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The Influence of the Traffic Self-similarity on the Choice of the Non-integer Order PI\(^\alpha \) Controller Parameters

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 935))

Abstract

The article discusses the problem of choosing the best parameters of the non-integer order \(PI^{\alpha }\) controller used in IP routers Active Queue Management for TCP/IP traffic flow control. The impact of the self-similarity of the traffic on the controller parameters is investigated with the use of discrete event simulation. We analyze the influence of these parameters on the length of the queue, the number of rejected packets and waiting times. The results indicate that the controller parameters strongly depend on the value of the Hurst parameter.

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References

  1. Leszczyński, J., Ciesielski, M.: A numerical method for solution of ordinary differential equations of fractional order. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 695–702. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-48086-2_77

    Chapter  Google Scholar 

  2. Cox, D.: Long-range dependance: a review. In: Statistics: An Appraisal, pp. 55–74. Iowa State University Press (1984)

    Google Scholar 

  3. Domańska, J., Augustyn, D., Domański, A.: The choice of optimal 3-rd order polynomial packet dropping function for NLRED in the presence of self-similar traffic. Bull. Pol. Acad. Sci Tech. Sci. 60, 779–786 (2012)

    Google Scholar 

  4. Domańska, J., Domański, A., Augustyn, D., Klamka, J.: A RED modified weighted moving average for soft real-time application. Int. J. Appl. Math. Comput. Sci. 24(3), 697–707 (2014)

    Article  Google Scholar 

  5. Domańska, J., Domański, A., Czachórski, T.: Fluid flow analysis of RED Algorithm with modified weighted moving average. In: Dudin, A., Klimenok, V., Tsarenkov, G., Dudin, S. (eds.) BWWQT 2013. CCIS, vol. 356, pp. 50–58. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35980-4_7

    Chapter  Google Scholar 

  6. Domańska, J., Domański, A., Czachórski, T., Klamka, J.: Fluid flow approximation of time-limited TCP/UDP/XCP streams. Bull. Pol. Acad. Sci. Tech. Sci. 62(2), 217–225 (2014)

    Google Scholar 

  7. Domańska, J., Domański, A., Czachórski, T., Klamka, J.: Use of a non integer order PI controller to active queue management mechanism. Int. J. Appl. Math. Comput. Sci. 26(4), 777–789 (2016)

    Article  MathSciNet  Google Scholar 

  8. Domańska, J., Domański, A., Czachórski, T., Klamka, J.: Self-similarity traffic and AQM mechanism based on non-integer order \(PI^{\alpha }D^\beta \) controller. In: Proceedings of 24th International Conference on Computer Networks, CN 2017, Ladek Zdroj (2017)

    Google Scholar 

  9. Domańska, J., Domański, A., Czachórski, T., Klamka, J., Szyguła, J.: The AQM dropping packet probability function based on non-integer order \(PI^{\alpha }D^\beta \) controller. In: International Conference on Non-Integer Order Calculus and its Applications (2017)

    Google Scholar 

  10. Domański, A., Domańska, J., Czachórski, T.: Comparison of AQM control systems with the use of fluid flow approximation. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2012. CCIS, vol. 291, pp. 82–90. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31217-5_9

    Chapter  Google Scholar 

  11. Floyd, S., Jacobson, V.: Random early detection gateways for congestion avoidance. IEEE/ACM Trans. Netw. 1(4), 397–413 (1993)

    Article  Google Scholar 

  12. Hooke, R., Jeeves, T.: Direct search solution of numerical and statistical problems. J. ACM 8(2), 212–229 (1961). (USA)

    Article  Google Scholar 

  13. Karagiannis, T., Molle, M., Faloutsos, M.: Long-range dependence: ten years of internet traffic modeling. IEEE Internet Comput. 8(5), 57–64 (2004)

    Article  Google Scholar 

  14. Kelley, C.: Iterative methods for optimization. Front. Appl. Math. (18) (1999) (SIAM, Philadelphia)

    Google Scholar 

  15. Latawiec, K., Stanisławski, R., Łukaniszyn, M., Czuczwara, W., Rydel, M.: Fractional-order modeling of electric circuits: modern empiricism vs. classical science. In: Progress in Applied Electrical Engineering (PAEE) (2017)

    Google Scholar 

  16. Lopez-Ardao, J., Lopez-Garcia, C., Suarez-Gonzalez, A., Fernandez-Veiga, M., Rodriguez-Rubio, R.: On the use of self-similar processes in network simulation. ACM Trans. Model. Comput. Simul. 10(2), 125–151 (2000)

    Article  Google Scholar 

  17. Mandelbrot, B., Ness, J.: Fractional brownian motions, fractional noises and applications. SIAM Rev. 10, 422–437 (1968)

    Article  MathSciNet  Google Scholar 

  18. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  19. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, USA (1999)

    MATH  Google Scholar 

  20. Samorodnitsky, G., Taqqu, M.: Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, New York (1994)

    MATH  Google Scholar 

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Acknowledgements

This work was partially financed by National Science Center project no. 2017/27/ B/ST6/00145.

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Correspondence to Tadeusz Czachórski .

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Domański, A., Domańska, J., Czachórski, T., Klamka, J., Marek, D., Szyguła, J. (2018). The Influence of the Traffic Self-similarity on the Choice of the Non-integer Order PI\(^\alpha \) Controller Parameters. In: Czachórski, T., Gelenbe, E., Grochla, K., Lent, R. (eds) Computer and Information Sciences. ISCIS 2018. Communications in Computer and Information Science, vol 935. Springer, Cham. https://doi.org/10.1007/978-3-030-00840-6_9

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  • DOI: https://doi.org/10.1007/978-3-030-00840-6_9

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  • Online ISBN: 978-3-030-00840-6

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