Systems and Means of Informatics

2024, Volume 34, Issue 2, pp 55-65

STATISTICAL CRITERION FOR QUEUING SYSTEM STABILITY BASED ON SOJOURN TIMES

  • M. P. Krivenko

Abstract

The article discusses the problem of statistical test of queuing system stability based on the characteristics of the sojourn time series {Vk}. To solve it, it is proposed to use the tests for unit roots. A relationship is established between the quantitative and temporal characteristics of the system in the style of the Little's formula for the nonstationary case which makes it possible to link the rate-stability with the stationarity {Vk}. Three basic models and the corresponding Dickey{Fuller tests are considered as the stationarity test. The limitations of the used statistical tables are discussed. The conducted simulation study allows one to draw the following conclusions: all three criteria solve the problem of stability analysis with a clear loss of the quality of decisions made in the case of a model with a deterministic linear trend, in the field of system stability, the test behaves worse than in the field of instability; the expected trends in the use of tests are clearly manifested; and some deviations from the expected results indicate the need to expand the range of the models used and to remove the limitations of the statistical tables used.

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