The on-off network traffic model under intermediate scaling

TL;DR

This paper investigates the intermediate scaling regime in heavy-tailed network traffic models, revealing that fluctuations are characterized by fractional Poisson motion, thus completing the understanding of different scaling behaviors.

Contribution

It introduces the limiting behavior of network traffic under intermediate scaling, bridging the gap between fractional Brownian motion and stable Lévy process models.

Findings

Fluctuations under fast connection rates are fractional Brownian motion.

Slow connection rates lead to stable Lévy process fluctuations.

Intermediate scaling results in fractional Poisson motion.

Abstract

The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source Poisson models, models based on aggregated renewal sequences, and models built from aggregated on-off sources. The versions of these models with finite variance transmission rate share the following pattern: if the sources connect at a fast rate over time the cumulative statistical fluctuations are fractional Brownian motion, if the connection rate is slow the traffic fluctuations are described by a stable L\'evy process, while the limiting fluctuations for the intermediate scaling regime are given by fractional Poisson motion.