Skip to main content

Self-similarity Traffic and AQM Mechanism Based on Non-integer Order \(PI^{\alpha }D^{\beta }\) Controller

  • Conference paper
  • First Online:
Computer Networks (CN 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 718))

Included in the following conference series:

Abstract

In this paper the performance of fractional order PID controller as AQM mechanism and impact of traffic self-similarity on network utilization are investigated with the use of discrete event simulation models. The researches show the influence of selection of PID parameters and degree of traffic self-similarity on queue behavior. During the tests we analyzed the length of the queue, the number of rejected packets and waiting times in queues. In particular, the paper uses fractional Gaussian noise as a self-similar traffic source. The quantitative analysis is based on simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    Article  Google Scholar 

  2. 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 

  3. 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). doi:10.1007/978-3-642-31217-5_9

    Chapter  Google Scholar 

  4. Domańska, J., Augustyn, D., Domański, A.: The choice of optimal 3rd order polynomial packet dropping function for NLRED in the presence of self-similar traffic. Bull. Pol. Acad. Sci. Tech. Sci. 60(4), 779–786 (2012)

    Google Scholar 

  5. Augustyn, D.R., Domański, A., Domańska, J.: A choice of optimal packet dropping function for active queue management. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2010. CCIS, vol. 79, pp. 199–206. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13861-4_20

    Chapter  Google Scholar 

  6. 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)

    MATH  Google Scholar 

  7. Domańska, J., Domański, A., Czachórski, T.: The drop-from-front strategy in AQM. In: Koucheryavy, Y., Harju, J., Sayenko, A. (eds.) NEW2AN 2007. LNCS, vol. 4712, pp. 61–72. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74833-5_6

    Chapter  Google Scholar 

  8. Hollot, C., Misra, V., Towsley, D., Gong, W.: On designing improved controllers for AQM routers supporting TCP flows. In: IEEE/INFOCOM 2001, pp. 1726–1734 (2001)

    Google Scholar 

  9. Michiels, W., Melchor-Aquilar, D., Niculescu, S.: Stability analysis of some classes of TCP/AQM networks. Int. J. Control 79, 1136–1144 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Melchor-Aquilar, D., Castillo-Tores, V.: Stability analysis of proportional-integral AQM controllers supporting TCP flows. Computacion y Sistemas 10, 401–414 (2007)

    Google Scholar 

  11. Ustebay, D., Ozbay, H.: Switching resilient pi controllers for active queue management of TCP flows. In: Proceedings of the 2007 IEEE International Conference on Networking, Sensing and Control, pp. 574–578 (2007)

    Google Scholar 

  12. Podlubny, I.: Fractional order systems and \({PI}^\lambda {D}^\mu \) controllers. IEEE Trans. Autom. Control 44(1), 208–214 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen, Y., Petras, I., Xue, D.: Fractional order control - a tutorial. In: American Control Coference, pp. 1397–1411 (2009)

    Google Scholar 

  14. Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M.: Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol. 407. Springer, Heidelberg (2017)

    Google Scholar 

  15. Krajewski, W., Viaro, U.: On robust fractional order PI controller for TCP packet flow. In: BOS Coference: Systems and Operational Research, Warsaw, Poland, September 2014

    Google Scholar 

  16. Domanski, A., Domanska, J., Czachorski, T., Klamka, J.: Use of a non integer order PI controller with an active queue management mechanism. Int. J. Appl. Math. Comput. Sci. 26, 777–789 (2016)

    Article  MATH  Google Scholar 

  17. Crovella, M., Bestavros, A.: Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Trans. Netw. 5, 835–846 (1997)

    Article  Google Scholar 

  18. Domański, A., Domańska, J., Czachórski, T.: The impact of self-similarity on traffic shaping in wireless LAN. In: Balandin, S., Moltchanov, D., Koucheryavy, Y. (eds.) NEW2AN 2008. LNCS, vol. 5174, pp. 156–168. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85500-2_14

    Chapter  Google Scholar 

  19. Domańska, J., Domańska, A., Czachórski, T.: A few investigations of long-range dependence in network traffic. In: Czachórski, T., Gelenbe, E., Lent, R. (eds.) Information Sciences and Systems 2014, pp. 137–144. Springer, Cham (2014). doi:10.1007/978-3-319-09465-6_15

    Google Scholar 

  20. Domańska, J., Domański, A., Czachórski, T.: Estimating the intensity of long-range dependence in real and synthetic traffic traces. In: Gaj, P., Kwiecień, A., Stera, P. (eds.) CN 2015. CCIS, vol. 522, pp. 11–22. Springer, Cham (2015). doi:10.1007/978-3-319-19419-6_2

    Chapter  Google Scholar 

  21. Domańska, J., Domański, A.: The influence of traffic self-similarity on QoS mechanism. In: Proceedings of the International Symposium on Applications and the Internet, SAINT, Trento, Italy, pp. 300–303 (2005)

    Google Scholar 

  22. Stallings, W.: High-Speed Networks: TCP/IP and ATM Design Principles. Prentice-Hall, New York (1998)

    Google Scholar 

  23. Norros, I.: On the use of fractional brownian motion in the theory of connectionless networks. IEEE J. Sel. Areas Commun. 13(6), 953–962 (1995)

    Article  Google Scholar 

  24. Erramilli, A., Singh, R., Pruthi, P.: An application of deterministic chaotic maps to model packet traffic. Queueing Syst. 20(1–2), 171–206 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  25. Harmantzis, F., Hatzinakos, D.: Heavy network traffic modeling and simulation using stable farima processes. In: 19th International Teletraffic Congress, Beijing, China, pp. 300–303 (2005)

    Google Scholar 

  26. Robert, S., Boudec, J.: New models for pseudo self-similar traffic. Perform. Eval. 30(1–2), 57–68 (1997)

    Article  Google Scholar 

  27. Andersen, A.T., Nielsen, B.F.: A Markovian approach for modeling packet traffic with long-range dependence. IEEE J. Sel. Areas Commun. 16(5), 719–732 (1998)

    Article  Google Scholar 

  28. Domańska, J., Domański, A., Czachórski, T.: Modeling packet traffic with the use of superpositions of two-state MMPPs. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2014. CCIS, vol. 431, pp. 24–36. Springer, Cham (2014). doi:10.1007/978-3-319-07941-7_3

    Chapter  Google Scholar 

  29. Domańska, J., Domański, A., Czachórski, T.: Internet traffic source based on hidden Markov model. In: Balandin, S., Koucheryavy, Y., Hu, H. (eds.) NEW2AN/ruSMART -2011. LNCS, vol. 6869, pp. 395–404. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22875-9_36

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  32. Rutka, G.: Neural network models for internet traffic prediction. Electron. Electr. Eng. 4(68), 55–58 (2006)

    Google Scholar 

  33. Paxson, V.: Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic. ACM SIGCOMM Comput. Commun. Rev. 27(5), 5–18 (1997)

    Article  Google Scholar 

  34. Domański, A., Domańska, J., Czachórski, T.: The impact of the degree of self-similarity on the NLREDwM mechanism with drop from front strategy. In: Gaj, P., Kwiecień, A., Stera, P. (eds.) CN 2016. CCIS, vol. 608, pp. 192–203. Springer, Cham (2016). doi:10.1007/978-3-319-39207-3_17

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adam Domański .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Domański, A., Domańska, J., Czachórski, T., Klamka, J. (2017). Self-similarity Traffic and AQM Mechanism Based on Non-integer Order \(PI^{\alpha }D^{\beta }\) Controller. In: Gaj, P., Kwiecień, A., Sawicki, M. (eds) Computer Networks. CN 2017. Communications in Computer and Information Science, vol 718. Springer, Cham. https://doi.org/10.1007/978-3-319-59767-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59767-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59766-9

  • Online ISBN: 978-3-319-59767-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics