Time-dependent analysis of virtual waiting time behaviour in discrete time queues
Discrete time queueing models have been shown previously to be of practical use for modelling the approximate time-dependent behaviour of queue length in systems of the form M( t)/ G/ c. In this paper we extend these models to include the time-dependent behaviour of virtual waiting time. Key compone...
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| Veröffentlicht in: | European journal of operational research 2007-04, Vol.178 (2), p.482-499 |
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| container_title | European journal of operational research |
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| creator | Wall, A.D. Worthington, D.J. |
| description | Discrete time queueing models have been shown previously to be of practical use for modelling the approximate time-dependent behaviour of queue length in systems of the form
M(
t)/
G/
c. In this paper we extend these models to include the time-dependent behaviour of virtual waiting time.
Key components of this research are the derivation of exact (algorithmic) expressions for virtual waiting time behaviour. Statistical approximations for the distributional form of virtual waiting times are then developed and tested. These approximations reduce the computational effort involved in the evaluation of the exact expressions by a factor of over 1000 whilst still maintaining very high accuracy levels.
The models have been implemented for use on a PC and are shown to be capable of modelling the time-dependent virtual waiting time behaviour of realistic queueing systems in just a few seconds.
Results from the models are compared with results obtained by the Simple Stationary Approximation, the Pointwise Stationary Approximation and Modified Offered Load approximations. They clarify further some of the strengths and weaknesses of these approaches and demonstrate the potential of the Discrete Time Modelling approach. |
| doi_str_mv | 10.1016/j.ejor.2005.12.038 |
| format | Article |
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M(
t)/
G/
c. In this paper we extend these models to include the time-dependent behaviour of virtual waiting time.
Key components of this research are the derivation of exact (algorithmic) expressions for virtual waiting time behaviour. Statistical approximations for the distributional form of virtual waiting times are then developed and tested. These approximations reduce the computational effort involved in the evaluation of the exact expressions by a factor of over 1000 whilst still maintaining very high accuracy levels.
The models have been implemented for use on a PC and are shown to be capable of modelling the time-dependent virtual waiting time behaviour of realistic queueing systems in just a few seconds.
Results from the models are compared with results obtained by the Simple Stationary Approximation, the Pointwise Stationary Approximation and Modified Offered Load approximations. They clarify further some of the strengths and weaknesses of these approaches and demonstrate the potential of the Discrete Time Modelling approach.</description><identifier>ISSN: 0377-2217</identifier><identifier>EISSN: 1872-6860</identifier><identifier>DOI: 10.1016/j.ejor.2005.12.038</identifier><identifier>CODEN: EJORDT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Applied sciences ; Approximation ; Customer waiting time ; Discrete time models ; Exact sciences and technology ; Operational research and scientific management ; Operational research. Management science ; Queueing ; Queuing theory ; Queuing theory. Traffic theory ; Simulation ; Studies ; Time dependent queues</subject><ispartof>European journal of operational research, 2007-04, Vol.178 (2), p.482-499</ispartof><rights>2006 Elsevier B.V.</rights><rights>2007 INIST-CNRS</rights><rights>Copyright Elsevier Sequoia S.A. Apr 16, 2007</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c523t-1237a3d5165f6572ae84d5675446077bd877dfaf7ba32b82cfb73babd1f743673</citedby><cites>FETCH-LOGICAL-c523t-1237a3d5165f6572ae84d5675446077bd877dfaf7ba32b82cfb73babd1f743673</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S037722170600124X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,3994,27903,27904,65309</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18402088$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeeejores/v_3a178_3ay_3a2007_3ai_3a2_3ap_3a482-499.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Wall, A.D.</creatorcontrib><creatorcontrib>Worthington, D.J.</creatorcontrib><title>Time-dependent analysis of virtual waiting time behaviour in discrete time queues</title><title>European journal of operational research</title><description>Discrete time queueing models have been shown previously to be of practical use for modelling the approximate time-dependent behaviour of queue length in systems of the form
M(
t)/
G/
c. In this paper we extend these models to include the time-dependent behaviour of virtual waiting time.
Key components of this research are the derivation of exact (algorithmic) expressions for virtual waiting time behaviour. Statistical approximations for the distributional form of virtual waiting times are then developed and tested. These approximations reduce the computational effort involved in the evaluation of the exact expressions by a factor of over 1000 whilst still maintaining very high accuracy levels.
The models have been implemented for use on a PC and are shown to be capable of modelling the time-dependent virtual waiting time behaviour of realistic queueing systems in just a few seconds.
Results from the models are compared with results obtained by the Simple Stationary Approximation, the Pointwise Stationary Approximation and Modified Offered Load approximations. They clarify further some of the strengths and weaknesses of these approaches and demonstrate the potential of the Discrete Time Modelling approach.</description><subject>Applied sciences</subject><subject>Approximation</subject><subject>Customer waiting time</subject><subject>Discrete time models</subject><subject>Exact sciences and technology</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Queueing</subject><subject>Queuing theory</subject><subject>Queuing theory. Traffic theory</subject><subject>Simulation</subject><subject>Studies</subject><subject>Time dependent queues</subject><issn>0377-2217</issn><issn>1872-6860</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNp9kE-LFDEQxRtRcFz9Ap4awWO3-dNJZcGLLK6KCyKs55BOKm6ame4xyYzMt7eaXvRmoFKBvFf1-DXNa856zrh-N_U4LbkXjKmei55J86TZcQOi00azp82OSYBOCA7PmxelTIwxrrjaNd_v0wG7gEecA861dbPbX0oq7RLbc8r15Pbtb5dqmn-2laTtiA_unJZTbtPchlR8xorb168TnrC8bJ5Fty_46rFfNT9uP97ffO7uvn36cvPhrvNKyNpxIcHJoLhWUSsQDs0QlAY1DJoBjMEAhOgijE6K0QgfR5CjGwOPMEgN8qp5s8095oU2l2onSkXxixVs4FJLUCQSm8jnpZSM0R5zOrh8sZzZlZyd7ErOruQsF5bIkenrZsqExf91IB2SYrFnKx0HQ_eFiqxALa1PqiPVYIQdrq_tQz3QtLePOV3xbh-zm30q_3KYgQlm1q3vNx0StHPCbItPOHsMKaOvNizpf6H_AFiXnbA</recordid><startdate>20070416</startdate><enddate>20070416</enddate><creator>Wall, A.D.</creator><creator>Worthington, D.J.</creator><general>Elsevier B.V</general><general>Elsevier</general><general>Elsevier Sequoia S.A</general><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20070416</creationdate><title>Time-dependent analysis of virtual waiting time behaviour in discrete time queues</title><author>Wall, A.D. ; Worthington, D.J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c523t-1237a3d5165f6572ae84d5675446077bd877dfaf7ba32b82cfb73babd1f743673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Applied sciences</topic><topic>Approximation</topic><topic>Customer waiting time</topic><topic>Discrete time models</topic><topic>Exact sciences and technology</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Queueing</topic><topic>Queuing theory</topic><topic>Queuing theory. Traffic theory</topic><topic>Simulation</topic><topic>Studies</topic><topic>Time dependent queues</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wall, A.D.</creatorcontrib><creatorcontrib>Worthington, D.J.</creatorcontrib><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>European journal of operational research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wall, A.D.</au><au>Worthington, D.J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Time-dependent analysis of virtual waiting time behaviour in discrete time queues</atitle><jtitle>European journal of operational research</jtitle><date>2007-04-16</date><risdate>2007</risdate><volume>178</volume><issue>2</issue><spage>482</spage><epage>499</epage><pages>482-499</pages><issn>0377-2217</issn><eissn>1872-6860</eissn><coden>EJORDT</coden><abstract>Discrete time queueing models have been shown previously to be of practical use for modelling the approximate time-dependent behaviour of queue length in systems of the form
M(
t)/
G/
c. In this paper we extend these models to include the time-dependent behaviour of virtual waiting time.
Key components of this research are the derivation of exact (algorithmic) expressions for virtual waiting time behaviour. Statistical approximations for the distributional form of virtual waiting times are then developed and tested. These approximations reduce the computational effort involved in the evaluation of the exact expressions by a factor of over 1000 whilst still maintaining very high accuracy levels.
The models have been implemented for use on a PC and are shown to be capable of modelling the time-dependent virtual waiting time behaviour of realistic queueing systems in just a few seconds.
Results from the models are compared with results obtained by the Simple Stationary Approximation, the Pointwise Stationary Approximation and Modified Offered Load approximations. They clarify further some of the strengths and weaknesses of these approaches and demonstrate the potential of the Discrete Time Modelling approach.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ejor.2005.12.038</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | European journal of operational research, 2007-04, Vol.178 (2), p.482-499 |
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| language | eng |
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| source | RePEc; Elsevier ScienceDirect Journals |
| subjects | Applied sciences Approximation Customer waiting time Discrete time models Exact sciences and technology Operational research and scientific management Operational research. Management science Queueing Queuing theory Queuing theory. Traffic theory Simulation Studies Time dependent queues |
| title | Time-dependent analysis of virtual waiting time behaviour in discrete time queues |
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