Statistical criterion for queuing system stability based on input and output flows

One of the basic properties of a queuing system is stability — the ability of the system to function, maintaining its structure and characteristics unchanged over time. The problem of statistical verification of the stability of the queuing system based on the characteristics of the input $A(t)$ and output $D(t)$ order flows is considered. The confirmation of stability is based on establishing the equality of the rates of these flows. Thus, in the language of statistical data analysis, one obtains the classic problem of comparing rates of occurrence. To solve it, the observation period is divided into fragments that give separate estimates. Together, they make up the sample that participates in the comparison. When analyzing stability, it is necessary to take into account possible dependence of $A(t)$ and $D(t)$; so, it is necessary to turn to methods for processing the so-called matched pairs of observations. Stability control makes it necessary to solve a number of auxiliary tasks: selection of volumetric parameters for rate estimation, checking the normality of the distribution, and analysis of correlations. In the course of experiments with the real system, a number of features were revealed: the effect of substituting the prelimit distribution with the real one during fragmentation as well as the presence of dependence of the rate estimates of analyzed flows which comes to naught for unstable systems.