IMPROVED GENERATOR OF LONG-MEMORY PROCESSES

Abstract

Simulations with long-memory 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 pro- cess. We present an optimized algorithm for simulating efficiently the occupancy process of the M/G/∞ system, which can be used as a sequential pseudo- random number generator of a broad class of long-memory sample paths. Our previous approach is the decomposition of the service time distribution as a lin- ear combination of 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. In this work we improve our previ- ous algorithm, taking into account the generation time of the random variables.