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Fast simulation of self-similar and correlated processes

2010; Elsevier BV; Volume: 80; Issue: 10 Linguagem: Inglês

10.1016/j.matcom.2010.01.010

1872-7166

M.E. Sousa‐Vieira, Andrés Suárez-González, Cándido López-Garcı́a, Manuel Fernández‐Veiga, J.C. López-Ardao, Raúl F. Rodríguez‐Rubio,

Stochastic processes and statistical mechanics

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.