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Fast simulation of self-similar and correlated processes

Author

Listed:
  • Sousa-Vieira, M.E.
  • Suárez-González, A.
  • López-García, C.
  • Fernández-Veiga, M.
  • López-Ardao, J.C.
  • Rodríguez-Rubio, R.F.

Abstract

Simulations with long-range dependent or self-similar input processes are hindered both by the slowness of convergence displayed by the output data and by the high computational complexity of the on-line methods for generating the input process. In this paper, we present optimized algorithms for simulating efficiently the occupancy process of a M/G/∞ system, which can be used as a sequential pseudo-random number generator of a broad class of self-similar and correlated sample-paths. We advocate the use of this approach in the simulation toolbox, as a simple method to overcome the drawbacks of other synthetic generators of Gaussian self-similar time series. Our approach to fast simulation of the M/G/∞ model is the decomposition of the service time distribution as a linear combination of deterministic and memoryless random variables, plus a residual term. Then, the original M/G/∞ system is replaced by a number of parallel, independent, virtual and easier to simulate M/G/∞ subsystems, the dynamics of which can be replicated sequentially or in parallel too. We report the results of several experiments demonstrating the substantial improvements attainable with this decomposition.

Suggested Citation

  • Sousa-Vieira, M.E. & Suárez-González, A. & López-García, C. & Fernández-Veiga, M. & López-Ardao, J.C. & Rodríguez-Rubio, R.F., 2010. "Fast simulation of self-similar and correlated processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2040-2061.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:10:p:2040-2061
    DOI: 10.1016/j.matcom.2010.01.010
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    References listed on IDEAS

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    1. Miron Livny & Benjamin Melamed & Athanassios K. Tsiolis, 1993. "The Impact of Autocorrelation on Queuing Systems," Management Science, INFORMS, vol. 39(3), pages 322-339, March.
    2. Purczynski, Jan & Wlodarski, Przemyslaw, 2006. "On fast generation of fractional Gaussian noise," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2537-2551, June.
    3. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
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