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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.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.4-083

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.

References

Akhin, M., Kolton, S., & Itsykson, V. (2015). Random model sampling: making craig interpolation work when it should not. Automatic Control and Computer Sciences, 49(7), 413-419.

Altiok, T., & Melamed, B. (2001). The case for modeling correlation in manufacturing systems. IIE Transactions, 33(9), 779-791.

Blatov, I.A., Kartashevskii, V.G., Kireeva, N.V., & Chupakhina, L.R. (2013). The method of approximating an arbitrary density distribution of the sum of exponents. Vestnik VGU, 2, 53–57.

Chupahina, L.R. (2013). Analysis of the characteristics of queuing systems in the transmission nonpoissonian traffic approximation method of distribution functions. Samara, Povolzhskiy State University of Telecommunications and Informatics Vol. 1.

Downey, A.B. (2005). Lognormal and Pareto distributions in the Internet. Computer Communications, 28(7), 790-801.

Heyman, D.P. (1976). Queueing systems: theory by Leonard Kleinrock. John Wiley & Sons. Inc., New York. Networks, 6(2), Vol. 1., 189-190.

Itsykson, V.M. (2017). Formalism and language tools for specification of the semantics of software libraries. Automatic Control and Computer Sciences, 51(7), 531-538.

Jagerman, D., Melamed, B., & Willinger, W. (1996, March). Stochastic modeling of traffic processes. In Frontiers in queueing: Models, Methods and Problems, CRC Press.

Jagerman, D.L., & Melamed, B. (1992). The transition and autocorrelation structure of TES processes: Part II: Special Cases. Communications in Statistics. Stochastic Models, 8(3), 499-527.

Jagerman, D.L., Balcıoglu, B., Altiok, T., & Melamed, B. (2004). Mean waiting time approximations in the G/G/1 queue. Queueing Systems, 46(3-4), 481-506.

Jagerman, D.L., Melamed, B. & Willinger, W. (1997). Stochastic modeling of traffic processes. In Frontiers in Queueing: Models and Applications in Science and Engineering (pp.271–320). CRC Press.

Kartashevskii, V.G., Kireeva, N.V., Buranova, M.A., & Chupakhina, L.R. (2015). Simulation and analysis of generalized queue system with arbitrary distributions of system parameters. Infokommunikacionnye Tehnologii, 3, 252-258.

Kartashevskiy, V., Kireeva, N., Buranova, M., & Chupakhina, L. (2016, October). Approximation of distributions in the problems of the analysis of self-similar traffic. In Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S&T), 2016, (pp. 105-108), IEEE.

Klochkov, Y., & Gazizulina, A. (2016). Application of the method of performance evaluation of the production process design using associative design. Key Engineering Materials, 684, 448-452.

Livny, M., Melamed, B., & Tsiolis, A.K. (1993). The impact of autocorrelation on queuing systems. Management Science, 39(3), 322-339.

Melamed, B. (1991). TES: A class of methods for generating auto correlated uniform variates. ORSA Journal on Computing, 3(4), 317-329.

Melamed, B. (1993). An overview of TES processes and modeling methodology. In Performance Evaluation of Computer and Communication Systems (pp. 359-393). Springer, Berlin, Heidelberg.

Patuwo, B.E., Disney, R.L., & McNickle, D.C. (1993). The effect of correlated arrivals on queues. IIE Transactions, 25(3), 105-110.

Shanthikumar, J.G., & Buzacott, J.A. (1980). On the approximations to the single server queue. International Journal of Production Research, 18(6), 761-773.

Skripal, B., & Itsykson, V. (2017, April). Aspect-oriented extension for the Kotlin programming language. In CEUR Workshop Proceedings, CEUR, pp. 1864.