Index Policies for the Admission Control and Routing of Impatient Customers to Heterogeneous Service Stations

Glazebrook, K. D.; Kirkbride, C.; Ouenniche, Jamal

doi:10.1287/opre.1080.0632

Cited by 37 publications

(44 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The optimization problem in (15) relates to station n alone, with U n the class of stationary policies for determining whether to admit (action a) or reject (action r) each generic arrival, the goal of optimization being the minimization of an aggregate customer waiting cost ( C n (u)) and rejection charges (W R n (u)). Call this station n problem P n (W ).…”

Section: Heuristic 2: Lagrangian Relaxation Methodsmentioning

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.

View full text Add to dashboard Cite

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.

show abstract

Section: Heuristic 2: Lagrangian Relaxation Methodsmentioning

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.

View full text Add to dashboard Cite

show abstract

“…Step 5 We declare a to be the action dictated by π W now that all S units of resource have been allocated.…”

Section: Lemma 1 Suppose That All K Products Are Fully Indexable Withmentioning

confidence: 99%

“…Write W * for the maximising W in (12). In a context much simpler than the current one, Glazebrook et al [5] discuss how the nature of solutions to (4) and (12) can shed light on the performance of a greedy index heuristic. Should it be the case that, under full indexability, the policy π(W * ) which achieves V * be such that, the system states which require that π(W * ) take an inadmissible action have small probability, in equilibrium, then V * will be close to V opt and π W will be close to optimal.…”

Section: The Greedy Index Heuristic and The Importance Of Full Indexamentioning

confidence: 99%

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

Hodge

Glazebrook

2011

Queueing Syst

Self Cite

View full text Add to dashboard Cite

. 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.

show abstract

“…For the random vector X N (t), we define the following Probability Generating Function (21) and the Moment Generating Function (22), conditioned on the environment vector d:…”

Section: Appendixmentioning

confidence: 99%

“…In this paper we will restrict our attention to optimal control in a restless bandit problem as this provides a powerful optimization framework to model dynamic scheduling of activities. In particular, regarding optimal control of computing systems, the restless bandit framework has been successfully applied in for example the context of wireless downlink scheduling [3,7,33], load balancing problems [26], systems with delayed state observation [19], broadcast systems [35], multi-channel access models [2,27], stochastic scheduling problems [4,23,30] and scheduling in the presence of impatient customers [9,22,25,31]. distribution of the modulated environments.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Optimal Control of Markov-Modulated Restless Bandits

Durán

Verloop

2018

Proc. ACM Meas. Anal. Comput. Syst.

View full text Add to dashboard Cite

This paper studies optimal control subject to changing conditions. This is an area that recently received a lot of attention as it arises in numerous situations in practice. Some applications being cloud computing systems where the arrival rates of new jobs fluctuate over time, or the time-varying capacity as encountered in power-aware systems or wireless downlink channels. To study this, we focus on a restless bandit model, which has proved to be a powerful stochastic optimization framework to model scheduling of activities. In particular, it has been extensively applied in the context of optimal control of computing systems. This paper is a first step to its optimal control when restless bandits are subject to changing conditions, the latter being modeled by Markov-modulated environments.We consider the restless bandit problem in an asymptotic regime, which is obtained by letting the population of bandits grow large, and letting the environment change relatively fast. We present sufficient conditions for a policy to be asymptotically optimal and show that a set of priority policies satisfies these. Under an indexability assumption, an averaged version of Whittle's index policy is proved to be inside this set of asymptotic optimal policies. The performance of the averaged Whittle's index policy is numerically evaluated for a multi-class scheduling problem in a wireless downlink subject to changing conditions. While keeping the number of bandits constant, we observe that the average Whittle index policy becomes close to optimal as the speed of the modulated environment increases.

show abstract

Index Policies for the Admission Control and Routing of Impatient Customers to Heterogeneous Service Stations

Cited by 37 publications

References 40 publications

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

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

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

Asymptotic Optimal Control of Markov-Modulated Restless Bandits

Contact Info

Product

Resources

About