L\'evy-driven GPS queues with heavy-tailed input

TL;DR

This paper analyzes the large-buffer behavior of a two-class GPS queue system with heavy-tailed Le9vy process inputs, providing exact asymptotics for different heavy-tailedness and rate scenarios.

Contribution

It derives exact large-buffer asymptotics for a two-class GPS queue with heavy-tailed Le9vy process inputs, covering four distinct scenarios based on tail heaviness and mean rates.

Findings

Asymptotic results for heavy-tailed Le9vy process inputs

Analysis of four different heavy-tailed scenarios

Illustrations with compound Poisson and b5-stable Le9vy motions

Abstract

In this paper we derive exact large-buffer asymptotics for a two-class Generalized Processor Sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed L\'evy processes. Four scenarios need to be distinguished, which differ in terms of (i)~the level of heavy-tailedness of the driving L\'evy processes as well as (ii)~the values of the corresponding mean rates relative to the GPS weights. The derived results are illustrated by two important special cases, in which the queues' inputs are modeled by heavy-tailed compound Poisson processes and by $\alpha$-stable L\'evy motions.