On the AIMD Algorithm Under Saturation Constraints

One of the most successful distributed resource allocation algorithms to be deployed in industry is the Additive-Increase Multiplicative-Decrease (AIMD) algorithm of Jain and Chiu. This algorithm already underpins the transport layer of the internet, and is now starting to find application in new areas in the context of Smart Grid and Smart Transportation applications. A distinguishing feature of these latter application areas, when compared with the internet, is the need to modify AIMD to account for lower and upper bounds in the resource allocated to individual agents. Our objective in this note is to demonstrate that the dynamic system arising from AIMD in this extended form has system theoretic properties similar to the classical algorithm.

[1]  Frank Kelly,et al.  Mathematical Modelling of the Internet , 2001 .

[2]  Injong Rhee,et al.  CUBIC: a new TCP-friendly high-speed TCP variant , 2008, OPSR.

[3]  Ilja Radusch,et al.  Cooperative Regulation and Trading of Emissions Using Plug-in Hybrid Vehicles , 2013, IEEE Transactions on Intelligent Transportation Systems.

[4]  Raj Jain,et al.  Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks , 1989, Comput. Networks.

[5]  Stephan Bohacek,et al.  A stochastic model of TCP and fair video transmission , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[6]  Sonja Stuedli,et al.  Distributed load management supporting power injection and reactive power balancing | NOVA. The University of Newcastle's Digital Repository , 2016 .

[7]  Robert Shorten,et al.  On the modified AIMD algorithm for distributed resource management with saturation of each user's share , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[8]  Balázs Sonkoly,et al.  A comprehensive TCP fairness analysis in high speed networks , 2009, Comput. Commun..

[9]  Joao P. Hespanha,et al.  Analysis of a TCP hybrid model , 2002 .

[10]  Seán McLoone,et al.  Enhanced AIMD-based decentralized residential charging of EVs , 2015 .

[11]  Laurent Massoulié,et al.  Stability of distributed congestion control with heterogeneous feedback delays , 2002, IEEE Trans. Autom. Control..

[12]  François Baccelli,et al.  AIMD, fairness and fractal scaling of TCP traffic , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[13]  Robert Shorten,et al.  An ergodic AIMD algorithm with application to high-speed networks , 2012, Int. J. Control.

[14]  Christopher V. Hollot,et al.  Nonlinear stability analysis for a class of TCP/AQM networks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[15]  I. Beil,et al.  A distributed wireless testbed for plug-in hybrid electric vehicle control algorithms , 2012, 2012 North American Power Symposium (NAPS).

[16]  Jia Yuan Yu,et al.  Nonhomogeneous Place-Dependent Markov Chains, Unsynchronised AIMD, and Network Utility Maximization , 2014, 1404.5064.

[17]  Fernando Paganini,et al.  Internet congestion control , 2002 .

[18]  Robert Shorten,et al.  Nonlinear AIMD Congestion Control and Contraction Mappings , 2007, SIAM J. Control. Optim..

[19]  Catherine Rosenberg,et al.  RealTime distributed congestion control for electrical vehicle charging , 2012, PERV.

[20]  Fabian R. Wirth,et al.  AIMD Dynamics and Distributed Resource Allocation , 2016 .

[21]  F. Baccelli,et al.  Interaction of TCP flows as billiards , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[22]  Catherine Rosenberg,et al.  How internet concepts and technologies can help green and smarten the electrical grid , 2011, CCRV.

[23]  Donald F. Towsley,et al.  Modeling TCP Reno performance: a simple model and its empirical validation , 2000, TNET.

[24]  Michael Welzl,et al.  An independent H-TCP implementation under FreeBSD 7.0: description and observed behaviour , 2008, CCRV.

[25]  F. Guillemin,et al.  A Markovian analysis of additive-increase multiplicative-decrease algorithms , 2002, Advances in Applied Probability.

[26]  Mingming Liu,et al.  Topics in Electromobility and RelatedApplications , 2015 .

[27]  Qian Zhang,et al.  Compound TCP: A scalable and TCP-friendly congestion control for high-speed networks , 2006 .

[28]  Robert Shorten,et al.  On the Fair Coexistence of Loss- and Delay-Based TCP , 2009, IEEE/ACM Transactions on Networking.

[29]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[30]  Robert Shorten,et al.  Plug-and-Play Distributed Algorithms for Optimized Power Generation in a Microgrid , 2014, IEEE Transactions on Smart Grid.

[31]  John T. Wen,et al.  A unifying passivity framework for network flow control , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[32]  Rayadurgam Srikant,et al.  The Mathematics of Internet Congestion Control , 2003 .

[33]  Robert Shorten,et al.  A flexible distributed framework for realising electric and plug-in hybrid vehicle charging policies , 2012, Int. J. Control.