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CLOUD STORAGE FACILITY AS A FLUID QUEUE CONTROLLED BY MARKOVIAN QUEUE

Published online by Cambridge University Press:  21 December 2020

A. H. El-Baz Open the ORCID record for A. H. El-Baz [Opens in a new window] ,
A. M. K. Tarabia  and
A. M. Darwiesh
A. H. El-Baz
Affiliation:
Department of Computer Science, Faculty of Computers and Information, Damietta University, New Damietta, Egypt E-mail: [email protected]
A. M. K. Tarabia
Affiliation:
Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt
A. M. Darwiesh
Affiliation:
Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt
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Abstract

Cloud storage faces many problems in the storage process which badly affect the system's efficiency. One of the most problems is insufficient buffer space in cloud storage. This means that the packets of data wait to have storage service which may lead to weakness in performance evaluation of the system. The storage process is considered a stochastic process in which we can determine the probability distribution of the buffer occupancy and the buffer content and predict the performance behavior of the system at any time. This paper modulates a cloud storage facility as a fluid queue controlled by Markovian queue. This queue has infinite buffer capacity which determined by the M/M/1/N queue with constant arrival and service rates. We obtain the analytical solution of the distribution of the buffer occupancy. Moreover, several performance measures and numerical results are given which illustrate the effectiveness of the proposed model.

Keywords

buffer content distributioncloud deploymentsfluid queueMarkovian queueperformance measures
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 237 - 253
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Adan, I.J.B.F. & Resing, J.A.C. (1996). Simple analysis of a fluid queue driven by an M/M/1 queue. Queueing Systems 22: 171–174.CrossRefGoogle Scholar
Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell Labs Technical Journal 61: 1871–1894.CrossRefGoogle Scholar
Arunachalam, V., Gupta, V., & Dharmaraja, S. (2010). A fluid queue modulated by two independent birth–death processes. Computers & Mathematics with Applications 60(8): 2433–2444.CrossRefGoogle Scholar
Coffman, E.G., Igelnik, B.M., & Kogan, Y.A. (1991). Controlled stochastic model of a communication system with multiple sources. IEEE Transactions on Information Theory 37: 1379–1387.CrossRefGoogle Scholar
Elwalid, A.I. & Mitra, D. (1991). Analysis and design of rate-based congestion control of high-speed networks. Part I: Stochastic fluid models, access regulation. Queueing Systems 9: 29–64.CrossRefGoogle Scholar
Ghazouani, S. & Slimani, Y. (2017). A survey in cloud service description. Network and Computer Applications 91: 61–74.CrossRefGoogle Scholar
Lenin, R.B. & Parthasarathy, P. R. (2000). Fluid queues driven by an M/M/1/N queue. Mathematical Problems in Engineering 6: 439–460.CrossRefGoogle Scholar
Losonczi, L. (1992). Eigenvalues and eigenvectors of some tridiagonal matrices. Acta Mathematica Hungarica 60: 309–322.CrossRefGoogle Scholar
Marinescu, D.C. (2017). Cloud computing: theory and practice, 2nd ed. USA: Morgan Kaufmann.Google Scholar
Meitra, D. (1988). Stochastic theory of a fluid model of produces and consumers coupled by a buffer. Advances in Applied Probability 20: 646–676.CrossRefGoogle Scholar
O'Reilly, P. (1986). A fluid-flow approach to performance analysis of integrated voice-date systems with speech interpolation. Modelling Techniques and Tools for Performance Analysis 85: 115–130.Google Scholar
Sericola, B. & Tuffin, B. (1993). A fluid queue driven by a Markovian queue. Queueing Systems 31: 253–264.CrossRefGoogle Scholar
Shortle, J.F., Thompson, J.M., Gross, D., & Harris, C.M. (2018). Fundamentals of queueing theory, 5th ed. New York: Wiley.CrossRefGoogle Scholar
Stern, T.E. & Elwalid, A.I. (1991). Analysis of separable Markov-modulated rate models for information-handling systems. Advances in Applied Probability 23: 105–139.CrossRefGoogle Scholar
Varma, P.S., Satyanarayana, A., & Sundari, M.V. (2012). Performance analysis of cloud computing using queuing models. In IEEE International Conference on Cloud Computing Technologies, Applications and Management (ICCCTAM). IEEE, Dubai, United Arab Emirates.Google Scholar
Virtamo, J. & Norros, I. (1994). Fluid queue driven by an M/M/1 queue. Queueing Systems 16: 373–386.CrossRefGoogle Scholar