Systems and Means of Informatics
2024, Volume 34, Issue 2, pp 55-65
STATISTICAL CRITERION FOR QUEUING SYSTEM STABILITY BASED ON SOJOURN TIMES
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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[+] About this article
Title
STATISTICAL CRITERION FOR QUEUING SYSTEM STABILITY BASED ON SOJOURN TIMES
Journal
Systems and Means of Informatics
Volume 34, Issue 2, pp 55-65
Cover Date
2024-05-20
DOI
10.14357/08696527240204
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; time series analysis; unit root tests; Dickey{Fuller tests; simulation
Authors
M. P. Krivenko
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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