DISCRETE STOCHASTIC PROCESSES (MIT)

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1、DISCRETESTOCHASTICPROCESSESDraftof2ndEditionR.G.GallagerJanuary31,2011iiiPrefaceThesenotesareadraftofamajorrewriteofatext[9]ofthesamename.Thenotesandthetextareoutgrowthsoflecturenotesdevelopedoversome20yearsfortheM.I.T.graduatesubject6.262,entitled‘DiscreteStochasticProcesses.’Theoriginalmot

2、ivationfor6.262wastoprovidesomeofthenecessarybackgroundforElectricalEngineering,ComputerScience,andOperationsResearchstudentsworkingintheburgeoningfieldofcomputer-communicationnetworks.Manyofthemostimportantandchallengingproblemsinthisareainvolvequeueingandcongestion,buttheliteratureonqueuein

3、gandcongestionwasrapidlybecomingsodi↵usethatamorecohesiveapproachwasneeded.Queuingproblemsareexamplesofstochasticprocesses,andmoreparticularly,discretestochasticprocesses.Discretestochasticprocessesformacohesivebodyofstudy,allowingqueueingandcongestionproblemstobediscussedwheretheynaturallya

4、rise.Intheinterveningyears,ithasbecomeincreasinglyapparentthatmanyproblemsinvolvinguncertaintyinalmostallbranchesoftechnologyandhumana↵airsprovideinterestingandimportantexamplesofdiscretestochasticprocesses.Discussingtheseproblemsastheyarisebothincreasestheapplicationdomainofthissubjectandal

5、soenhancesourintuitionandunderstandingaboutthegeneralprinciples.Thepurposeofthistextisbothtohelpstudentsunderstandthegeneralprinciplesofdiscretestochasticprocesses,andtodeveloptheunderstandingandintuitionnecessarytoapplystochasticprocessmodelstoproblemsinengineering,science,andoperationsrese

6、arch.Althoughtheultimateobjectiveisapplications,thereisrelativelylittledetaileddescriptionofrealapplications.Rather,therearemanysimpleexamplesdesignedbothtobuildinsightaboutparticularprinciplesinstochasticprocessesandtoillustratethegenerice↵ectofthesephenomenainrealsystems.Iamconvincedthatth

7、e”casestudy”method,inwhichmanyapplicationsarestudiedintheabsenceofgeneralprinciples,isinappropriateforunderstandingstochasticprocesses(andsimilarlyinappropriateforanyfieldthathasarichandhighlycohesivemathematicalstructure).Whenwetrytoeitherdesignnew