandyam M |
| description | The M X / G /1 queueing system is studied under the following two situations:
(1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty.
(2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty.
For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented. |
| doi_str_mv | 10.1287/mnsc.35.6.708 |
| format | Article |
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(1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty.
(2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty.
For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.</description><identifier>ISSN: 0025-1909</identifier><identifier>EISSN: 1526-5501</identifier><identifier>DOI: 10.1287/mnsc.35.6.708</identifier><identifier>CODEN: MSCIAM</identifier><language>eng</language><publisher>Linthicum, MD: INFORMS</publisher><subject>Algebra ; Applied sciences ; batch arrival queueing systems ; Cost efficiency ; Cost structure ; Exact sciences and technology ; Mathematical moments ; Minimization of cost ; Network servers ; Operational research and scientific management ; Operational research. Management science ; optimal control ; Queuing theory. Traffic theory ; Random variables ; server vacation models ; Start up firms ; Unit costs ; Vacations</subject><ispartof>Management science, 1989-06, Vol.35 (6), p.708-721</ispartof><rights>Copyright 1989 The Institute of Management Sciences</rights><rights>1990 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2632117$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/mnsc.35.6.708$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,780,784,803,4008,27869,27924,27925,58017,58250,62616</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=6578288$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/inmormnsc/v_3a35_3ay_3a1989_3ai_3a6_3ap_3a708-721.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Lee, Hyo-Seong</creatorcontrib><creatorcontrib>Srinivasan, Mandyam M</creatorcontrib><title>Control Policies for the MX/G/1 Queueing System</title><title>Management science</title><description>The M X / G /1 queueing system is studied under the following two situations:
(1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty.
(2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty.
For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>batch arrival queueing systems</subject><subject>Cost efficiency</subject><subject>Cost structure</subject><subject>Exact sciences and technology</subject><subject>Mathematical moments</subject><subject>Minimization of cost</subject><subject>Network servers</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>optimal control</subject><subject>Queuing theory. Traffic theory</subject><subject>Random variables</subject><subject>server vacation models</subject><subject>Start up firms</subject><subject>Unit costs</subject><subject>Vacations</subject><issn>0025-1909</issn><issn>1526-5501</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><sourceid>K30</sourceid><recordid>eNpFkc1v2zAMxYViBZqlO-7Wg4EO2KVOKCn68HEI1i-06IZtwG6C7dCJgthOJadF_vsydZocnnjgj3wPFGNfOYy4sGZcN7EcSTXSIwP2hA24EjpVCvgnNgAQKuUZZGfsc4xLADDW6AEbT9umC-0q-dWufOkxJlUbkm6ByeP_8c2YJ783uEHfzJM_29hhfc5Oq3wV8cu-Dtm_659_p7fpw9PN3fTHQzqXCmw60wWUaLJqNoHSTrQEYSbGlpZyFGit1IgKJcgCBehCKglc5zzjEqvCGiGH7LLfuw7t8wZj55btJjRk6bjIjIVM8R1131MB11i6dfB1HrbON3UbdtdwL07mUtGzJfHMZlQ8SZPWJDqUM4K7RVfTsm97yzyW-aoKeVP6eFiqlbGCkg_ZRY8tY9eGQ1toKTg31L7q276hS9bHeQ5u90vuPRdl0o7MCf_e4ws_X7z6gO5jrs4J9EfyDSerjpQ</recordid><startdate>19890601</startdate><enddate>19890601</enddate><creator>Lee, Hyo-Seong</creator><creator>Srinivasan, Mandyam M</creator><general>INFORMS</general><general>Institute of Management Sciences</general><general>Institute for Operations Research and the Management Sciences</general><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope><scope>SAAPM</scope></search><sort><creationdate>19890601</creationdate><title>Control Policies for the MX/G/1 Queueing System</title><author>Lee, Hyo-Seong ; Srinivasan, Mandyam M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-g3508-d6b0ce79fd40c8463027478c8002be8836ee5e303be206b353016a1913efb8723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>batch arrival queueing systems</topic><topic>Cost efficiency</topic><topic>Cost structure</topic><topic>Exact sciences and technology</topic><topic>Mathematical moments</topic><topic>Minimization of cost</topic><topic>Network servers</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>optimal control</topic><topic>Queuing theory. Traffic theory</topic><topic>Random variables</topic><topic>server vacation models</topic><topic>Start up firms</topic><topic>Unit costs</topic><topic>Vacations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lee, Hyo-Seong</creatorcontrib><creatorcontrib>Srinivasan, Mandyam M</creatorcontrib><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><collection>Periodicals Index Online Segment 42</collection><jtitle>Management science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lee, Hyo-Seong</au><au>Srinivasan, Mandyam M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Control Policies for the MX/G/1 Queueing System</atitle><jtitle>Management science</jtitle><date>1989-06-01</date><risdate>1989</risdate><volume>35</volume><issue>6</issue><spage>708</spage><epage>721</epage><pages>708-721</pages><issn>0025-1909</issn><eissn>1526-5501</eissn><coden>MSCIAM</coden><abstract>The M X / G /1 queueing system is studied under the following two situations:
(1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty.
(2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty.
For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.</abstract><cop>Linthicum, MD</cop><pub>INFORMS</pub><doi>10.1287/mnsc.35.6.708</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Management science, 1989-06, Vol.35 (6), p.708-721 |
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| language | eng |
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| source | RePEc; INFORMS PubsOnLine; Periodicals Index Online; EBSCOhost Business Source Complete; JSTOR Archive Collection A-Z Listing |
| subjects | Algebra Applied sciences batch arrival queueing systems Cost efficiency Cost structure Exact sciences and technology Mathematical moments Minimization of cost Network servers Operational research and scientific management Operational research. Management science optimal control Queuing theory. Traffic theory Random variables server vacation models Start up firms Unit costs Vacations |
| title | Control Policies for the MX/G/1 Queueing System |
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