I.V. Kartashevsky – Ph. D. (Eng.), Associate Professor of Department of Software and Management in Technical

Systems, Volga State University of Telecommunications and Informatics (Samara)

E-mail: ivk@psuti.ru

A.V. Saprykin – Engineer, JSC «Concern «Avtomatika» (Moscow) E-mail: mail@ao-avtomatika.ru

This article is about the calculation of the average waiting time for a request in a queueing system G/G/1, where we use Dagum distribution to describe time inter-arrival time, and this sequence of time intervals has pronounced correlation properties. The methods of the classical queueing theory do not allow us to analyze the system G/G/1 with correlated inter-arrival and correlated service time. To analyze the average waiting time of the request in the queue we provide an approximation of the Dahuma distribution by a second-order hyper-exponential distribution, which no longer possesses the indicated correlation properties. The spectral method of solving the Lindley integral equation is used to find the average waiting time of the request in the queue for known parameters of an equivalent system with a hyper-exponentially distributed inter-arrival and service time. Also, we made a comparison between the waiting time of the request in the queue when processing correlated and non-correlated traffic.

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