Fast simulation of self-similar and correlated processes

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

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 80, issue 10, 2040-2061

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.

Keywords: Persistent correlations; M/G/∞ process; Efficient on-line generation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2010:i:10:p:2040-2061

DOI: 10.1016/j.matcom.2010.01.010

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