OVERVIEW

Random numbers are used in simulation to sample realizations of random variables with prescribed distributions, as well as stochastic processes with prescribed probability laws (see Chapter 3). For instance, customer arrivals are often generated according to a Poisson process, namely, the interarrival times are iid exponential. (Equivalently, the number of arrivals obeys the appropriate Poisson distribution, but it is far more convenient to generate interarrival times in the simulation run.)

Random numbers are generally produced via a random number generator (RNG) procedure ( generator, for short), used to generate iid numbers that are uniformly distributed between 0 and 1. These numbers are often further transformed so as to conform to a prescribed distribution (see Section 4.2). Although we use the term "random numbers" in the RNG term, it should be pointed out that the numbers generated are not truly random. For one thing, an RNG is a deterministic procedure whose generated number stream can always be recreated. An RNG is "random" in the sense that its random number sequence passes statistical tests for randomness, in this case the uniformity of the generated numbers and their mutual independence. For this reason, RNGs are sometimes referred to as pseudo RNGs, but for all practical purposes an RNG can be thought of as a stochastic sequence, { U _n }, of iid random variables, such that U Unif(0,1).

In simulation, an RNG is implemented as a computer algorithm in some programming language, and is made available...