Factors affecting warm-up periods in discrete event simulation

Abstract

In this paper, we discuss the factors affecting the initialization bias in discrete event simulation. Specifically, we assume that the time average is used to find the equilibrium expectation of a certain variable [Formula: see text], say the number in a queueing network, and we would like to minimize the mean squared error (MSE) between the time average of [Formula: see text] and its equilibrium expectation. To do this, a warm-up period is often used during which no data is collected, and we want to find the length of this period such that the MSE is minimal. We show that if starting in what Tocher calls a “typical condition”, warm-ups tend to be redundant. This result is strengthened by theoretical arguments and numerical experiments. If starting in a typical state is inconvenient, warm-up periods should be used, and methods to find optimal warm-up periods are discussed. The numerical methods used for our experiments do not rely on Monte Carlo simulation. Instead, we determine the MSE of the time average by the randomization method and other deterministic methods.