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

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5513))

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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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Author information

Authors and Affiliations

  1. Department of Telematics Engineering, University of Vigo, Spain

    Maria-Estrella Sousa-Vieira, Andrés Suárez-González, José-Carlos López-Ardao & Cándido López-García

Authors
  1. Maria-Estrella Sousa-Vieira
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  2. Andrés Suárez-González
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  3. José-Carlos López-Ardao
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  4. Cándido López-García
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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, CF37 1DL, Pontypridd, UK

    Khalid Al-Begain

  2. Department TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Dieter Fiems

  3. Budapest University of Technology and Economics, P.O. Box 91, 1521, Budapest, Hungary

    Gábor Horváth

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© 2009 Springer-Verlag Berlin Heidelberg

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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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