Random Number and Variate Generation

Random numbers are used in simulation to sample realizations of random variables with prescribed distributions, as well as stochastic processes with prescribed probability laws. For instance, customer arrivals are often generated according to a Poisson processnamely, 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, 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. 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.