Multiple independent streams of random numbers are often required in simulation studies, for instance, to facilitate synchronization for variance-reduction purposes, and for making independent replications. A portable set of software utilities is described for uniform randomnumber generation. It provides for multiple generators (streams) running simultaneously, and each generator (stream) has its sequence of numbers partitioned into many long disjoint contiguous substreams. The basic underlying generator for this implementation is a combined multiple recursive generator with period length of approximately 2 191 , proposed in a previous paper. A C++ interface is described here. Portable implementations are available in C, C++, and Java via the On-line Companion to this paper on the Operations Research website.This report is an expanded version of the article by L' Ecuyer et al. (2001).

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This article discusses the implementation of using finite differences to construct a confidence interval for a simulation estimator of the derivative of the steady-state distribution of a stochastic process. The quasi-independent procedure increases the simulation run length progressively until a certain number of essentially independent and identically distributed systematic samples are obtained. The author computes sample quantiles at certain grid points and constructs a histogram from those grid points. The derivative estimate is then computed from the histogram (i.e., the empirical distribution). An experimental performance evaluation demonstrates the validity of using this procedure to estimate the derivatives.