Near optimal control of queueing networks over a finite time horizon
We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partition...
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| Published in: | Annals of operations research Vol. 170; no. 1; pp. 233 - 249 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Springer US
01.09.2009
Springer Nature B.V |
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| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line. |
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| AbstractList | We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line. [PUBLICATION ABSTRACT] We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line. |
| Author | Nazarathy, Yoni Weiss, Gideon |
| Author_xml | – sequence: 1 givenname: Yoni surname: Nazarathy fullname: Nazarathy, Yoni organization: Department of Statistics, The University of Haifa – sequence: 2 givenname: Gideon surname: Weiss fullname: Weiss, Gideon email: gweiss@stat.haifa.ac.il organization: Department of Statistics, The University of Haifa |
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| Keywords | Continuous linear programming Infinite virtual queues Fluid approximations Multi-class queueing networks Queueing control Maximum pressure policies |
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| Snippet | We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid... |
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| SubjectTerms | Approximation Business and Management Combinatorics Job shops Linear programming Mathematical models Operations research Operations Research/Decision Theory Optimization Queuing Servers Statistical analysis Studies Theory of Computation Wireless networks |
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| Title | Near optimal control of queueing networks over a finite time horizon |
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