Stability criterion of a multiserver model with simultaneous service

Rumyantsev, Alexander; Morozov, Evsey

doi:10.1007/s10479-015-1917-2

Cited by 51 publications

(34 citation statements)

References 21 publications

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“…We establish the QBD process following the work of [30], where a model with constant speed was considered. Let ( ) be the number of customers in the system at time , and let ( ) be the system configuration at time , that is, ( ) = ( 1 ( ), .…”

Section: Matrix-analytic Modelmentioning

confidence: 99%

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A Three-Level Modelling Approach for Asynchronous Speed Scaling in High-Performance Data Centres

Rumyantsev

Basmadjian

Golovin

et al. 2021

Proceedings of the Twelfth ACM International Conference on Future Energy Systems

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In data centres, there exist several techniques for energy efficiency purposes. When applied, most of those techniques have impact on the quality (e.g. performance) of the underlying services. A careful study is required in order to optimise such an energy-performance trade-off. In this paper, we study the speed scaling as an energy efficiency technique within the scope of high-performance computing (HPC) data centres. We propose a methodology based on threelevels: analytic, simulation and technical. At the analytical level, the matrix-analytic method (MAM) allows one to obtain energyperformance measures explicitly for a small-scale system. At the simulation level, discrete-event simulation (DES) based on the generalised semi-Markov processes (GSMP) is used to derive the corresponding estimates. Finally, at the technical level, a real small-scaled system in a controlled environment is used. The preliminary results demonstrate that simulation and technical models go well together with the theoretical one with an accuracy of more than 95%. CCS CONCEPTS• Hardware → Enterprise level and data centers power issues; • Mathematics of computing → Queueing theory; • Computing methodologies → Discrete-event simulation.

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Section: Matrix-analytic Modelmentioning

confidence: 99%

“…, min( ( ), ) ( )), where ( ) is the number of servers requested by -th oldest customer in the system among present at time , and we omit ( ) for ( ) = 0. Note that the ( + )-th oldest customers, ≥ 1 (if any) are generic, and thus the configuration is a -component vector [30]. Finally, let ( ) be the system speed at time .…”

Section: Matrix-analytic Modelmentioning

confidence: 99%

A Three-Level Modelling Approach for Asynchronous Speed Scaling in High-Performance Data Centres

Rumyantsev

Basmadjian

Golovin

et al. 2021

Proceedings of the Twelfth ACM International Conference on Future Energy Systems

Self Cite

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“…In the Multiserver-Job model, not all policies achieve the same stability region. For instance, the FCFS policy, while natural, often leaves servers empty due to head-of-theblocking, shrinking its stability region [6,36]. As a result, FCFS does not have optimal stability region, or equivalently it is not throughput optimal.…”

Section: Stability Regionmentioning

confidence: 99%

WCFS: A new framework for analyzing multiserver systems

Grosof¹,

Scheller‐Wolf²

2021

Preprint

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Multiserver queueing systems are found at the core of a wide variety of practical systems. Unfortunately, existing tools for analyzing multiserver models have major limitations: Techniques for exact analysis often struggle with high-dimensional models, while techniques for deriving bounds are often too specialized to handle realistic system features, such as variable service rates of jobs. New techniques are needed to handle these complex, important, high-dimensional models.In this paper we introduce the work-conserving finite-skip class of models. This class includes many important models, such as the heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the threshold parallelism model, and the multiserver-job model under a simple scheduling policy.We prove upper and lower bounds on mean response time for any model in the work-conserving finite-skip class. Our bounds are separated by an additive constant, giving a strong characterization of mean response time at all loads. When specialized to each of the models above, these bounds represent the first bounds on mean response time known for each setting.

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“…Attempts to derive the steady-state distribution have assumed highly simplified systems. Even characterizing the stability region of the system is an open problem except for the special cases where all jobs have the same service rates [1,8,9], or where there are only two job classes with different service rates [4].…”

Section: Introductionmentioning

confidence: 99%

Zero Queueing for Multi-Server Jobs

Wang

Xie

2021

Abstract Proceedings of the 2021 ACM SIGMETRICS / International Conference on Measurement and Modeling of Computer Systems

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Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit" into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multiserver job queueing systems; even understanding the exact stability region is a very hard problem.In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

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Stability criterion of a multiserver model with simultaneous service

Cited by 51 publications

References 21 publications

A Three-Level Modelling Approach for Asynchronous Speed Scaling in High-Performance Data Centres

A Three-Level Modelling Approach for Asynchronous Speed Scaling in High-Performance Data Centres

WCFS: A new framework for analyzing multiserver systems

Zero Queueing for Multi-Server Jobs

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