Informatics and Applications
2025, Volume 19, Issue 1, pp 61-66
COMPARATIVE ANALYSIS OF QUEUING SYSTEM STABILITY TESTS
Abstract
The article discusses two types of procedures for statistical control of the stability of the queuing system: comparison of the intensities of input and output flows and detection of nonstationarity of the sequence of sojourn times. In the first case, we are talking about methods for processing matched pairs and in the second case, we are talking about single-root tests for first-order autoregression models. The procedure for collecting and fixing initial data is specified, since in one case, it is tied to moments in time and in the second - to event numbers. The two types of stability tests used refer to weak significance tests, for which the basic null hypotheses are different and complement each other. This is immediately evident when they are compared: the results are better when the assumptions of the corresponding null hypotheses are satisfied. To take into account such features, a composite criterion is built on the basis of consensus and randomization, which leads to an increase in the number of error-free solutions. Further improvement in the quality of decisions can be achieved in the procedure for comparing the critical levels of significance of individual criteria. The results were obtained by the Monte-Carlo method for a specific type of queuing system operating with a simple Poisson input flow. Violation of this assumption can become a destabilizing factor, for the description of which the model of the batch Poisson process was introduced. For it, by varying the intensity of batch arrival and the batch size mean, it is possible to form input streams of different structures with the same intensity. It was found that as the batch increases, the number of implementations generated by the queuing system that demonstrate instability increases; the size of the batch can be a source of a significant increase in the time spent in the system in comparison with the option of single batches; and the use of single root tests can lead to erroneous conclusions about instability.
[+] References (5)
- Krivenko, M. P. 2024. Modelirovanie vkhodnogo potoka rabochikh nagruzok vychislitel'nogo klastera LANL Mustang [Modeling of the input flow of LANL Mustang computing cluster workloads]. Sistemy i Sredstva Informati- ki - Systems and Means of Informatics 34(3): 109-122. doi 10.14357/08696527240308. EDN: FRSPMK.
- Krivenko, M. P. 2024. Statisticheskiy kriteriy stabil'nosti sistemy massovogo obsluzhivaniya, osnovannyy na vkhodnom i vykhodnom potokakh [Statistical criterion for queuing system stability based on input and output flows]. Informatika i ee Primeneniya - Inform. Appl. 18(1):54-60. doi 10.14357/19922264240108. EDN: JNJJMU.
- Krivenko, M.P. 2024. Statisticheskiy kriteriy stabil'nosti sistemy massovogo obsluzhivaniya, osnovannyy na posledovatel'nosti vremen prebyvaniya [Statistical criterion for queuing system stability based on sojourn times]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 34(2):55-65. doi 10.14357/08696527240204. EDN: RVWWXQ.
- Fuller, W. A. 1996. Introduction to statistical time series. 2nd ed. Hoboken, NJ: Wiley. 728 p. doi: 10.1002/ 9780470316917.
- Amvrosiadis, G., V. Kuchnik, J.W. Park, C. Cranor, G. R. Ganger, E. Moore, and N. DeBardeleben. 2018. The Atlas cluster trace repository. Login USENIX Mag. 43(4):29-35.
[+] About this article
Title
COMPARATIVE ANALYSIS OF QUEUING SYSTEM STABILITY TESTS
Journal
Informatics and Applications
2025, Volume 19, Issue 1, pp 61-66
Cover Date
2025-04-01
DOI
10.14357/19922264250108
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; sample-path stability; matched pairs tests; unit root tests; Dickey-Fuller tests; omnibus test of stability; batch Poisson process; size of batch as a destabilizing factor
Authors
M. P. Krivenko 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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