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Efficient On-Line Generation of the Correlation Structure of F-ARIMA Processes

  • Conference paper
Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2009)

Abstract

Several traffic measurement studies have shown the presence of persistent correlations in modern networks. The use of stochastic processes able to capture this kind of correlations, as self-similar processes, has opened new research fields in network performance analysis, mainly in simulation studies, where the efficient synthetic generation of samples is one of the main topics. Although F-ARIMA processes are very flexible to capture both short- and long-range correlations in a parsimonious way, only off-line methods for synthesizing traces are efficient enough to be of practical use. In order to overcome this disadvantage, in this paper we propose a M/G/∞-based efficient and on-line generator of the correlation structure of F-ARIMA processes.

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References

  1. Ansari, N., Liu, H., Shi, Y.Q.: On modeling MPEG video traffics. IEEE Transactions on Broadcasting 48(4), 337–347 (2002)

    Article  Google Scholar 

  2. Beran, J.: Statistics for Long-Memory Processes. Chapman and Hall, Boca Raton (1994)

    MATH  Google Scholar 

  3. Beran, J., Shreman, R., Taqqu, M.S., Willinger, W.: Long-Range Dependence in Variable-Bit-Rate video traffic. IEEE Transactions on Communications 43(2/4), 1566–1579 (1995)

    Article  Google Scholar 

  4. Casilari, E., Reyes, A., Díaz, A., Sandoval, F.: Characterization and modeling of VBR video traffic. Electronics Letters 34(10), 968–969 (1998)

    Article  Google Scholar 

  5. Conti, M., Gregori, E., Larsson, A.: Study of the impact of MPEG-1 correlations on video sources statistical multiplexing. IEEE Journal on Selected Areas in Communications 14(7), 1455–1471 (1996)

    Article  Google Scholar 

  6. Cox, D.R., Isham, V.: Point Processes. Chapman and Hall, Boca Raton (1980)

    MATH  Google Scholar 

  7. Cox, D.R.: Long-Range Dependence: A review. In: Statistics: An Appraisal, pp. 55–74. Iowa State University Press (1984)

    Google Scholar 

  8. Crovella, M.E., Bestavros, A.: Self-similarity in World Wide Web traffic: Evidence and possible causes. IEEE/ACM Transactions on Networking 5(6), 835–846 (1997)

    Article  Google Scholar 

  9. Davies, R.B., Harte, D.S.: Tests for Hurst effect. Biometrika 74(1), 95–102 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  10. Duffield, N.: Queueing at large resources driven by long-tailed M/G/∞ processes. Queueing Systems 28(1/3), 245–266 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. Erramilli, A., Narayan, O., Willinger, W.: Experimental queueing analysis with Long-Range Dependent packet traffic. IEEE/ACM Transactions on Networking 4(2), 209–223 (1996)

    Article  Google Scholar 

  12. Garrett, M.W., Willinger, W.: Analysis, modeling and generation of self-similar VBR video traffic. In: Proc. ACM SIGCOMM 1994, London, UK, pp. 269–280 (1994)

    Google Scholar 

  13. Granger, C.W.J.: Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14(2), 227–238 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  14. Granger, C.W.J., Joyeux, R.: An introduction to long-range time series models and fractional differencing. Journal of Time Series Analysis 1, 15–30 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  15. Haslett, J., Raftery, A.E.: Space-time modeling with long-memory dependence: Assessing Ireland’s wind power resource. Applied Statistics 38(1), 1–50 (1989)

    Article  Google Scholar 

  16. Hosking, J.R.M.: Fractional differencing. Biometrika 68(1), 165–176 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hosking, J.R.M.: Modeling persistence in hydrological time series using fractional differencing. Water Resources Research 20(12), 1898–1908 (1984)

    Article  Google Scholar 

  18. Hurst, H.E.: Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers 116, 770–799 (1951)

    Google Scholar 

  19. Jiang, M., Nikolic, M., Hardy, S., Trajkovic, L.: Impact of self-similarity on wireless data network performance. In: Proc. IEEE ICC 2001, Helsinki, Finland, pp. 477–481 (2001)

    Google Scholar 

  20. Krunz, M., Makowski, A.: Modeling video traffic using M/G/∞ input processes: A compromise between Markovian and LRD models. IEEE Journal on Selected Areas in Communications 16(5), 733–748 (1998)

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. Li, S.Q., Hwang, C.L.: Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking 1(5), 317–329 (1993)

    Google Scholar 

  23. Likhanov, N., Tsybakov, B., Georganas, N.D.: Analysis of an ATM buffer with self-similar (“fractal”) input traffic. In: Proc. IEEE INFOCOM 1995, Boston, MA, USA, pp. 985–992 (1995)

    Google Scholar 

  24. López, J.C., López, C., Suárez, A., Fernández, M., Rodríguez, R.F.: On the use of self-similar processes in network simulation. ACM Transactions on Modeling and Computer Simulation 10(2), 125–151 (2000)

    Article  Google Scholar 

  25. Mandelbrot, B.B., Van Ness, J.W.: Fractional Brownian Motions, Fractional Noises and applications. SIAM Review 10(4), 422–437 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  26. Norros, I.: A storage model with self-similar input. Queueing Systems 16, 387–396 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  27. Parulekar, M.: Buffer engineering for M/G/∞ input processes. Ph.D. Thesis, University of Maryland, College Park, MD, USA (2001)

    Google Scholar 

  28. Paxson, V., Floyd, S.: Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Transactions on Networking 3(3), 226–244 (1995)

    Article  Google Scholar 

  29. Poon, W., Lo, K.: A refined version of M/G/∞ processes for modeling VBR video traffic. Computer Communications 24(11), 1105–1114 (2001)

    Article  Google Scholar 

  30. Resnick, S., Rootzen, H.: Self-similar communication models and very heavy tails. Annals of Applied Probability 10(3), 753–778 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  31. Sousa, M.E., Suárez, A., Fernández, M., López, C., Rodríguez, R.F.: A highly efficient M/G/∞ generator of self-similar traces. In: Proc. 2006 Winter Simulation Conference, Monterey, CA, USA, pp. 2146–2153 (2006)

    Google Scholar 

  32. Sousa, M.E., Suárez, A., López, J.C., López, C., Fernández, M.: On improving the efficiency of a M/G/∞ generator of correlated traces. Operations Research Letters 36(2), 184–188 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. Suárez, A., López, J.C., López, C., Fernández, M., Rodríguez, R.F., Sousa, M.E.: A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation. Performance Evaluation 47(2/3), 197–219 (2002)

    Article  MATH  Google Scholar 

  34. Taqqu, M.S., Teverovsky, V.: On estimating the intensity of Long-Range Dependence in finite and infinite variance time series. In: A Practical Guide to Heavy Tails, pp. 177–218. Birkhauser, Basel (1998)

    Google Scholar 

  35. Tsoukatos, K.P., Makowski, A.M.: Heavy traffic analysis for a multiplexer driven by M/G/∞ input processes. In: Proc. 15th International Teletraffic Congress, Washington, DC, USA, pp. 497–506 (1997)

    Google Scholar 

  36. Whittle, P.: Estimation and information in stationary time series. Arkiv. Matematick 2(23), 423–434 (1953)

    Article  MathSciNet  MATH  Google Scholar 

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Sousa-Vieira, ME., Suárez-González, A., López-Ardao, JC., López-García, C. (2009). Efficient On-Line Generation of the Correlation Structure of F-ARIMA Processes. In: Al-Begain, K., Fiems, D., Horváth, G. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2009. Lecture Notes in Computer Science, vol 5513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02205-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-02205-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02204-3

  • Online ISBN: 978-3-642-02205-0

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