ON A DISTRIBUTION OF THE PROCESS DESCRIBING A SERVICE SYSTEM WITH UNRELIABLE DEVICES

Year 2019, Volume: 9 Issue: 2, 357 - 365, 01.06.2019

T. M. Aliev E. A. Ibayev V. M. Mamedov

Abstract

In the paper, the distribution is found for the process ft; tg; t 0; in the terms of Laplace transformation. The considered process describes the queuing system with nonhomogeneous Poisson stream of demands and n unreliable devices. It is essential that the process ft; tg; t 0; for t n is a homogeneous with respect to the second component Markov process. The results obtained in the paper are based on the theory of matrices and solution of the system of linear integral equations.

Keywords

Poisson process, Laplace transformation, Generating function, Markov chain, Homogeneous with respect to the second component.

References

• [1] Borovkov, A.A., (1972), Probability Processes in the theory of a queuing, Moscow, Nauka.
• [2] Aliyev, T.M., Ibayev, E.A., Mamedov, V.M., (2014), On controlled Poisson processes, TWMS Journal of Applied and Engeneering Mathematics, 4(2), pp.252-258.
• [3] Aliyev, T.M., Sardarov, B.Y., Maharramov, A.P., (2006), On erdodicity of the process describing the multichannel service system with reliable devices, Proceedings of the Institute of Mathematics and Mechanics ANAS, XXIV, Baku, pp.29-34.
• [4] Ejov, I.I., (1965), On a service system GI/M/S in the case of nonhomogeneous demand stream, Doklady USSR, 8.
• [5] Ejov, I.I., Skorokhod, A.B., (1969), Homogeneous with respect to the second component Markov processes, Probability Theory and Applications, 14(1), pp.3-14.
• [6] Gantmakher, F.R., (1967), Theory of Matrices, Moscow, Nauka.