Transform Methods for Heavy-Traffic Analysis

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,...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Hurtado-Lange, Daniela, Maguluri, Siva Theja
Format: Article
Language:English
Subjects:
Ad hoc networks
Drift
Markov analysis
Queues
Queuing theory
Switches
Switching theory
Wireless networks
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1811.05595