Advertisement

The Analysis of Cloud Computing System as a Queueing System with Several Servers and a Single Buffer

  • Ivan ZaryadovEmail author
  • Andrey Kradenyh
  • Anastasiya Gorbunova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10684)

Abstract

The mathematical model of cloud computing system based on the queuing system with the splitting of the incoming queries and synchronization of services is considered. The queuing system consists of a single buffer and N servers (\(N>2\)), service times are independent and exponentially distributed. The incoming query enters the system as a whole and only before service is divided into subqueries, each subquery is served by its device. The servers with parts of the same query are considered to be employed as long as the query is not serviced as a whole: the query is handled only when the last of it is out and a new query may be served only when there are enough free servers (the response time is the maximum of service times of all parts of this query). Expressions for the stationary performance characteristics of the system are presented.

Keywords

Cloud computing system Splitting of incoming queries Queueing system Response time Stationary probability-time characteristics Inhomogeneous servers Homogeneous servers 

Notes

Acknowledgments

The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008) and partially supported by RFBR Grants No. 15-07-03007, No. 15-07-03406 and No. 14-07-00090.

References

  1. 1.
    Buyya, R., Broberg, J., Goscinski, A.M.: Introduction to Cloud Computing. Cloud Computing: Principles and Paradigms. Wiley, Hoboken (2011)CrossRefGoogle Scholar
  2. 2.
    Khazaei, H., Misic, J., Misic, V.B.: A fine-grained performance model of cloud computing centers. IEEE Trans. Parallel Distrib. Syst. 24(11), 2138–2147 (2012)CrossRefGoogle Scholar
  3. 3.
    Flatto, L., Hahn, S.: Two parallel queues created by arrivals with two demands. SIAM J. Appl. Math. 44(5), 1041–1053 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Nelson, R., Tantawi, A.N.: Approximate analysis of fork/join synchronization in parallel queues. IEEE Trans. Comput. 37(6), 739–743 (1988)CrossRefGoogle Scholar
  5. 5.
    Thomasian, A.: Analysis of fork/join and related queueing systems. ACM Comput. Surv. (CSUR) 47(17), 17.1–17.71 (2014)Google Scholar
  6. 6.
    Gorbunova, A., Zaryadov, I., Matyushenko, S., Sopin, E.: The estimation of probability characteristics of cloud computing systems with splitting of requests. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2016. CCIS, vol. 678, pp. 418–429. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-51917-3_37 CrossRefGoogle Scholar
  7. 7.
    Duda, A., Czachórski, T.: Performance evaluation of fork and join synchronization primitives. Acta Informatica 24(5), 525–533 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kim, M.Y., Tantawi, A.N.: Asynchronous disk interleaving: approximating access delays. IEEE Trans. Comput. 40(7), 801–810 (1991)CrossRefGoogle Scholar
  9. 9.
    Fiorini, P.M.: Exact analysis of some split merge queues. SIGMETRICS Perform. Eval. Rev. 43(2), 51–53 (2015)CrossRefGoogle Scholar
  10. 10.
    Moiseeva, S., Sinyakova, I.: Investigation of Queueing System GI(2)—M2—\(\infty \). In: Proceedings of the Internattional Conference on Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks, pp. 219–225 (2011)Google Scholar
  11. 11.
    Moiseeva, S., Sinyakova, I.: Investigation of output flows in the system with parallel service of multiple requests. In: Problems of Cybernetics and Informatics (PCI-2012) : IV International Conference (IEEE), pp. 180–181, Baku, Azerbaijan (2012)Google Scholar
  12. 12.
    Tsimashenka, I., Knottenbelt, W.J.: Reduction of subtask dispersion in fork-join systems. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 325–336. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40725-3_25 CrossRefGoogle Scholar
  13. 13.
    Dean, J., Barroso, L.: The tail at scale. Commun. ACM 56(2), 74–80 (2013)CrossRefGoogle Scholar
  14. 14.
    Joshi, G., Soljanin, E., Wornell, G.: Efficient redundancy techniques for latency reduction in cloud systems. arXiv preprint. arXiv:1508.03599 (2015)
  15. 15.
    Gardner, K., Harchol-Balter, M., Scheller-Wolf, A.: A better model for job redundancy: decoupling server slowdown and job size. In: Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS), pp. 1–10. IEEE (2016)Google Scholar
  16. 16.
    Gorbunova, A.V., Kradenyh, A.A., Zaryadov, I.S.: The mathematical model of a cloud computing system. In: Proceedings of the Nineteenth International Scientific Conference: Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN-2016), Youth School-Seminar, vol. 3, pp. 169–175 (2016)Google Scholar
  17. 17.
    Bocharov, P.P., D’Apice, C., Pechinkin, A.V., Salerno, S.: Queueing Theory. VSP, Utrecht, Boston (2004)zbMATHGoogle Scholar
  18. 18.
    Harrison, P., Zertal, S.: Queueing models with maxima of service times. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 152–168. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-45232-4_10 CrossRefGoogle Scholar
  19. 19.
    Neuts, M.F.: Matrix Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981)zbMATHGoogle Scholar
  20. 20.
    Neuts, M.F.: Matrix-analytic methods in queuing theory. Eur. J. Oper. Res. 15(1), 2–12 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Neuts, M.F.: Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker Inc., New York (1989)zbMATHGoogle Scholar
  22. 22.
    Chakravarthy, S., Alfa, A.S., Attahiru, S.: Matrix-Analytic Methods in Stochastic Models. Taylor & Francis Group, Routledge (1996)CrossRefzbMATHGoogle Scholar
  23. 23.
    Breuer, L., Baum, D.: An Introduction to Queueing Theory and Matrix-Analytic Methods. Springer, Dordrecht (2005)zbMATHGoogle Scholar
  24. 24.
    Ibe, O.: Markov Processes for Stochastic Modeling. Elsevier Science, Amsterdam (2013)Google Scholar
  25. 25.
    He, Q.-M.: Fundamentals of Matrix-Analytic Methods. Springer, New-York (2014).  https://doi.org/10.1007/978-1-4614-7330-5 CrossRefzbMATHGoogle Scholar
  26. 26.
    Trivedi, K.S.: Probability and Statistics with Reliability, Queuing, and Computer Science Applications. Wiley, Hoboken (2016)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ivan Zaryadov
    • 1
    • 2
    Email author
  • Andrey Kradenyh
    • 1
  • Anastasiya Gorbunova
    • 1
  1. 1.Department of Applied Probability and InformaticsPeoples Friendship University of Russia (RUDN University)MoscowRussia
  2. 2.Institute of Informatics Problems of the Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia

Personalised recommendations