Стохастическое моделирование вычислительного кластера с гистерезисным управлением скоростью обслуживания

Александр Сергеевич Румянцев, Ксения Алексеевна Калинина, Таисия Евсеевна Морозова, Alexander Rumyantsev, Ksenia Kalinina, Taisia Morozova

Аннотация


Предлагается стохастическая модель многосерверной системы массового обслуживания с одновременным занятием и одновременным освобождением заявкой случайного числа серверов, и пороговым (гистерезисным) управлением скоростью обслуживающих устройств. Для предложенной модели определены характеристики качества обслуживания и производительности системы. Представлены результаты численного эксперимента, иллюстрирующего зависимость характеристик модели от порога переключения. Предложенная модель позволяет оценить возможности экономии энергии на вычислительном кластере при контроле качества обслуживания без вмешательства в работу реальной системы.

Ключевые слова


стохастическое моделирование, пороговое управление, вычислительный кластер, энергоэффективность

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Литература


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References

Bekker R., Borst S. C., Boxma O. J.,

Kella O. Queues with workload-dependent

arrival and service rates. Queueing Systems.

Vol. 46. P. 537–556. doi:

1023/B:QUES.0000027998.95375.ee

Brill P. H., Green L. Queues in which

customers receive simultaneous service from a

random number of servers: a system point

approach. Management Science. 1984. Vol. 30,

no. 1. P. 51–68. doi: 10.1287/mnsc.30.1.51

Chakravarthy S. R., Karatza H. D. Twoserver

parallel system with pure space sharing

and Markovian arrivals. Computers & Operations

Research. 2013. Vol. 40, no. 1. P. 510–519. doi:

1016/j.cor.2012.08.002

Evans R. V. Queuing when Jobs Require

Several Services which Need Not be Sequenced.

Management Science. 1964. Vol. 10, no. 2. P. 298–

doi: 10.1287/mnsc.10.2.298

Feitelson D. G. Metrics for parallel job

scheduling and their convergence. Lecture Notes in

Computer Science. Job Scheduling Strategies for

Parallel Processing. 2001. Vol. 2221. P. 188–205.

doi: 10.1007/3-540-45540-X_11

Feitelson D. G. Workload modeling for

computer systems performance evaluation.

Cambridge University Press, 2015. doi:

1017/CBO9781139939690

Gandhi A., Harchol-Balter M., Das R.,

Lefurgy C. Optimal power allocation in

server farms. ACM SIGMETRICS Performance

Evaluation Review. 2009. Vol. 37. P. 157–168. doi:

1145/1555349.1555368

Gebrehiwot M. E., Aalto S. A., Lassila P.

Optimal sleep-state control of energyaware

M/G/1 queues. Proceed. of the

th Int. Conf. on Performance Evaluation

Methodologies and Tools. 2014. P. 82–89. doi:

4108/icst.valuetools.2014.258149

Horvath T., Skadron K. Multi-mode energy

management for multi-tier server clusters.

Proceed. of the 17th Int. Conf. on Parallel

Architectures and Compilation Techniques. 2008.

P. 270–279. doi: 10.1145/1454115.1454153

Hyyti¨a E., Righter R., Aalto S. Task

assignment in a heterogeneous server farm with

switching delays and general energy-aware cost

structure. Performance Evaluation. 2014. Vol. 75–

P. 17–35. doi: 10.1016/j.peva.2014.01.002

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queues with many servers. Transactions of the

American Mathematical Society. 1955. P. 1–18.

doi: 10.1090/S0002-9947-1955-0066587-3

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Customers Demand Multiple Server Use, Ph.D.

Dissertation, Southern Methodist University,

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Dependent Control for Green Computing. Lecture

Notes in Electrical Engineering. Information

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doi: 10.1007/978-3-319-22635-4_5

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of a MAP/M/s Cluster Model by Matrix-

Analytic Method. Lecture Notes in Computer

Science. Computer Performance Engineering:

th European Workshop. 2016. Vol. 9951. P. 63–

doi: 10.1007/978-3-319-46433-6_5

Rumyantsev A., Morozov E. Stability criterion

of a multiserver model with simultaneous service.

Annals of Operations Research. 2017 (First

Online: 2015). Vol. 252, no. 1. P. 29–39. doi:

1007/s10479-015-1917-2

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and performance in backfilling schedulers.

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Morozov E. V., Rumyantsev A. S. Modeli

mnogoservernykh sistem dlya analiza vychislitel’nogo

klastera [Multi-server models to analyze

high performance cluster]. Trudy KarNTs RAN

[Trans. KarRC RAS]. 2011. No. 5. P. 75–85.




DOI: http://dx.doi.org/10.17076/mat663

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