Optimality of routing and servicing in dependent parallel processing systems

Menich, Ronald; Serfozo, Richard F.

doi:10.1007/bf01159224

Cited by 61 publications

(56 citation statements)

References 25 publications

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“…Menich and Serfozo [7] consider a very special multi-server, multi-product model in the symmetric case in which product characteristics are identical. They study a queueing problem with both customer routing available and flexible service placement.…”

Section: Introductionmentioning

confidence: 99%

Dynamic resource allocation in a multi-product make-to-stock production system

Hodge

Glazebrook

2011

Queueing Syst

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. Dynamic resource allocation in a multi-product make-to-stock production system. Queueing Systems, Springer Verlag, 2011, pp.333-364. <10.1007/s11134-011-9217-2>. QUES9217_source.tex; 10/02/2011; 8:16 p. 1 Queueing Systems manuscript No. (will be inserted by the editor) Dynamic resource allocation in a multi-product make-to-stock production system D. J. Hodge · K. D. GlazebrookReceived: date / Accepted: date Abstract We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails.Keywords backordering · dynamic programming · dynamic resource allocation · index heuristic · Lagrangian relaxation · make-to-stock policy · queueing control Fig. 1: An illustration of a three-product (K = 3) queueing system currently in state (−2, 5, 0). White circles can be seen as customers waiting for backorders to be fulfilled.

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Section: Introductionmentioning

confidence: 99%

Dynamic resource allocation in a multi-product make-to-stock production system

Hodge

Glazebrook

2011

Queueing Syst

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“…This method of preemption and the use of longest queue in symmetric system has been studied in Zipkin (1995). LQ policies have also been studied in Zheng and Zipkin (1990), Menich andSerfozo (1991), andVan Mieghem (2003), and shown to be optimal in specific settings. We expect this policy to be optimal in our setting.…”

Section: A Two-type Symmetric Modelmentioning

confidence: 99%

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

Bassamboo

Randhawa

Mieghem

2012

Operations Research

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We analytically study optimal capacity and flexible technology selection in parallel queuing systems. We consider N stochastic arrival streams that may wait in N queues before being processed by one of many resources (technologies) that differ in their flexibility. A resource's ability to process k different arrival types or classes is referred to as level-k flexibility. We determine the capacity portfolio (consisting of all resources at all levels of flexibility) that minimizes linear capacity and linear holding costs in high-volume systems where the arrival rate → . We prove that "a little flexibility is all you need": the optimal portfolio invests O in specialized resources and only O √ in flexible resources and these optimal capacity choices bring the system into heavy traffic. Further, considering symmetric systems (with type-independent parameters), a novel "folding" methodology allows the specification of the asymptotic queue count process for any capacity portfolio under longest-queue scheduling in closed form that is amenable to optimization. This allows us to sharpen "a little flexibility is all you need": the asymptotically optimal flexibility configuration for symmetric systems with mild economies of scope invests a lot in specialized resources but only a little in flexible resources and only in level-2 flexibility, but effectively nothing (o √ ) in level-k > 2 flexibility. We characterize "tailored pairing" as the theoretical benchmark configuration that maximizes the value of flexibility when demand and service uncertainty are the main concerns.

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“…Here, "Shortest Delay Routing" (SDR) has been shown to be optimal under a range of conditions. See, for example, Weber [47], Winston [52], Johri [23], Hordijk and Koole [21], Menich and Serfozo [33], Sparaggis, Towsley, and Cassandras [39], Towsley, Sparaggis, and Cassandras [44], and Koole, Sparaggis, and Towsley [26]. However, Whitt [49] showed that SDR might not be optimal even for very simple cases.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Routing of Customers With General Delay Costs in a Multiserver Queuing System

Argon¹,

Ding²,

Glazebrook³

et al. 2009

Prob. Eng. Inf. Sci.

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider a network of parallel service stations each modeled as a single-server queue. Each station serves its own dedicated customers as well as generic customers who are routed from a central controller. We suppose that the cost incurred by a customer is an increasing function of her time spent in the system. In a significant advance on most previous work, we do not require waiting costs to be convex, still less linear. With the objective of minimizing the long-run average waiting cost, we develop two heuristic routing policies, one of which is based on dynamic programming policy improvement and the other on Lagrangian relaxation. In developing the latter policy, we show that each station is "indexable" under mild conditions for customers' waiting costs and also prove some structural results on the admission control problem that naturally arises as a result of the Lagrangian relaxation. We then test the performance of our heuristics in an extensive numerical study and show that the Lagrangian heuristic demonstrates a strong level of performance in a range of traffic conditions. In particular, it clearly outperforms both a greedy heuristic, which is a standard proposal in complex routing problems, and a recent proposal from the heavy traffic literature.

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Optimality of routing and servicing in dependent parallel processing systems

Cited by 61 publications

References 25 publications

Dynamic resource allocation in a multi-product make-to-stock production system

Dynamic resource allocation in a multi-product make-to-stock production system

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

Dynamic Routing of Customers With General Delay Costs in a Multiserver Queuing System

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