The Analysis of Cloud Computing System as a Queueing System with Several Servers and a Single Buffer
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.
KeywordsCloud computing system Splitting of incoming queries Queueing system Response time Stationary probability-time characteristics Inhomogeneous servers Homogeneous servers
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.
- 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.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
- 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.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
- 14.Joshi, G., Soljanin, E., Wornell, G.: Efficient redundancy techniques for latency reduction in cloud systems. arXiv preprint. arXiv:1508.03599 (2015)
- 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.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
- 24.Ibe, O.: Markov Processes for Stochastic Modeling. Elsevier Science, Amsterdam (2013)Google Scholar