Waiting time distributions in the accumulating priority queue
Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classe...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Stanford, David A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Queueing systems - Springer US, 1986, 77(2013), 3 vom: 07. Dez., Seite 297-330 |
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| Übergeordnetes Werk: |
volume:77 ; year:2013 ; number:3 ; day:07 ; month:12 ; pages:297-330 |
| Links: |
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| DOI / URN: |
10.1007/s11134-013-9382-6 |
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OLC2058615565 |
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| 520 | |a Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. | ||
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10.1007/s11134-013-9382-6 doi (DE-627)OLC2058615565 (DE-He213)s11134-013-9382-6-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Stanford, David A. verfasserin aut Waiting time distributions in the accumulating priority queue 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2013 Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. Priority queues Time-dependent priority Non-preemptive priority Accumulating priority Taylor, Peter aut Ziedins, Ilze aut Enthalten in Queueing systems Springer US, 1986 77(2013), 3 vom: 07. Dez., Seite 297-330 (DE-627)129219673 (DE-600)56281-6 (DE-576)034178309 0257-0130 nnns volume:77 year:2013 number:3 day:07 month:12 pages:297-330 https://doi.org/10.1007/s11134-013-9382-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4193 AR 77 2013 3 07 12 297-330 |
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10.1007/s11134-013-9382-6 doi (DE-627)OLC2058615565 (DE-He213)s11134-013-9382-6-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Stanford, David A. verfasserin aut Waiting time distributions in the accumulating priority queue 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2013 Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. Priority queues Time-dependent priority Non-preemptive priority Accumulating priority Taylor, Peter aut Ziedins, Ilze aut Enthalten in Queueing systems Springer US, 1986 77(2013), 3 vom: 07. Dez., Seite 297-330 (DE-627)129219673 (DE-600)56281-6 (DE-576)034178309 0257-0130 nnns volume:77 year:2013 number:3 day:07 month:12 pages:297-330 https://doi.org/10.1007/s11134-013-9382-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4193 AR 77 2013 3 07 12 297-330 |
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10.1007/s11134-013-9382-6 doi (DE-627)OLC2058615565 (DE-He213)s11134-013-9382-6-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Stanford, David A. verfasserin aut Waiting time distributions in the accumulating priority queue 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2013 Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. Priority queues Time-dependent priority Non-preemptive priority Accumulating priority Taylor, Peter aut Ziedins, Ilze aut Enthalten in Queueing systems Springer US, 1986 77(2013), 3 vom: 07. Dez., Seite 297-330 (DE-627)129219673 (DE-600)56281-6 (DE-576)034178309 0257-0130 nnns volume:77 year:2013 number:3 day:07 month:12 pages:297-330 https://doi.org/10.1007/s11134-013-9382-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4193 AR 77 2013 3 07 12 297-330 |
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10.1007/s11134-013-9382-6 doi (DE-627)OLC2058615565 (DE-He213)s11134-013-9382-6-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Stanford, David A. verfasserin aut Waiting time distributions in the accumulating priority queue 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2013 Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. Priority queues Time-dependent priority Non-preemptive priority Accumulating priority Taylor, Peter aut Ziedins, Ilze aut Enthalten in Queueing systems Springer US, 1986 77(2013), 3 vom: 07. Dez., Seite 297-330 (DE-627)129219673 (DE-600)56281-6 (DE-576)034178309 0257-0130 nnns volume:77 year:2013 number:3 day:07 month:12 pages:297-330 https://doi.org/10.1007/s11134-013-9382-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4193 AR 77 2013 3 07 12 297-330 |
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Waiting time distributions in the accumulating priority queue |
| abstract |
Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. © The Author(s) 2013 |
| abstractGer |
Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. © The Author(s) 2013 |
| abstract_unstemmed |
Abstract We are interested in queues in which customers of different classes arrive to a service facility, and where performance targets are specified for each class. The manager of such a queue has the task of implementing a queueing discipline that results in the performance targets for all classes being met simultaneously. For the case where the performance targets are specified in terms of ratios of mean waiting times, as long ago as the 1960s, Kleinrock suggested a queueing discipline to ensure that the targets are achieved. He proposed that customers accumulate priority as a linear function of their time in the queue: the higher the urgency of the customer’s class, the greater the rate at which that customer accumulates priority. When the server becomes free, the customer (if any) with the highest accumulated priority at that time point is the one that is selected for service. Kleinrock called such a queue a time-dependent priority queue, but we shall refer to it as the accumulating priority queue. Recognising that the performance of many queues, particularly in the healthcare and human services sectors, is specified in terms of tails of waiting time distributions for customers of different classes, we revisit the accumulating priority queue to derive its waiting time distributions, rather than just the mean waiting times. We believe that some elements of our analysis, particularly the process that we call the maximum priority process, are of mathematical interest in their own right. © The Author(s) 2013 |
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| container_issue |
3 |
| title_short |
Waiting time distributions in the accumulating priority queue |
| url |
https://doi.org/10.1007/s11134-013-9382-6 |
| remote_bool |
false |
| author2 |
Taylor, Peter Ziedins, Ilze |
| author2Str |
Taylor, Peter Ziedins, Ilze |
| ppnlink |
129219673 |
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n |
| isOA_txt |
false |
| hochschulschrift_bool |
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| doi_str |
10.1007/s11134-013-9382-6 |
| up_date |
2024-07-03T19:28:50.970Z |
| _version_ |
1803587347787284480 |
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