Index policies for the routing of background jobs

Glazebrook, K. D.; Kirkbride, Christopher

doi:10.1002/nav.20034

Cited by 3 publications

(6 citation statements)

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“…Book length treatments of restless bandits can be found in [26] and [44]. In the particular area of load balancing, there has been several previous works that have applied the restless banding framework, and who have calculated Whittle's index either in closed-form or via an iterative scheme (see [3,6,17,37,39]). For example, in [6], servers are PS and an iterative scheme is reported to compute Whittle's index in the case of linear cost functions and no blocking.…”

Section: Related Literaturementioning

confidence: 99%

“…For example, in [6], servers are PS and an iterative scheme is reported to compute Whittle's index in the case of linear cost functions and no blocking. The load balancing problem in [3,17] deals with FCFS servers with dedicated arrivals for each queue. Dedicated arrivals have priority over new arrivals in the load balancing model of [17].…”

Section: Related Literaturementioning

confidence: 99%

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Load balancing with heterogeneous schedulers

Ayesta¹,

Gupta²,

Verloop³

2018

Preprint

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Load balancing is a common approach in web server farms or inventory routing problems. An important issue in such systems is to determine the server to which an incoming request should be routed to optimize a given performance criteria. In this paper, we assume the server's scheduling disciplines to be heterogeneous. More precisely, a server implements a scheduling discipline which belongs to the class of limited processor sharing (LPSd) scheduling disciplines. Under LPS-d, up to d jobs can be served simultaneously, and hence, includes as special cases First Come First Served (d = 1) and Processor Sharing (d = ∞).In order to obtain efficient heuristics, we model the above load-balancing framework as a multi-armed restless bandit problem. Using the relaxation technique, as first developed in the seminal work of Whittle, we derive Whittle's index policy for general cost functions and obtain a closed-form expression for Whittle's index in terms of the steady-state distribution. Through numerical computations, we investigate the performance of Whittle's index with two different performance criteria: linear cost criterion and a cost criterion that depends on the first and second moment of the throughput. Our results show that (i) the structure of Whittle's index policy can strongly depend on the scheduling discipline implemented in the server, i.e., on d, and that (ii) Whittle's index policy significantly outperforms standard dispatching rules such as Join the Shortest Queue (JSQ), Join the Shortest Expected Workload (JSEW), and Random Server allocation (RSA).

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Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Load balancing with heterogeneous schedulers

Ayesta¹,

Gupta²,

Verloop³

2018

Preprint

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“…See Niño-Mora [10] and Whittle [16]. Glazebrook and Kirkbride [3] have latterly espoused an approach to complex routing problems which is a hybrid of these methodologies.…”

Section: Introductionmentioning

confidence: 99%

Dynamic routing to heterogeneous collections of unreliable servers

Glazebrook

Kirkbride

2006

Queueing Syst

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We argue the importance of problems concerning the dynamic routing of tasks for service in environments where the servers have diverse characteristics and are subject to breakdown. We propose a general model in which both service times and repair times at each machine are i.i.d. with some general distribution. Routing decisions take account of queue lengths, machine states (up or down), the elapsed processing times of jobs in service and the times to date of any machine repairs in progress. We develop an approach to machine calibration which yields a machine index which is a function of all of the preceding information. The heuristic which routes all tasks to the machine of current smallest index performs outstandingly well. The approach of the paper is flexible and is capable of yielding strongly performing routing policies for a range of variants of the basic model. These include cases where job processing is lost at each breakdown and where the machine state may be only partially observed.

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“…Further, a range of empirical studies have demonstrated the power and practicability of Whittle's approach in a range of application contexts. See, for example, Ansell et al [2], Opp et al [23], Glazebrook et al [14,15], and Glazebrook and Kirkbride [12,13].…”

mentioning

confidence: 99%

“…We call this problem p n . Plainly, from (12), an optimal policy for (6) and (9) simply runs optimal policies for the p n 1 ≤ n ≤ N , in parallel. We now follow Whittle [30] in requiring structure in optimal policies for each p n that will permit development of an appropriate calibrating function n a b × n → + for bandit n. In order to do this, we write b n u n for the passive set corresponding to policy u n , which is stationary for p n , namely Under (I) and (II), the corresponding index for bandit n n a b × n → + is given by n x n = inf ∈ + x n ∈ b n u n (13) From (13), n x n has an interpretation as a fair charge (per unit of resource) for the additional resource consumed in going from passive (b) to active (a) when bandit n is in state x n .…”

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confidence: 99%

A Generalized Gittins Index for a Class of Multiarmed Bandits with General Resource Requirements

Glazebrook

Minty

2009

Mathematics of OR

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We generalise classical multiarmed bandits to allow for the distribution of a (fixed amount of a) divisible resource among the constituent bandits at each decision point. Bandit activation consumes amounts of the available resource, which may vary by bandit and state. Any collection of bandits may be activated at any decision epoch, provided they do not consume more resource than is available. We propose suitable bandit indices that reduce to those proposed by Gittins [Gittins, J. C. 1979. Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B41 148-177] for the classical models. The index that emerges is an elegant generalization of the Gittins index, which measures in a natural way the reward earnable from a bandit per unit of resource consumed. The paper discusses both how such indices may be computed and how they may be used to construct heuristics for resource distribution. We also describe how to develop bounds on the closeness to optimality of index heuristics and demonstrate a form of asymptotic optimality for a greedy index heuristic in a class of simple models. A numerical study testifies to the strong performance of a weighted index heuristic.

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Index policies for the routing of background jobs

Cited by 3 publications

References 31 publications

Load balancing with heterogeneous schedulers

Load balancing with heterogeneous schedulers

Dynamic routing to heterogeneous collections of unreliable servers

A Generalized Gittins Index for a Class of Multiarmed Bandits with General Resource Requirements

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