网络上的随机行走及其在通信工程中的应用

《网络上的随机行走及其在通信工程中的应用》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、东南大学博士学位论文网络上的随机行走及其在通信工程中的应用姓名：王少平申请学位级别：博士专业：信息与信号处理指导教师：裴文江20090601AbstractRandomwalksareoneofthebasicdynamicprocessesonnetworks．Itsinvestigationwillhelpdiscovergoverninglawsongeneraldynamicprocessesonnetworks．Inrecentyears，researchworksonrandomwalksonnetworkswerefruitfulin

2、botllitstheoryandapplications．Inthetheoryofrandomwalks，classicalconceptssuchasfirstpassagetime，displacemenLcovertime，spectrmntheoryhavebeenstudiedonsmall—worldnetworksandscale—freenetworks．Newconceptsandtechniqueshavealsobeendeveloped，suchasrandomwalkbetweenness，detectingcommu

3、nitystructurebyrandomwalks，self-avoidrandomwalksonscale·freenetworks，andSOon．Initsapplications，researchinterestfocusesmainlyonrandomwalksoncommunicationnetworks，tryingtoprovidebetterSOlutiontosuchproblemsassearchingwebpagesonW州locatingfilesonP2Pnetworks，transportationonnetwork

4、s，virusspreadingonInteract,modelingandsamplingscale—freenetworks，etc．Inthisdissertation，wemainlyfocusonthetopicofrandomwalksonnetworksanditsapplicationtocommunicationnetworks．Themaincontributionofthisdissertationarelistedasfollows：First,westudysometheoreticalandtechnologicalpr

5、oblemswithrelationtomultipleBrownianparticlesonnetworks．WeareespeciallyinterestedinthebehaviorofthefirstarrivingBrownianparticlewhenalltheBrownianparticlesstartoutfromthesourcenodesimultaneouslyandheadtothetargetnoderandomly．Weanalyzethefn'stpassagetime(FPT)andthemeanfirstpass

6、agetime(MFPT)ofmultipleBrownianparticlesoncomplexnetworks．EquationsofFPTandMFPTareobtained．ThedistributionofFPTisalsoanalyzedinavarietyofnetworks．Onavarietyofcommonlyencounterednetworks．weobservefn'stpassagepropertiesofmultipleBrownianparticlesfromdifferentaspects．WefmdthatMFP

7、TofmultipleBrownianparticlesdropssubstantiallywhenparticlenumberZincreasesatthefirststage，andconvergesto如，thedistancebetweenthesourceandthedestinationwhen舔z—o。．ThedistributionofFPTProb{Y,h(z)=t)，t=0，1，2，．．．isalsoanalyzedinthesenetworks．Thedistributioncurvepeaksuptowardst=dmwhe

8、nZincreases．Consequently,ifparticlenumberZissetappropriatelyl