On One Analytical Model of a Probability Estimation of Quality and Efficiency of Functioning of Complex Technical Queuing Systems


The work is dedicated to the development of analytical model of probability estimation of reliability, productivity, quality and efficiency of functioning of the complex technical queuing system consisting of the arbitrary number of marked groups of the service devises (channels, facilities, servers) differing with reliable characteristics (parameters of refusals and restorations) of forming their composition (also of arbitrary number) marked, identical, unreliable and restorable serving channels in which for serving come in requirements with intensities depending on marking of channels. In the considered system it is supposed that the currents of refusals of serving devices and currents of coming requirements are subdued to Poisson, and the currents of restorations of refused devices and the currents of services of coming requirements—exponential laws of distribution of probabilities. A stochastic process of transfers of a system by that is Markovian process with continuous time and discrete states. Correlations linking the basic parameters and exit characteristics of the systems of the pointed out type are obtained in a view of probabilities of the system location in the given moment of time in one of the possible states.

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Shamugia, R. (2015) On One Analytical Model of a Probability Estimation of Quality and Efficiency of Functioning of Complex Technical Queuing Systems. International Journal of Communications, Network and System Sciences, 8, 295-303. doi: 10.4236/ijcns.2015.88029.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Gnedenko, B.V. and Kovalenko, I.N. (2012) Introduction to Queuing Theory. LKT, 400.
[2] Saati, T.L. (1965) Elements of Queuing Theory and Its Application. Sov. Radio, 510.
[3] Cherkesov, G.N. (1974) Dependability of Technical Systems with Time Redundancy. Sov. Radio, 296.
[4] Feller, W. (1971) An Introduction to Probability Theory and Its Applications. Vol. 2, John Willey and Sons, New York, 766.
[5] Kulgin, M. (2000) Technology of Corporative Networks. SPb, “Peter” Publishing House, 704.
[6] Lazarev, V.G. (1996) Intellectual Digital Networks. Finances and Statistics.
[7] Martin, D., Chapman, K. and Liben, D. (2000) ATM. Architecture and Realization. “Dori” Publishing House, 213.
[8] Nazarov, A.N. and Simonov, N.V. (1998) ATM Technology of High Speed Networks. “ECO-TRENDT” Publishing House.
[9] Basharin, G.P., Bacharov, P.P. and Kogan, Y.A. (1989) Analysis of Queues in Computing Networks. Theory and Methods of Calculation. “Nauka” Publishing House.
[10] Bacharov, P.P. and Penichkin, A.V. (1998) Theory of Mass Service. “Russian University of Peoples’ Friendship” Publishing House.
[11] Yershov, M.A. and Kuznetsov, N.A. (1995) Theoretical Fundamentals of Construction of the Digital Network with Integration of Services. IPPI RAN.
[12] Khurodze, R.A., Shamugia, R.R. and Kukava, R.R. (2006) Research of Dependability Characteristics of Technical Systems with Equipment and Time Duplications. Bulletin of the Georgian National Academy of Sciences, 174, 110-113.
[13] Shamugia, R. (2014) On One Model of Multichannel Queuing System with Unreliable Repairable Servers and Input Memory. Int’l J. of Communications, Network and System Sciences, 7, 279-285.
[14] Shamugia, R. (2014) On One Model of Complex Technical Queuing System with Unreliable Devices and with Time Redundancy. Int’l J. of Communications, Network and System Sciences, 7, 257-264.

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