Journal ArticleDOI
On Unique Ergodicity Of Coupled AIMD Flows
Pietro Ferraro,Jia Yuan Yu,Ramen Ghosh,Syed Eqbal Alam,Jakub Mareček,Fabian Wirth,Robert Shorten +6 more
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TLDR
The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks, which has important consequences for the convergence of the aforementioned optimization algorithms.Abstract:
The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation, energy, and mathematical biology. A very recent development in the use of AIMD is its application in solving large-scale optimization and distributed control problems without the need for inter-agent communication. In this context, an interesting problem arises when multiple AIMD networks that are coupled in some sense (usually through a nonlinearity). The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks. This result has important consequences for the convergence of the aforementioned optimization algorithms. The arguments in the paper also correct conceptual and technical errors in [1].read more
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Proceedings ArticleDOI
Existence of a Unique Invariant Measure and Ergodic Property in AIMD-based Multi-resource Allocation
Syed Eqbal Alam,Dhirendra Shukla +1 more
TL;DR: In this article , an additive increase and multiplicative decrease algorithm (AIMD)-based distributed solution for multi-resource allocation is presented. And the authors show that the time-averaged allocations over the finite window size converge to a unique invariant measure.
References
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Journal ArticleDOI
Analysis of the increase and decrease algorithms for congestion avoidance in computer networks
Dah Ming Chiu,Raj Jain +1 more
TL;DR: It is shown that a simple additive increase and multiplicative decrease algorithm satisfies the sufficient conditions for con- vergence to an efficient and fair state regardless of the starting state of the network.
Book
AIMD Dynamics and Distributed Resource Allocation
TL;DR: Basic and fundamental properties of the AIMD algorithm are described, examples are used to illustrate the richness of the resulting dynamical systems, and applications are provided to show how the algorithm can be used in the context of smart cities, intelligent transportation system, and the smart grid.
BookDOI
Analytics for the Sharing Economy: Mathematics, Engineering and Business Perspectives
Emanuele Crisostomi,Bissan Ghaddar,Florian Hausler,Joe Naoum-Sawaya,Giovanni Russo,Robert Shorten +5 more
Journal ArticleDOI
On the ergodic control of ensembles
André R. Fioravanti,Jakub Marecek,Robert Shorten,Robert Shorten,Robert Shorten,Matheus Souza,Fabian Wirth +6 more
TL;DR: In this paper, a theoretical framework is proposed to both analyse and design control systems for the regulation of large scale ensembles of agents with a probabilistic intent, and examples are given to illustrate their results.
Journal ArticleDOI
Nonhomogeneous Place-dependent Markov Chains, Unsynchronised AIMD, and Optimisation
TL;DR: A stochastic algorithm is presented for a class of optimisation problems that arise when a group of agents compete to share a single constrained resource in an optimal manner, and it is shown that almost sure convergence of the average access to the social optimum is shown.