Insensitive Job Assignment With Throughput and Energy Criteria for Processor-Sharing Server Farms

Rosberg, Z.; Yu, Peng; Fu, Jing; Guo, Jun; Wong, E.W.M.; Zukerman, Moshe

doi:10.1109/tnet.2013.2276427

Cited by 12 publications

(11 citation statements)

References 40 publications

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“…The value 1−A ℓ represents the blocking probability of job class ℓ under the policy φ 0 . Thus, for any φ ∈ Φ, we can further relax (14) as…”

Section: B Asymptotic Optimalitymentioning

confidence: 99%

“…Research on the development of dynamic resource allocation methodologies for large-scale server farms (networks) with the reuse of released physical resources has been conducted under a certain simplifying assumption. The work in [14]- [17] considered heterogeneous servers but under the assumption of negligible power consumption of idle servers, while in [18]- [21] it was assumed that servers either reach their peak power consumption rates or stay idle. Then, in [22]- [26], it was assumed that servers' power consumption linearly increases as a function of their service rates.…”

Section: Introductionmentioning

confidence: 99%

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A Restless Bandit Model for Energy-Efficient Job Assignments in Server Farms

Fu¹,

Wang²,

Wang³

et al. 2021

Preprint

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We aim to maximize the energy efficiency, gauged as average energy cost per job, in a large-scale server farm with various storage or/and computing components, which are modeled as parallel abstracted servers. Each server works in multiple power modes characterized by potentially different service and energy consumption rates. The heterogeneity of servers and multiple power modes significantly complicate the maximization problem, where optimal solutions are generally intractable. Relying on the Whittle relaxation technique, we resort to a near-optimal and scalable job-assignment policy. Under certain conditions including the assumption of exponentially distributed job sizes, we prove that our proposed policy approaches optimality as the size of the entire system tends to infinity; that is, it is asymptotically optimal. Nevertheless, we demonstrate by simulations that the effectiveness of our policies is not significantly limited by the conditions used for mathematical rigor and that our model still has wide practical applicability. In particular, the asymptotic optimality is very much relevant for many real-world large-scale systems with tens or hundreds of thousands of components, where conventional optimization techniques can hardly apply. Furthermore, for non-asymptotic scenarios, we show the effectiveness of the proposed policy through extensive numerical simulations, where the policy substantially outperforms all the tested baselines, and we especially demonstrate numerically its robustness against heavy-tailed job-size distributions.

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“…The value 1−A ℓ represents the blocking probability of job class ℓ under the policy φ 0 . Thus, for any φ ∈ Φ, we can further relax (14) as…”

Section: B Asymptotic Optimalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Restless Bandit Model for Energy-Efficient Job Assignments in Server Farms

Fu¹,

Wang²,

Wang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [6], [15], such server farms are called dynamic right-sizing server farms. In similar vein to [17], [18], [22], for the purposes of this paper, a fixed number of working servers is postulated in a server farm with no possibility of powering off or state switching, with substantial delay, during the time period under consideration. In practice, this corresponds to periods during which no powering off or state switching, with concomitant substantial delays, takes place.…”

Section: Other Related Workmentioning

confidence: 99%

“…Since A j * > 1, there exists a ν j * ≥ min s∈S j * λ j * (1 − e * (ε k(s) − ε 0 k(s) )/µ k(s) ), such that Note that φ * s is dependent on ν j * . On the other hand, the setting of γ j * guarantees that there is a policy ϕ ∈ Φ j * maximizing the objective function defined by (17), and satisfying α ϕ j * = 0 and Θ(a ϕ j * ) = 0 = Θ(1 − A j * ), e.g., equations (11) and (13) achieve equality. That is, such a ν j * , γ j * , φ * s ∈ Φ s , s ∈ S j * and ϕ ∈ Φ j * , make the complementary slackness condition satisfied.…”

Section: Appendix a Proof Of Propositionmentioning

confidence: 99%

Energy-Efficient Job-Assignment Policy With Asymptotically Guaranteed Performance Deviation

Moran

2020

IEEE/ACM Trans. Networking

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We study a job-assignment problem in a largescale server farm system with geographically deployed servers as abstracted computer components (e.g., storage, network links, and processors) that are potentially diverse. We aim to maximize the energy efficiency of the entire system by effectively controlling carried load on networked servers. A scalable, near-optimal jobassignment policy is proposed. The optimality is gauged as, roughly speaking, energy cost per job. Our key result is an upper bound on the deviation between the proposed policy and the asymptotically optimal energy efficiency, when job sizes are exponentially distributed and blocking probabilities are positive. Relying on Whittle relaxation and the asymptotic optimality theorem of Weber and Weiss, this bound is shown to decrease exponentially as the number of servers and the arrival rates of jobs increase arbitrarily and in proportion. In consequence, the proposed policy is asymptotically optimal and, more importantly, approaches asymptotic optimality quickly (exponentially). This suggests that the proposed policy is close to optimal even for relatively small systems (and indeed any larger systems), and this is consistent with the results of our simulations. Simulations indicate that the policy is effective, and robust to variations in job-size distributions.Index Terms-server farm, energy efficiency, restless multiarmed bandit problem.

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“…Additionally, we show that the mean response time in an M/G/1-PS is no longer insensitive to the service time distribution when a setup delay is introduced, whereas with LCFS the insensitivity property is preserved. The insensitivity property is generally desired as it enhances robustness [3], [4].…”

Section: Introductionmentioning

confidence: 99%

Energy-aware job assignment in server farms with setup delays under LCFS and PS

Hyytiä

Righter

Aalto

2014

2014 26th International Teletraffic Congress (ITC)

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Abstract-We consider the job (or task) assignment problem to heterogeneous parallel servers, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient job assignment (dispatching) policies that minimize the long-run average cost. In our earlier work, we assumed FCFS scheduling at the servers. In this paper, we focus on LCFS and PS, where the latter in particular serves as an important model, e.g., for server farms where jobs are processed concurrently. LCFS, on the other hand, is a robust policy that works especially well when service times are highly variable, and is easier to implement than the standard alternative policy for high variability, LAS (least attained service time). Our costs include energy related running costs, as well as performance related mean response times. The efficiency of the resulting operating policies is illustrated with numerical examples, where we also compare FCFS to LCFS and PS.

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Insensitive Job Assignment With Throughput and Energy Criteria for Processor-Sharing Server Farms

Cited by 12 publications

References 40 publications

A Restless Bandit Model for Energy-Efficient Job Assignments in Server Farms

A Restless Bandit Model for Energy-Efficient Job Assignments in Server Farms

Energy-Efficient Job-Assignment Policy With Asymptotically Guaranteed Performance Deviation

Energy-aware job assignment in server farms with setup delays under LCFS and PS

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