Open AccessMathematical model of delay based on a system with gamma distribution
Author(s) -
В. Н. Тарасов,
В. Н. Тарасов
Publication year - 2021
Publication title -
fizika volnovyh processov i radiotehničeskie sistemy
Language(s) - English
Resource type - Journals
eISSN - 2782-294X
pISSN - 1810-3189
DOI - 10.18469/1810-3189.2021.24.2.62-67
Subject(s) - queueing theory , queue , decomposition , computer science , distribution (mathematics) , mathematics , fair queuing , queue management system , spectral power distribution , physics , mathematical analysis , computer network , ecology , fair share scheduling , optics , biology , quality of service , round robin scheduling
This article is devoted to the analysis of a queuing system formed by two flows with density functions of the gamma distribution law in order to derive a solution for the average delay of requests in the queue, which is the main characteristic for any queuing system. According to this characteristic, for example, packet delays in packet-switched networks are estimated when they are modeled using the queuing system. In queuing theory, studies of G/G/1 systems are especially relevant because there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In the study of G/G/1 systems, an important role is played by the method of spectral decomposition of the solution of the Lindley integral equation, and most of the results in the theory of queuing were obtained using this method. The article presents the derivation of the calculation formula for the average delay of requests in the queue in the system under consideration, also based on the spectral decomposition method.