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 Chebyshevskii Sb., 2017, Volume 18, Issue 2, Pages 222–234 (Mi cheb553)

On the approximation of the flow of events for a Poisson

E. V. Larkina, D. V. Gorbacheva, A. N. Privalovb

a Tula State University
b Tula State Pedagogical University

Abstract: When modeling an extensive class of technical systems, the mathematical apparatus of queuing systems (QMS) is widely used. An example of such a system is the computer network, where computer applications are generated and executed. Applications are generated usually not regularly, but by accident, forming the so-called random order of applications (requirements). Service requests, it also continues some random time. One of the central issues in the organization of mass-service systems is the elucidation of the regularities that subordinate the moments when system requirements for service are submitted.
The article explores the flow of events in technical systems of various purposes. On the basis of the fact that under the Poisson character of the flow mathematical modeling of the systems is greatly simplified, the problem of obtaining a simple criterion for determining the degree of approximation of the flow of events to a Poisson one is posed. Pearson's criterion, regression, correlation and parametric criteria were investigated. A criterion based on the calculation of the waiting function was obtained again. On the example of the study of the system with "competitions" it is shown that the flow of events generated by the system tends to Poisson with an infinite increase in the number of "competing" subjects.
Bibliography: 14 titles.

Keywords: Event flow, Poisson flow, semi-Markov process, Pearson's criterion, correlation, regression, expectation function, uniform law.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 2.3121.2017/Ï×

DOI: https://doi.org/10.22405/2226-8383-2017-18-2-222-234

Full text: PDF file (664 kB)
References: PDF file   HTML file

UDC: 519.21
Accepted:12.06.2017

Citation: E. V. Larkin, D. V. Gorbachev, A. N. Privalov, “On the approximation of the flow of events for a Poisson”, Chebyshevskii Sb., 18:2 (2017), 222–234

Citation in format AMSBIB
\Bibitem{LarGorPri17} \by E.~V.~Larkin, D.~V.~Gorbachev, A.~N.~Privalov \paper On the approximation of the flow of events for a Poisson \jour Chebyshevskii Sb. \yr 2017 \vol 18 \issue 2 \pages 222--234 \mathnet{http://mi.mathnet.ru/cheb553} \crossref{https://doi.org/10.22405/2226-8383-2017-18-2-222-234} \elib{http://elibrary.ru/item.asp?id=30042552}