software for uniform random number generator

software for uniform random number generator - Proceedings...

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Proceedings of the 2001 Winter Simulation Conference B .A .Pe ters ,J .S .Sm i th ,D .J .Mede iros ,andM .W .Rohrer ,eds . SOFTWARE FOR UNIFORM RANDOM NUMBER GENERATION: DISTINGUISHING THE GOOD AND THE BAD Pierre L’Ecuyer Département d’Informatique et de Recherche Opérationnelle Université de Montréal, C.P. 6128, Succ. Centre-Ville Montréal, H3C 3J7, CANADA ABSTRACT The requirements, design principles, and statistical testing approaches of uniform random number generators for sim- ulation are brieFy surveyed. An object-oriented random number package where random number streams can be cre- ated at will, and with convenient tools for manipulating the streams, is presented. A version of this package is now implemented in the Arena and AutoMod simulation tools. We also test some random number generators available in popular software environments such as Microsoft’s Excel and Visual Basic , SUN’s Java , etc., by using them on two very simple simulation problems. They fail the tests by a wide margin. 1 WHAT ARE WE LOOKING FOR? 1.1 Introduction The aim of (pseudo)random number generators (RNGs) is to implement an imitation of the abstract mathematical con- cept of mutually independent random variables uniformly distributed over the interval [ 0 , 1 ] (i.i.d. U [ 0 , 1 ] , for short). Such RNGs are required not only for stochastic simulation, but for many other applications involving computers, such as statistical experiments, numerical analysis, probabilistic algorithms, computer games, cryptology and security proto- cols in communications, gambling machines, virtual casinos over the internet, and so on. Random variables from other distributions than the standard uniform are simulated by ap- plying appropriate transformations to the uniform random numbers (Law and Kelton 2000). Various RNGs are available in computer software li- braries. These RNGs are in fact small computer programs implementing (ideally) carefully crafted algorithms, whose design should be based on solid mathematical analysis. Are these RNGs all reliable? Unfortunately, despite repeated warnings over the past years about certain classes of genera- tors, and despite the availability of much better alternatives, simplistic and unsafe RNGs still abound in commercial software. Concrete examples are given in Section 4 of this paper. A single RNG does not always suf±ce for simulation. In many applications, several “independent” random number streams (which can be interpreted as distinct RNGs) are required, with appropriate tools to jump around within these streams, for instance to make independent runs and to facilitate the implementation of certain variance reduction techniques(Bratley, ²ox, and Schrage 1987; Law and Kelton 2000). Packages implementing such RNG streams are now available. One of them, which we describe in Section 5, has been implemented in the most recent releases of the Arena and AutoMod simulation environments.
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software for uniform random number generator - Proceedings...

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