Author(s)

G. Sh. Tsitsiashvili

Institute for Applied mathematics, Far Eastern Branch of Russian Academy Sciences, Vladivostok, Russia.

In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.

A Queuing System, An Ergodicity, An Input Flow, A Randomly Varying Intensity

Tsitsiashvili, G. (2018) Ergodicity and Invariance of Flows in Queuing Systems. Journal of Applied Mathematics and Physics, 6, 1454-1459. doi: 10.4236/jamp.2018.67122.