排队论的matlab仿真(包括仿真代码)Word文档下载推荐.docx

排队论的matlab仿真(包括仿真代码)Word文档下载推荐.docx

《排队论的matlab仿真(包括仿真代码)Word文档下载推荐.docx》由会员分享，可在线阅读，更多相关《排队论的matlab仿真(包括仿真代码)Word文档下载推荐.docx（21页珍藏版）》请在冰豆网上搜索。

INTRODUCTION

Aqueueisawaitinglineandqueueingtheoryisthemathematicaltheoryofwaitinglines.Moregenerally,queueingtheoryisconcernedwiththemathematicalmodelingandanalysisofsystemsthatprovideservicetorandomdemands.Incommunicationnetworks,queuesareencounteredeverywhere.Forexample,theincomingdatapacketsarerandomlyarrivedandbuffered,waitingfortheroutertodeliver.Suchsituationisconsideredasaqueue.Aqueueingmodelisanabstractdescriptionofsuchasystem.Typically,aqueueingmodelrepresents

（1）thesystem'

sphysicalconfiguration,byspecifyingthenumberandarrangementoftheservers,and

（2）thestochasticnatureofthedemands,byspecifyingthevariabilityinthearrivalprocessandintheserviceprocess.

Theessenceofqueueingtheoryisthatittakesintoaccounttherandomnessofthearrivalprocessandtherandomnessoftheserviceprocess.ThemostcommonassumptionaboutthearrivalprocessisthatthecustomerarrivalsfollowaPoissonprocess,wherethetimesbetweenarrivalsareexponentiallydistributed.Theprobabilityoftheexponentialdistributionfunctionisft=λe-λt.

lErlangBmodel

OneofthemostimportantqueueingmodelsistheErlangBmodel（i.e.,M/M/n/n）.ItassumesthatthearrivalsfollowaPoissonprocessandhaveafinitenservers.InErlangBmodel,itassumesthatthearrivalcustomersareblockedandclearedwhenalltheserversarebusy.TheblockedprobabilityofaErlangBmodelisgivenbythefamousErlangBformula,

wherenisthenumberofserversandA=λ/μistheofferedloadinErlangs,λisthearrivalrateand1/μistheaverageservicetime.Formula（1.1）ishardtocalculatedirectlyfromitsrightsidewhennandAarelarge.However,itiseasytocalculateitusingthefollowingiterativescheme:

lErlangCmodel

TheErlangdelaymodel（M/M/n）issimilartoErlangBmodel,exceptthatnowitassumesthatthearrivalcustomersarewaitinginaqueueforaservertobecomeavailablewithoutconsideringthelengthofthequeue.Theprobabilityofblocking（alltheserversarebusy）isgivenbytheErlangCformula,

Whereρ=1ifA>

nandρ=AnifA<

n.Thequantityρindicatestheserverutilization.TheErlangCformula（1.3）canbeeasilycalculatedbythefollowingiterativescheme

wherePB（n,A）isdefinedinEq.（1.1）.

DESCRIPTIONOFTHEEXPERIMENTS

1.Usingtheformula（1.2）,calculatetheblockingprobabilityoftheErlangBmodel.DrawtherelationshipoftheblockingprobabilityPB（n,A）andofferedtrafficAwithn=1,2,10,20,30,40,50,60,70,80,90,100.Compareitwiththetableinthetextbook（P.281,table10.3）.

Fromtheintroduction,weknowthatwhenthenandAarelarge,itiseasytocalculatetheblockingprobabilityusingtheformula1.2asfollows.

PBn,A=APB（n-1,A）m+APB（n-1,A）

itusethetheoryofrecursionforthecalculation.Butthedenominatorandthenumeratoroftheformulabothneedtorecurs（PBn-1,A）whendoingthematlabcalculation,itwastetimeandreducethematlabcalculationefficient.Sowechangetheformulatobe:

PBn,A=APB（n-1,A）n+APB（n-1,A）=1n+APBn-1,AAPBn-1,A=1（1+nAPBn-1,A）

Thenthecalculationonlyneedrecursoncetimeandismoreefficient.

Thematlabcodefortheformulais:

erlang_b.m

%**************************************

%File:

erlanb_b.m

%A=offeredtrafficinErlangs.

%n=numberoftrunckedchannels.

%Pbistheresultblockingprobability.

function[Pb]=erlang_b（A,n）

ifn==0

Pb=1;

%P（0,A）=1

else

Pb=1/（1+n/（A*erlang_b（A,n-1）））;

%userecursion"

erlang（A,n-1）"

end

end

Aswecanseefromthetableonthetextbooks,itusesthelogarithmcoordinate,sowealsousethelogarithmcoordinatetoplottheresult.Wedividethenumberofservers（n）intothreeparts,foreachpartwecandefineaintervalofthetrafficintensity（A）basedonthefigureonthetextbooks:

1.when0<

n<

10,0.1<

A<

10.

2.when10<

20,3<

20.

3.when30<

100,13<

120.

Foreachpart,usethe“erlang_b”functiontocalculateandthenuse“loglog”functiontofigurethelogarithmcoordinate.

Thematlabcodeis:

%*****************************************

%forthethreeparts.

%nisthenumberservers.

%Aisthetrafficindensity.

%Pistheblockingprobability.

n_1=[1:

2];

A_1=linspace（0.1,10,50）;

%50pointsbetween0.1and10.

n_2=[10:

10:

20];

A_2=linspace（3,20,50）;

n_3=[