Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals
An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the M t / GI / s t + GI many-server queueing model, which has a nonhomogeneous Poisson arrival process (the M t ), has gene...
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| Veröffentlicht in: | Operations research 2012-11, Vol.60 (6), p.1551-1564 |
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| creator | Liu, Yunan Whitt, Ward |
| description | An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the
M
t
/
GI
/
s
t
+
GI
many-server queueing model, which has a nonhomogeneous Poisson arrival process (the
M
t
), has general service times (the first
GI
), and allows customer abandonment according to a general patience distribution (the +
GI
). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime. |
| doi_str_mv | 10.1287/opre.1120.1104 |
| format | Article |
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M
t
/
GI
/
s
t
+
GI
many-server queueing model, which has a nonhomogeneous Poisson arrival process (the
M
t
), has general service times (the first
GI
), and allows customer abandonment according to a general patience distribution (the +
GI
). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime.</description><identifier>ISSN: 0030-364X</identifier><identifier>EISSN: 1526-5463</identifier><identifier>DOI: 10.1287/opre.1120.1104</identifier><identifier>CODEN: OPREAI</identifier><language>eng</language><publisher>Hanover, MD: INFORMS</publisher><subject>Algorithms ; Analysis ; Applied sciences ; Approximation ; capacity planning ; Consumer attitudes ; Exact sciences and technology ; Firm modelling ; infinite-server queues ; Inventory control, production control. Distribution ; Learning models (Stochastic processes) ; many-server queues ; METHODS ; Modeling ; offered-load approximations ; Operational research and scientific management ; Operational research. Management science ; Parametric models ; Performance metrics ; Poisson process ; queues with abandonment ; queues with time-varying arrivals ; Queuing theory ; Queuing theory. Traffic theory ; Random variables ; service systems ; Staffing ; Stochastic models ; Studies ; Time dependence ; Waiting rooms ; Workforce planning</subject><ispartof>Operations research, 2012-11, Vol.60 (6), p.1551-1564</ispartof><rights>2012 INFORMS</rights><rights>2014 INIST-CNRS</rights><rights>COPYRIGHT 2012 Institute for Operations Research and the Management Sciences</rights><rights>Copyright Institute for Operations Research and the Management Sciences Nov/Dec 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c532t-73f8ae2d7f63001aeec57caf3aea7df8e87b2948740f9514bf55d164a29cd1dc3</citedby><cites>FETCH-LOGICAL-c532t-73f8ae2d7f63001aeec57caf3aea7df8e87b2948740f9514bf55d164a29cd1dc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/23323718$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://pubsonline.informs.org/doi/full/10.1287/opre.1120.1104$$EHTML$$P50$$Ginforms$$H</linktohtml><link.rule.ids>314,776,780,799,3679,27901,27902,57992,58225,62589</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26736269$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Yunan</creatorcontrib><creatorcontrib>Whitt, Ward</creatorcontrib><title>Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals</title><title>Operations research</title><description>An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the
M
t
/
GI
/
s
t
+
GI
many-server queueing model, which has a nonhomogeneous Poisson arrival process (the
M
t
), has general service times (the first
GI
), and allows customer abandonment according to a general patience distribution (the +
GI
). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime.</description><subject>Algorithms</subject><subject>Analysis</subject><subject>Applied sciences</subject><subject>Approximation</subject><subject>capacity planning</subject><subject>Consumer attitudes</subject><subject>Exact sciences and technology</subject><subject>Firm modelling</subject><subject>infinite-server queues</subject><subject>Inventory control, production control. Distribution</subject><subject>Learning models (Stochastic processes)</subject><subject>many-server queues</subject><subject>METHODS</subject><subject>Modeling</subject><subject>offered-load approximations</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Parametric models</subject><subject>Performance metrics</subject><subject>Poisson process</subject><subject>queues with abandonment</subject><subject>queues with time-varying arrivals</subject><subject>Queuing theory</subject><subject>Queuing theory. Traffic theory</subject><subject>Random variables</subject><subject>service systems</subject><subject>Staffing</subject><subject>Stochastic models</subject><subject>Studies</subject><subject>Time dependence</subject><subject>Waiting rooms</subject><subject>Workforce planning</subject><issn>0030-364X</issn><issn>1526-5463</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>N95</sourceid><recordid>eNqFkU1r3DAQhkVpodsk194KhtJbvdG37OOypB-QUkKS0puQ5ZGjxZa3kp2S_vrKJHRbWCgCDdI874z0DkKvCV4TWqnzcR9hTQjNR4L5M7QigspScMmeoxXGDJdM8u8v0auUdhjjWkixQlfXk2l873_50BXbOU3jALHYNCa0YxggTIUPxRcTHspriPc5dTXDDKn46ae74sYPUH4z8WERb2L096ZPp-iFywHOnuIJuv1wcbP9VF5-_fh5u7ksrWB0KhVzlQHaKicZxsQAWKGsccyAUa2roFINrXmlOHa1ILxxQrREckNr25LWshP09rHuPo4_8pMmvRvnGHJLne3gghNaVweqMz1oH9w4RWMHn6zeMMJURmqVqfII1UGAaPoxgPP5-h9-fYTPq4XB26OC938Jmjn5AClvyXd3U-rMnNLR-jaOKUVweh_9kI3WBC-_U3oZtl6GrZdhZ8G7JzNMsqZ30QTr0x8VlYpJKuvMvXnkdnnS8ZBnjDJFqoMRy5_ikP7X9zexF8Ed</recordid><startdate>20121101</startdate><enddate>20121101</enddate><creator>Liu, Yunan</creator><creator>Whitt, Ward</creator><general>INFORMS</general><general>Institute for Operations Research and the Management Sciences</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>N95</scope><scope>XI7</scope><scope>JQ2</scope><scope>K9.</scope></search><sort><creationdate>20121101</creationdate><title>Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals</title><author>Liu, Yunan ; Whitt, Ward</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c532t-73f8ae2d7f63001aeec57caf3aea7df8e87b2948740f9514bf55d164a29cd1dc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Algorithms</topic><topic>Analysis</topic><topic>Applied sciences</topic><topic>Approximation</topic><topic>capacity planning</topic><topic>Consumer attitudes</topic><topic>Exact sciences and technology</topic><topic>Firm modelling</topic><topic>infinite-server queues</topic><topic>Inventory control, production control. Distribution</topic><topic>Learning models (Stochastic processes)</topic><topic>many-server queues</topic><topic>METHODS</topic><topic>Modeling</topic><topic>offered-load approximations</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Parametric models</topic><topic>Performance metrics</topic><topic>Poisson process</topic><topic>queues with abandonment</topic><topic>queues with time-varying arrivals</topic><topic>Queuing theory</topic><topic>Queuing theory. Traffic theory</topic><topic>Random variables</topic><topic>service systems</topic><topic>Staffing</topic><topic>Stochastic models</topic><topic>Studies</topic><topic>Time dependence</topic><topic>Waiting rooms</topic><topic>Workforce planning</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Yunan</creatorcontrib><creatorcontrib>Whitt, Ward</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Gale Business Insights</collection><collection>Business Insights: Essentials</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><jtitle>Operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Yunan</au><au>Whitt, Ward</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals</atitle><jtitle>Operations research</jtitle><date>2012-11-01</date><risdate>2012</risdate><volume>60</volume><issue>6</issue><spage>1551</spage><epage>1564</epage><pages>1551-1564</pages><issn>0030-364X</issn><eissn>1526-5463</eissn><coden>OPREAI</coden><abstract>An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the
M
t
/
GI
/
s
t
+
GI
many-server queueing model, which has a nonhomogeneous Poisson arrival process (the
M
t
), has general service times (the first
GI
), and allows customer abandonment according to a general patience distribution (the +
GI
). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime.</abstract><cop>Hanover, MD</cop><pub>INFORMS</pub><doi>10.1287/opre.1120.1104</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0030-364X |
| ispartof | Operations research, 2012-11, Vol.60 (6), p.1551-1564 |
| issn | 0030-364X 1526-5463 |
| language | eng |
| recordid | cdi_proquest_journals_1284541298 |
| source | 美国运筹学和管理学研究协会期刊（NSTL购买）; JSTOR Complete Journals; EBSCOhost Business Source Complete |
| subjects | Algorithms Analysis Applied sciences Approximation capacity planning Consumer attitudes Exact sciences and technology Firm modelling infinite-server queues Inventory control, production control. Distribution Learning models (Stochastic processes) many-server queues METHODS Modeling offered-load approximations Operational research and scientific management Operational research. Management science Parametric models Performance metrics Poisson process queues with abandonment queues with time-varying arrivals Queuing theory Queuing theory. Traffic theory Random variables service systems Staffing Stochastic models Studies Time dependence Waiting rooms Workforce planning |
| title | Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals |
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