Central-limit-theorem version of L = λW

Extending the FCLT version of L=λW

The functional central limit theorem (FCLT) version of Little’s law (L = λW ) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exploit...

On the FCLT Version of L = λW

The functional central limit theorem (FCLT) version of Little’s law (L = λW ) shows that the fundamental relation between cumulative processes underlying L = λW leads to a corresponding relation among the limits for the FCLT-scaled stochastic processes. It supports statistical analysis, e.g., estimating confidence intervals. Here, this statistical motivation is reviewed and then the FCLT in Gly...

A radial version of the Central Limit Theorem

In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating Gaussian filters in [1]. It was shown in [1] how a certain “radial” form of the Central Limit Theorem (CLT) could be used to approximate isotropic Gaussians on the plane. The main idea was to approximate the Gaussian using box distributions that had been uniformly distributed over the half-c...

A Central-Limit-Theorem Version of the Periodic Little’s Law

Abstract We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL), which complements the sample-path and stationary versions of the PLL which we recently established in order to explain the remarkable accuracy in comparisons of data-generated model simulations to direct estimates from the data for the aggregate occupancy level in a hospital emergency department. Our...

A Purely Martingale Version of Lindeberg's Central Limit Theorem