## Capacity Realization in Stochastic Batch-Processing Networks Using Discrete-Review Policies (1999)

Citations: | 3 - 0 self |

### BibTeX

@TECHREPORT{Maglaras99capacityrealization,

author = {Constantinos Maglaras and Sunil Kumar},

title = {Capacity Realization in Stochastic Batch-Processing Networks Using Discrete-Review Policies},

institution = {},

year = {1999}

}

### OpenURL

### Abstract

We present difficulties with realizing the capacity of queueing networks with batch servers under well known scheduling disciplines. We introduce a family of scheduling policies called discrete-review policies, which not only guarantee capacity realization for queueing networks with batch servers, but also contain among them policies that allow us to realize desired behavior on "fluid" scale, including asymptotically optimal policies. In this family of policies system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed, which is then executed in open-loop fashion. We outline a proof of capacity realization for every policy in this family, and provide results of simulation studies that establish the usefulness of the proposed family of policies.

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Citation Context ...thout bound [14, 19]. However, there have been some positive results which have demonstrated that at least some policies can be guaranteed to realize capacity, at least in the case of reentrant lines =-=[6, 8, 18, 19]-=-. It is not at all clear how capacity realization can be achieved in queueing networks with batch servers, which arise as natural models of manufacturing systems with batch processing servers. In fact... |

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Citation Context ... whether a general procedure to achieve this goal exists. Finally, one of the main approaches to verifying capacity realization for queueing networks involves analyzing their associated \ uid limits&q=-=uot; [3, 5, 6, 7, 17, 19]-=-. As it will become apparent in the next section, it is not clear how one can describesuid limits of networks with batch servers, and thus direct application of this method is dicult. There is a consi... |

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Citation Context ... whether a general procedure to achieve this goal exists. Finally, one of the main approaches to verifying capacity realization for queueing networks involves analyzing their associated \ uid limits&q=-=uot; [3, 5, 6, 7, 17, 19]-=-. As it will become apparent in the next section, it is not clear how one can describesuid limits of networks with batch servers, and thus direct application of this method is dicult. There is a consi... |

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Citation Context ...licies weresrst introduced in Harrison's BIGSTEP approach to dynamicsow management [13] and later, they were 4 formally described and analyzed for a general class of networks by one of the authors in =-=[22, 23]-=-. In a discrete-review policy, system status is reviewed at discrete instants in time and processing decisions are made over a planning horizon whose length depends on the amount of work present in th... |

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Citation Context ...thout bound [14, 19]. However, there have been some positive results which have demonstrated that at least some policies can be guaranteed to realize capacity, at least in the case of reentrant lines =-=[6, 8, 18, 19]-=-. It is not at all clear how capacity realization can be achieved in queueing networks with batch servers, which arise as natural models of manufacturing systems with batch processing servers. In fact... |

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Citation Context ...lysis of single station networks [27, 24], or of product form networks [29, 26] which form a very small class of queueing network models, or on designing batching control policies using simple models =-=[10, 1-=-1]. In a dierent spirit from the work mentioned above, signicant contributions have been made in addressing the complexity of scheduling problems with batch servers in a combinatorial optimization fra... |

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Citation Context ... application of this method is dicult. There is a considerable literature on queueing networks with batch servers. Most of it is either concentrated on performance analysis of single station networks =-=[27, 24-=-], or of product form networks [29, 26] which form a very small class of queueing network models, or on designing batching control policies using simple models [10, 11]. In a dierent spirit from the w... |

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Citation Context ...works which are unstable at throughput rates much smaller than the bottleneck capacity [4, 20, 28], as well as closed networks that do not achieve bottleneck throughput as the WIP grows without bound =-=[14, 19]-=-. However, there have been some positive results which have demonstrated that at least some policies can be guaranteed to realize capacity, at least in the case of reentrant lines [6, 8, 18, 19]. It i... |

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Citation Context ...ich arise in queueing network models of semiconductor fabs. There have been many recent examples of both open networks which are unstable at throughput rates much smaller than the bottleneck capacity =-=[4, 20, 28]-=-, as well as closed networks that do not achieve bottleneck throughput as the WIP grows without bound [14, 19]. However, there have been some positive results which have demonstrated that at least som... |

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Citation Context ...rk mentioned above, signicant contributions have been made in addressing the complexity of scheduling problems with batch servers in a combinatorial optimization framework. The reader is referred to [=-=1]-=- and some of the references therein for some recent results. In all these cases, capacity realization is either obvious or implicitly assumed. In fact, none of the existing literature would lead the r... |

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Citation Context ... There is a considerable literature on queueing networks with batch servers. Most of it is either concentrated on performance analysis of single station networks [27, 24], or of product form networks =-=[29, 2-=-6] which form a very small class of queueing network models, or on designing batching control policies using simple models [10, 11]. In a dierent spirit from the work mentioned above, signicant contri... |

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Citation Context ...always achieves capacity realization in queueing networks with batch servers under very general assumptions. These policies weresrst introduced in Harrison's BIGSTEP approach to dynamicsow management =-=[13]-=- and later, they were 4 formally described and analyzed for a general class of networks by one of the authors in [22, 23]. In a discrete-review policy, system status is reviewed at discrete instants i... |

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Citation Context ... whether a general procedure to achieve this goal exists. Finally, one of the main approaches to verifying capacity realization for queueing networks involves analyzing their associated \ uid limits&q=-=uot; [3, 5, 6, 7, 17, 19]-=-. As it will become apparent in the next section, it is not clear how one can describesuid limits of networks with batch servers, and thus direct application of this method is dicult. There is a consi... |

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Citation Context ...thout bound [14, 19]. However, there have been some positive results which have demonstrated that at least some policies can be guaranteed to realize capacity, at least in the case of reentrant lines =-=[6, 8, 18, 19]-=-. It is not at all clear how capacity realization can be achieved in queueing networks with batch servers, which arise as natural models of manufacturing systems with batch processing servers. In fact... |

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Citation Context ... There is a considerable literature on queueing networks with batch servers. Most of it is either concentrated on performance analysis of single station networks [27, 24], or of product form networks =-=[29, 2-=-6] which form a very small class of queueing network models, or on designing batching control policies using simple models [10, 11]. In a dierent spirit from the work mentioned above, signicant contri... |

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Citation Context ...s it is necessary to build up the levels tosand the remaining of the logic in [23] applies without any modication. Note that in simpler network models, such as reentrant lines introduced by Kumar in [=-=15-=-], this infeasible planning step is much easier to implement. There, the system issrst idled to accumulate jj external arrivals and subsequently, work is pushed through the network until all job class... |

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Citation Context ...works which are unstable at throughput rates much smaller than the bottleneck capacity [4, 20, 28], as well as closed networks that do not achieve bottleneck throughput as the WIP grows without bound =-=[14, 19]-=-. However, there have been some positive results which have demonstrated that at least some policies can be guaranteed to realize capacity, at least in the case of reentrant lines [6, 8, 18, 19]. It i... |

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Citation Context ... application of this method is dicult. There is a considerable literature on queueing networks with batch servers. Most of it is either concentrated on performance analysis of single station networks =-=[27, 24-=-], or of product form networks [29, 26] which form a very small class of queueing network models, or on designing batching control policies using simple models [10, 11]. In a dierent spirit from the w... |

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Citation Context ... limits will be optimal under the criterion dened in (7.2). Policies designed using this asymptotic criterion may prove to be useful heuristic policies for a manufacturing. The reader is referred to [=-=25-=-] for motivation and denition of the property ofsuid-scale asymptotic optimality and to [22] for a detailed discussion in the context of discrete-review policies. From an implementation point of view,... |