Research of queuing system with displaced exponential input distributions
Автор: Tarasov V.N., Bakhareva N.F., Akhmetshina E.G.
Журнал: Инфокоммуникационные технологии @ikt-psuti
Рубрика: Технологии телекоммуникаций
Статья в выпуске: 2 т.17, 2019 года.
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The problem of determining characteristics of a queuing system (QS) produced by two flows with displaced exponential distributions is considered. Such a system is considered for the first time. For the classical M/M/1 system the coefficients of variation of the input flow intervals and the service time are equal to one, and for the new system they become less than one and we get a non-Markov queueing model of G/G/1 type. By varying the time displaced parameter in the input distributions, it is possible to change the values of the variation coefficients of the arrival intervals and the service time. Thus, the displaced exponential distributions widen the range of the arrival time variation coefficients and service time, thereby expanding the scope of the new queuing system. The problem is solved by the classical method of queuing theory - the method of spectral decomposition of the solution of the Lindley integral equation. It is shown that the load in such a system is higher than in the classical M/M/1 system, and the average waiting time is shorter because of reduced variation coefficients of the intervals between the receipt and the service time. It is known that the average waiting time is related to the coefficients of variation by a quadratic dependence. Thus, the article presents a solution for the new G/G/1 system. The possible applications for this new QS have yet to be assessed.
Qs m/m/1, qs m-/m-/1, method of spectral decomposition, lindley integral equation, laplace transform, average waiting time
Короткий адрес: https://sciup.org/140255715
IDR: 140255715 | DOI: 10.18469/ikt.2019.17.2.06