Systems and Means of Informatics

2025, Volume 35, Issue 3, pp 90-104

ARIMA-MODELING OF THE SEQUENCE OF SOJOURN TIMES IN QUEUEING SYSTEMS

  • M. P. Krivenko

Abstract

The article constructs a model of the sequence of sojourn times {V} based on the available assumptions regarding the characteristics of the queuing system and the specified data sets. For statistical control of the stability of the queuing system, the ARIMA-model (AutoRegressive Integrated Moving Average) has been used. The main reasons for this are as follows: the process {Vi} can be both stationary and nonstationary with the dependence of individual states; testing a simplified version of the ARIMA-model when instability is detected has shown its effectiveness; and there is a corresponding software implementation - the forecasting package of the R platform. At the same time, statistical stability control is a pioneer direction and there is practically no experience in building appropriate statistical models. The article clarifies the subtleties of the general principles of model construction taken into action in the case of monitoring the stability of the queuing system. To illustrate the capabilities of ARIMA-modeling, sequences for a dual-processor M/M/2 job processing system with a random selection of the number The ARIMA-model takes into account the features of the process {Vi}; the adopted method of fitting the model demonstrates reliability; and using only model parameters for stability control is not effective. The emerged predictive capability does not contradict the overall results on the behavior of stable or unstable systems, can make adjustments to the decision on stability, and can also serve as a starting point for analyzing and assessing the risks of using queueing system. The adequacy of the proposed model is investigated.

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