Statistical Analysis with Little's Law

Abstract

The theory supporting Little's Law (L = λW) is now well developed, applying to both limits of averages and expected values of stationary distributions, but applications of Little's Law with actual system data involve measurements over a finite-time interval, which are neither of these. We advocate taking a statistical approach with such measurements. We investigate how estimates of L and λ can be used to estimate W when the waiting times are not observed. We advocate estimating confidence intervals. Given a single sample-path segment, we suggest estimating confidence intervals using the method of batch means, as is often done in stochastic simulation output analysis. We show how to estimate and remove bias due to interval edge effects when the system does not begin and end empty. We illustrate the methods with data from a call center and simulation experiments.