Determining of Parameters of a Distribution Approximating Unimodal Distribution
Marina Buranova, Vyacheslav Kartashevskiy, Victor Ushakov, Ahmed Aziz · 2024
Numerous results of traffic analysis show the presence of a "complex" structure, which is determined by "heavy tails", correlations within the sequences of requests processed in the network.As is known, this nature of traffic requires the use of G/G/1 type models when studying the performance of processing systems.The analysis of such models is complicated, therefore, hyperexponential distributions are often used to approximate arbitrary distributions of G.In this paper, we consider an example of a unimodal distribution, where a polynomial is used to approximate the "ascending" part, and a hyperexponential distribution is used to approximate the "descending" part.In this case, the components of the approximating "descending" part of the hyperexponential distribution are determined using recursive selection.This approach allows us to estimate the average waiting time for an application in the queue by solving the Lindley equation.As an example, the paper analyzes the average waiting time for an application in a queue in the L/P/1 system.The shown universal technique can be used as a model for analyzing systems when processing traffic with unimodally distributed time intervals between requests or processing requests.