ESTIMATING CUSTOMER AND TIME AVERAGES

In this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a Markov framework. The limiting values of the two averages appear in th e translation terms. This central limit theorem helps to construct con fidence intervals for estimators and perform statistical tests. It thu s helps determine which finite average is a more asymptotically effici ent estimator of its limit. As a basis for testing for PASTA (Poisson arrivals see time averages), we determine the variance constant associ ated with the central limit theorem for the difference between the two averages when PASTA holds.