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Analysis of Cumulative Distribution Function of the Response Time in Cloud Computing Systems with Dynamic Scaling

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Abstract

One of the key performance measures of cloud computing systems is the response time. However, the mean value of this characteristic does not give the full picture of quality of service. Therefore, we derive the cumulative distribution function (CDF) of the response time in terms of Laplace-Stieltjes transform and use it to evaluate moments of the response time. Moreover, we introduce a simplification of the mathematical model that significantly reduces computing complexity for the response time CDF and provide analysis of approximation accuracy of the simplified model.

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References

  1. ETSI Cloud Standards Coordination. Final Report 2013, ver. 1.0. http://www.etsi.org/images/files/Events/ 2013/2013_CSC_Delivery_WS/CSC-Final_report-013-CSC_Final_report_v1_0_PDF_format-.PDF. Accessed March 12, 2015.

  2. Andronov, A.M., On a generalization of Erlang formulas, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1970, no. 6, pp. 93–100.

    MathSciNet  Google Scholar 

  3. Andronov, A.M. and Rebezova, M.I., Polynomial approximation of the activity completion time distribution in network chart, Autom. Control Comput. Sci., 2013, vol. 47, no. 4, pp. 192–201.

    Article  Google Scholar 

  4. Basharin, G.P., Gaidamaka, Yu.V., and Samuilov, K.E., Mathematical teletraffic theory and its application to the analysis of the next generations multiservice networks, Autom. Control Comput. Sci., 2013, vol. 47, no. 2, pp. 11–21.

    Google Scholar 

  5. Bocharov, P.P., D’Apice, C.D., Pechinkin, A.V., and Salerno, S., Queueing Theory, Ultrecht, Boston: VSP Publishing, 2004.

    MATH  Google Scholar 

  6. Gaidamaka, Yu.V., Pechinkin, A.V., Razumchik, R.V., Samuilov, A.K., Samuilov, K.E., Sokolov, I.A., Sopin, E.S., and Shorgin, S.Ya., The distribution of the return time from the set of overload states to the set of normal load states in a system M | M | 1 | <L,H> | <H,R> with hysteretic load control, Inf. Its Appl., 2013, vol. 7, no. 4, 2013, pp. 20–33.

    Google Scholar 

  7. Goswami, V., Patra, S.S., and Mund, G.B., Performance analysis of cloud with queue-dependent virtual machines, Proc. of 1st Int’l Conf. on Recent Advances in Information Technology, Dhanbad, 2012, pp. 357–362.

    Google Scholar 

  8. Golubchik, L. and Lui, J.C.S., Bounding of performance measures for threshold-based queuing systems: Theory and application to dynamic resource management in video-on-demand servers, IEEE Trans. Comput., vol. 51, no. 4, 2002, pp. 353–372.

    Article  MathSciNet  Google Scholar 

  9. Kaxiras, S. and Martonosi, M., Computer architecture techniques for power-efficiency, Synth. Lect. Comput. Archit., 2008, vol. 3, no. 1, pp. 1–207.

    Article  Google Scholar 

  10. Lin, M., Wierman, A., Andrew, L.L.H., and Thereska, E., Dynamic right-sizing for power-proportional data centers, INFOCOM, Proceedings IEEE, 2011, pp. 1098–1106.

    Google Scholar 

  11. Meisner, D., Gold, B.T., and Wenisch, T.F., Powernap: Eliminating server idle power, CM SIGPLAN Not., 2009, vol. 44, pp. 205–216.

    Article  Google Scholar 

  12. Miyoshi, A., Lefurgy, C., Hensbergen, E.V., Rajamony, R., and Rajkumar, R., Critical power slope: Understanding the runtime effects of frequency scaling, Proceedings of the 16th Annual ACM International Conference on Supercomputing, 2002, pp. 35–44.

    Google Scholar 

  13. Mokrov, E.V. and Chukarin, A.V., Performance analysis of cloud computing system with live migration, T-Comm— Telecommun. Transp., 2014, vol. 8, no. 8, pp. 64–67.

    Google Scholar 

  14. Mokrov, E.V. and Samouylov, K.E., Modeling of cloud computing as a queuing system with batch arrivals, T-Comm— Telecommun. Transp., 2013, no. 11, pp. 139–141.

    Google Scholar 

  15. Shorgin, S.Y., Pechinkin, A.V., Samouylov, K.E., Gaidamaka, Y.V., Gudkova, I.A., and Sopin, E.S., Threshold-based queuing system for performance analysis of cloud computing system with dynamic scaling, Proc. of the 12th International Conference of Numerical Analysis and Applied Mathematics ICNAAM-2014, Rhodes, Greece, 2014, United States: AIP Publishing, 2015, vol. 1648, pp. 1–3.

    Google Scholar 

  16. Gaidamaka, Yu.V., Sopin, E.S., and Talanova, M., Approach to the analysis of probability measures of cloud computing systems with dynamic scaling, Commun. Comput. Inf. Sci., 2016, vol. 601, pp. 121–131.

    Google Scholar 

  17. Wu, Q., Juang, P., Martonosi, M., Peh, L.-S., and Clark, D.W., Formal control techniques for power performance management, IEEE Micro, 2005, vol. 25, pp. 52–62.

    Google Scholar 

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University) Applied Probability and Informatics Department, Moscow, 117198, Russia

    E. S. Sopin, A. V. Gorbunova, Yu. V. Gaidamaka & E. R. Zaripova

Authors
  1. E. S. Sopin
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  2. A. V. Gorbunova
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  3. Yu. V. Gaidamaka
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  4. E. R. Zaripova
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Correspondence to E. S. Sopin.

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Sopin, E.S., Gorbunova, A.V., Gaidamaka, Y.V. et al. Analysis of Cumulative Distribution Function of the Response Time in Cloud Computing Systems with Dynamic Scaling. Aut. Control Comp. Sci. 52, 60–66 (2018). https://doi.org/10.3103/S0146411618010066

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  • DOI: https://doi.org/10.3103/S0146411618010066

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