Control Techniques for Complex Networks

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1、ControlTechniquesforComplexNetworksSeanMeynLIDSSpecialSenimarMonday’sfrom5-6pm(allsemester-inBd32-Room144)IntroductionandoutlineThestochasticnetworkscommunityhasbecomeincreasinglydiverseandcreativeoverthepastdecade.Abiasedsampleofexamplesincludesthecho

2、iceofsimplicityoveroptimalityintheMaxWeightpolicy,relaxationtechniquesemergingfromthetheoryofnetworksinheavytraffic,theintroductionofconceptsfromeconomics,andthemergingofsimulationandstabilitytechniquesforperformanceevaluation.Intheselectureswewillexplor

3、emanyoftheseissues.ThematerialisbasedonabookofthesamenametoappearinCambridgeUniversityPress,2007.Samplechapterswillbemadeavailabletothosewithinterest.Thefollowingthreetopicsarepersonalfavorites,buttheplancanchangedependingonthepreferencesoftheaudience.

4、(i)WhydoestheMaxWeightpolicywork?Howcanitbegeneralized?Howcanitbeevaluated?Wewillconsiderbroadgeneralizations,andtouchonasymptoticoptimalitybasedonarelaxationtechniqueintroducedinthePhDthesisofNeilLaws,aswellastechniquesbasedupona”fluidmodel”.(ii)CanIun

5、derstandthestructureofanoptimalpolicyforacomplexnetwork?Beau-tifulstructureisrevealedthrougha”workloadrelaxation”,aswellastrulypracticalapproachestodesign.(iii)StochasticLyapunovtheoryisthefoundationformuchofthisresearch.Thistheoryalsohastremendousvalu

6、eforimprovingsimulationalgorithms.Itisconjecturedthatthesametechniquescanbeusedtospeedmachinelearningalgorithms.Forsamplechaptersandotherreferencespleasecontactmebyemail.ThebookandlecturesleanheavilyonMeyn&Tweedie(availablefreeon-line[MT].)TheAppendixo

7、f[26]containsa“mini-[MT]”.UntilJanuary1,2007,thetableofcontents,Chapter11,andtheAppendixcanbefoundon-lineatthehiddenlink,black.csl.uiuc.edu/meyn/CTCNchapter11.pdf(1)ControlTechniquesforComplexNetworksDraftcopyDecember10,20062Contents0WhatisaGoodModel?2

8、1OptimalandMaxWeightPolicies31.1Basicmodels...................................31.2Whatdooptimalpolicieslooklike?.......................41.3MaxWeightandMinDrift............................42WorkloadRelaxations62.1Workloadinunitsofinvento