DOI: 10.17586/2226-1494-2018-18-3-473-478


QUEUE SYSTEMS WITH POLYMODAL QUERY FLOWS

S. A. Zhmylev, T. I. Aliev


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Article in Russian

For citation: Zhmylev S.A., Aliev T.I. Queue systems with polymodal query flows. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 3, pp. 473–478 (in Russian). doi: 10.17586/2226-1494-2018-18-3-473-478

Abstract
 In queuing systems modeling it is traditionally assumed that the distribution of the inter-arrival time between requests entering the system is unimodal. At the same time, in practice, systems with a multimodal inter-arrival time distribution having two or more modes are encountered. The multimodal distribution is usually replaced by a unimodal one with appropriate numerical moments, which simplifies the modeling process, but introduces a methodical error in the obtained results. The subject of the study is the analysis of properties of multimodal flows and the estimation of such an error. Simulation modeling in the AnyLogic environment is used as a re-search method provided to discover the error dependence on the system load. It was revealed that in the high-load systems the error introduced by the replacement is not higher than 15%, but with a decrease in the system load, the error increases and can reach hundreds of percent. In the course of extensive experiments, it was found out that with an increase in the inter-arrival time the value of the variation coefficient between incoming queries in a polymodal flow tends to a constant value not greater than unity. The practical importance of the work lies in simplification of design process for high-load computing systems with the use of simulation and analytical models by replacing the polymodal flows with unimodal providing required accuracy of calculations.

Keywords: polymodal distribution, queue system, polymodal distribution approximation, statistical moment, multi-exponential distribution

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