Transform Methods for Heavy-Traffic Analysis
Abstract
The drift method was recently developed to study queueing systems in steady-state. It was successfully used to obtain bounds on the moments of the scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide variety of systems including generalized switches, input-queued switches, bandwidth sharing networks, etc. In this paper we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment generating functions. This approach simplifies the proofs of the drift method, and provides a new perspective on the drift method. We present a general framework and then use the MGF method to obtain the stationary distribution of queue lengths in heavy-traffic in queueing systems that satisfy the Complete Resource Pooling condition. In particular, we study load balancing systems and generalized switches under general settings.
Cite
@article{arxiv.1811.05595,
title = {Transform Methods for Heavy-Traffic Analysis},
author = {Daniela Hurtado-Lange and Siva Theja Maguluri},
journal= {arXiv preprint arXiv:1811.05595},
year = {2022}
}