Anisotropic scaling of random grain model with application to network traffic

TL;DR

This paper characterizes the anisotropic scaling limits of a random grain model with heavy-tailed distributions, revealing diverse stable and Gaussian fields, and applies findings to network traffic analysis.

Contribution

It provides a comprehensive description of anisotropic scaling limits for the random grain model, including new types of infinitely divisible fields and their covariance structures.

Findings

Scaling limits include stable, Gaussian, and intermediate fields.

Covariance functions exhibit specific asymptotic behaviors.

Application demonstrated in network traffic modeling.

Abstract

We obtain a complete description of anisotropic scaling limits of random grain model on the plane with heavy tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both coordinate axes and include stable, Gaussian and some `intermediate' infinitely divisible random fields. Asymptotic form of the covariance function of the random grain model is obtained. Application to superposed network traffic is included.