### International Journal of Mathematical, Engineering and Management Sciences

#### ISSN: 2455-7749

Comparison of Approximation Methods for the Estimation of Distributions in the Analysis of the G/G/1 Queue

#### Comparison of Approximation Methods for the Estimation of Distributions in the Analysis of the G/G/1 Queue

O. Karaulova
The Department of Multi-Service Network and Information Security , Povolzhskiy State University of Telecommunications and Informatics (PSUTI), Samara, 443010, Russia.

N. Kireeva
The Department of Multi-Service Network and Information Security, Povolzhskiy State University of Telecommunications and Informatics (PSUTI), Samara, 443010, Russia.

L. Chupakhina
The Department of Multi-Service Network and Information Security, Povolzhskiy State University of Telecommunications and Informatics (PSUTI), Samara, 443010, Russia.

A. Gazizulina
Center of Monitoring Science and Education, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, 195251, Russia.

Received on November 25, 2018
;
Accepted on May 11, 2019

Abstract

The analysis of Weibull and Pareto distribution functions in the approximation of the density of a sum of damping functions, PMRQ approximation and approximation of service distribution in the peak mode of the flow. There was found one of the characteristics of the network, the average waiting time of packets in the queue after application of spectral method of the Lindley’s integral equation. Finally, PMRQ approximation of the average waiting time in TES+/G/1, MMPR, was compared with the analytic values of the same value in the spectral solution of the Lindley’s integral equation obtained by simulation with real traffic. Traffic is captured using the Wireshark protocol analyzer program. The time distributions were obtained in the EasyFit data analysis program, designed for quick statistical data analysis and decision making. Methods of approximation of network traffic allows us to estimate the average packet latency using statistical data analysis, which will improve the quality of service and predict the behavior of traffic.

Keywords- Approximation, PMRQ, PMRS, Damping function, Lindley’s equation.

Citation

Karaulova, O., Kireeva, N., Chupakhina, L., & Gazizulina, A. (2019). Comparison of Approximation Methods for the Estimation of Distributions in the Analysis of the G/G/1 Queue. International Journal of Mathematical, Engineering and Management Sciences, 4(4), 1040-1050. https://dx.doi.org/10.33889/IJMEMS.2019.4.4-083.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.

Acknowledgements

The research carried out with the financial support of the grant from the Program Competitiveness Enhancement of Peter the Great St. Petersburg Polytechnic University, Project 5-100-2020.

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