On the approximation of the flow of events for a Poisson

E. V. Larkin ; D. V. Gorbachev ; A. N. Privalov

Čebyševskij sbornik, Tome 18 (2017) no. 2, pp. 222-234

Résumé

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.

Détail

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