Stochastic simulation: A simplified LRE-algorithm for discrete random sequences

The LRE-algorithm III (LRE: Limited Relative Error) for the statistical evaluation of discrete random x-sequences yields by simple rules the stationary d.f. F(x) and the so-called local correlation function rho(x), -1 less than or equal to rho less than or equal to 1, to be included in a mean quadratic error measure for controlling the simulation run time. The use of this error statement instead of confidence interval statements and the principle of measuring correlation evidence instead of trying to eliminate correlation represent essentials for overcoming the deficiencies of the widespread Batch Means evaluation method. The LRE-algorithm III has been verified by test simulations of analytically described queueing systems and recently applied as part of the so called RESTART/LRE-algorithm for simulating very small probabilities of rare cell loss events in ATM-networks: in a situation being affected by various correlation phenomena the error and run time control procedures of the LRE-method secure the objectivity of numerical simulation results.