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Internet router modeling using Circulant Markov modulated Poisson process- impact of fractal onset time (FOT)

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Abstract

Fractal point process (FPP) emulates self-similar traffic and its important characteristic is fractal onset time (FOT). However, this process being asymptotic in nature has less effective in queueing based performance analysis. In this paper, we propose a model of variance based Markovian fitting. The proposed method is to match the variance of FPP and that of superposed Circulant Markov modulated Poisson Process (CMMPP). Superposition consists of several 2-state CMMPPs and Poisson process. We present how well resultant CMMPP could approximate FPP which emulates self-similar traffic. We investigate queueing behavior of resultant queueing system in terms of packet loss probability. We demonstrate how FOT affects the fitting model and queueing behavior. Analytical results are compared with the simulation results without FOT for the validation. We conclude from the numerical example that network nodes with a self-similar input traffic can be well represented by a queueing system with CMMPP input.

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References

  1. Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, W.V.: On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Trans. Networking 2, 1–15 (1994)

    Article  Google Scholar 

  2. Paxson, V., Floyd, S.: Wide area traffic: the failure of Poisson modeling. IEEE/ACM Trans. Networking 3, 226–244 (1995)

    Article  Google Scholar 

  3. Crovella, M., Bestavros, A.: Self-similarity in World Wide Web traffic: evidence and possible causes. IEEE/ ACM Trans. Networking. 835–846 (1997)

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

    Article  Google Scholar 

  5. Yoshihara, T., Kasahara, S., Takahashi, Y.: Practical time-scale fitting of self-similar traffic with Markov modulated Poisson process. Telecommun. Syst. 17, 185–211 (2001)

    Article  Google Scholar 

  6. Kasahara, S.: Internet traffic modelling : Markovian approach to self-similar traffic and prediction of loss probability for finite queues. Spec. Issue Internet Technol. IEICE Trans. Commun. E84-B(8), 2134–2141 (2001)

    Google Scholar 

  7. Shao, S.K., Malla Reddy, P., Tsai, M.G., Tsao, H.W., Wu, J.: Generalized variance-based Markovian fitting for self-similar traffic modeling. IEICE Trans. Commun. E88-B(12), 4659–4663 (2005)

    Article  Google Scholar 

  8. Salvador, P., Pacheco, A., Valadas, R.: Multiscale fitting procedure using Markov modulated Poisson processes. Telecommun. Syst. 23(1–2), 123–148 (2003)

    Article  Google Scholar 

  9. Kim, G.Y., Shiravi, A., Min, P.S.: Congestion prediction of self-similar network through parameter estimation. Network Operations and Management Symposium, NOMS 2006. 10thIEEE/IFIP (2006)

  10. Ryu, B.K., Lowen, S.B.: Point process approaches to the modeling and analysis of self similar traffic: Part I - Model construction, In: Proc. IEEE INFOCOM, San Francisco, CA. 1468–1475 (1996)

  11. Ryu, B.K., Lowen, S.B.: Point process models for self-similar network traffic, with applications. Stoch. Model. 14(3), 735–761 (1998)

    Article  Google Scholar 

  12. Malla Reddy, P., Chang, C.-H., Shao, S.-K., Wu, J.: An efficient approximate markovian model for optical packet switches employing partial buffer sharing mechanism under self-similar traffic input. Proceedings of IEEE HPSR-2007 held at Polytechnic University, Brooklyn, New York, USA, May 30-June1, ISBN:1-4244-1206-4, IEEE Catalog number: 07EX1775C (2007)

  13. Lau, W.C., Erramilli, A., Wang, J.L., Willinger, W.: Self-similar traffic generation: the random midpoint displacement algorithm and its properties. Proc. ICC’95, Seattle, WA, pp. 466–472 (1995)

  14. Blondia, C.: The N/G/l finite capacity queue. Commum. Stat. Stoch. Model. 5, 273–294 (1989)

    Article  Google Scholar 

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Acknowledgments

One of the two authors (RD) wishes to acknowledge Council of Scientific and Industrial Research (CSIR), Government of India for its funding under Senior Research Fellowship (CSIR-UGC-SRF) scheme (File No.09/384(0148)/2011-EMR-1).

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Authors and Affiliations

  1. Department of Mathematics, Kakatiya Institute of Technology & Science, Warangal, TS, India

    Ramesh Renikunta

  2. Department of Mathematics, Kakatiya University, Warangal, TS, India

    Rajaiah Dasari & Malla Reddy Perati

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  1. Ramesh Renikunta
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  2. Rajaiah Dasari
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  3. Malla Reddy Perati
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Correspondence to Ramesh Renikunta.

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Renikunta, R., Dasari, R. & Perati, M.R. Internet router modeling using Circulant Markov modulated Poisson process- impact of fractal onset time (FOT). OPSEARCH 53, 317–328 (2016). https://doi.org/10.1007/s12597-015-0239-0

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  • DOI: https://doi.org/10.1007/s12597-015-0239-0

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