外文翻译--等待队列与模式-精品

外文翻译--等待队列与模式-精品附件外文翻译英文WaitinglinesandsimulationThe“missmanners”articlepokesfunatoneoflife’srealities;havingtowaitinline.noboubtthosewaitinginlinewouldallagreethatthesolutiontotheproblemisobvious;simplyaddmoreserversorelsedosomethingtospeedupservice.althoughbothedeasmaybepotentialsolutions,therearecertainsubletiesthatmustbedealtwith.Foronething,mostservicesystemshavethecapacitytoprocessmorecustomersoverthelongrunthantheyarecalledontoprocess.Hence,theproblemofcustomerswaitingisashort-termphenomenon.Theothersideofthethecoinisthatatcertaintimestheserversareidle,waitingforcustomers.Thusbyincreasingtheservicecapacity,theserveridletimewouldincreaseevenmore.Consequently,indesigningservicesystems,thedesignermustweihtthecostofprovidingagivenlevelofservicecapacityagainstthepotential(implicit)costofhavingcustomerswaitforservice.Thisplanningandanalysisofservicecapacityfrequentlylendsitselftoqueuingtheory,whichisamathematicalapproachtotheanalysisofwaitinglines.ThefoundationofmodernqueuingtheoryisbasedonstudiesaboutautomaticdialingequipmentmadeinearlypartofthetwentiethcenturybyDanishtelephoneengineerA.K.Erlang.PriortoWorldWarII,veryfewattemptsweremadetoapplyqueuingtheorytobusinessproblems.Sincethattime,queuingtheoryhasbeenappliedtoawiderangeofproblems.Themathematicsofqueuingcanbecomplex;forthatreason,theemphasisherewillnotbeonthemathematicsbuttheconceptsthatunderlietheuseofqueuinginanalyzingwaiting-lineproblems.Weshallrelyontheuseofformulasandtablesforanalysis.Waitinglinesarecommonlyfoundwherevercustomersarriverandomlyforservices.Someexamplesofwaitinglinesweencounterinourdailylivesincludethelinesatsupermarkdtcheckouts,fast-foodrestaurants,aipportticketcounters,theaters,postoffices,andtollbooths.In manysituations,the“customers”arenotpeoplebutorderswaitingtobefilled,truckswaitingtobeunloaded,jobswaitingtobeprocessed,orequipmentawitingrepairs.Stillotherexamplesincludeshipswaitingtodock,planeswaitingtoland,hospitalpatientswaitingforanurse,andcarswaitingatastopsign.Onereasonthatqueuinganalysisisimportantisthatcustomersregardwaitingasanon-value-addedactivity.Customersmaytendtoassociatethiswithpoorservicequality，especiallyifthewaitislong.Similarly,inanorganizationalsetting,havingworkoremployeeswaitisnon-value-added—thesortofwastethatworkersinJITsystemsstrivetoreduce.Thediscussionofqueuingbeginswithanexaminationofwhatisperhapsthemostfundamentalissueinwaiting-linetheory:whyistherewaiting?Whyistherewaiting?Manypeoplearesurprisedtolearnthatwaitinglinestendtoformeventhoughasystemisbasicallyunderloaded.Forexample,afast-foodrestaurantmayhavethecapacitytohandleanaverageof200ordersperhourandyetexperiencewaitinglineseventhoughtheaveragenumberofordersisonly150perhour.Thekeywordisaverage.Inreality,customersarrivesatrandomintervalsratherthanatevenlyspacedintervals,andsomeorderstakelongertofillthanothers.Inotherwords,botharrivalsandservicetimesexhibitahighdegreeofvariability.Asaresult,thesystemattimesbecomestemporarilyoverloaded,givingrisetowaitinglines;atothertimes,thesystemsisidlebecausetherearenocustomers.Thus,althoughasystemmaybeunderloadedfromamacrostandpoint,varialilitiesinarrivalsandservicemeanthatattimesthesystemisoverloadedfromamicrostandpoint.Itfollowsthatinsystemswherevariabilityisminimalofnonexistent(e.g.,becausearrivalscanbescheduledandservicetimeisconstant),waitinglinesdonotordinarilyform.ManagerialImplicationsofWaitingLinesManagershaveanumberofverygoodreasonstobeconcernedwithwaitinglines.Chiefamongthosereasonsarethefollowing:1.Thecosttoprovidewaitingspace.2.Apossiblelossofbusinessshouldcustomersleavethelinebeforebeingservedorrefusetowaitatall3.Apossiblelossofgoodwill.4.Apossiblereductionincustomersatisfaction.5.Theresultingcongestionmaydisruptotherbusinessoperationsand/orcustomers.GoalofWaiting-LineAnalysisThegoalofqueuingisessentiallytominimizetotalcosts.Therearetwobasiccategoriesofcostinaqueuingsituation:thoseassociatedwithcustomerswaitingforserviceandthoseassociatedwithcapacity.Capacitycostsarethecostsofmaintainingtheabilitytoprovideservice.Examplesincludethenumberofbaysatacarwash,thenumberofchechkoutsatasupermarket,thenumberofrepairpeopletohandleequipmentbreakdowns,andthenumberoflanesonahighway.Whenaservicefacilityisidle,capacityislostsinceitcannotbestored.Thecostsofcustomerwaitingincludethesalariespaidtoemployeeswhiletheywaitforservice(mechanicswaitingfortools,thedriversoftruckswaitingtounload),thecostofthespaceforwaiting(sizeofdoctor’swaitingroom,lengthofdrivewayatacarwash,fuelconsumedbyplaneswaitingtoland),andanylossofbusinessduetocustomersrefusingtowaitandpossiblygoingelsewhereinthefuture.Apracticaldifficultyfrequentlyencounteredispinningdownthecostofcustomerwaitingtime,especiallysincemajorportionsofthatcostarenotapartofaccountingdata.Oneapproachoftenusedistotreatwaitingtimesorlinelengthsasapolicyvariable:Amanagersimplyspecifiesanacceptablelevelofwaitinganddirectsthatcapacitybeestablishedtoachievethatlevel.Thetraditionalgoalofqueuinganalysisistobalancethecostofprovidingalevelofservicecapacitywiththecostofcustomerswaitingforservice.Figure1illustratesthisconcept.Notethatascapacityincreases,itscostincreases.Forsimplicity,theincreaseisshownasalinearrelationship.Althoughastepfunctionisoftenmoreappropriate,useofastraightlinedoesnotsignificantlydistortthepicture.Ascapacityincreases,thenumberofcustomerswaitingandthetimetheywaittendtodecrease,therebydecreasingwaitingcosts.Asistypicalintrade-offrelationships,totalcostscanberepresentedasaU-shapedcurve.Thegoalofanalysisistoidentifyalevelofservicecapacitythatwillminimizetotalcost.(UnlikethesituationintheinventoryEOQmodel,theminimumpointonthetotalcostcurveisnotusuallywherethetwocostlinesintersect.)Insituationswherethosewaitinginlineareexternalcustomers(asopposedtoemployees),theexistenceofwaitinglinescanreflectnegativelyonanorganization’squalityimage.Consequently,someorganizationsarefocusingtheirattentiononprovidingfasterservice—speedinguptherateatwhichserviceisdeliveredratherthanmerelyincreasingthenumberofservers.Theeffectofthisistoshiftthetotalcostcurvedownwardifthecostofcustomerwaitingdecreasesbymorethanthecostofthefasterservice.Figure1:Thegoalofqueuinganalysisistominimizethesumoftwocosts:customerwaitingcostsandservicecapacitycost.SystemCharacteristicsTherearenumerousqueuingmodelsfromwhichananalystcanchoose.Naturally,muchofthesuccessoftheanalysiswilldependonchoosinganappropriatemodel.Modelchoiceisaffectedbythecharacteristicsofthesystemunderinvestigation.Themaincharacteristicsare:1、Populationsource.2、Numberofservers(channels)3、Arrivalandservicepatterns.4、Queuediscipline(orderofservice).Figure2depictsasimplequeuingsystem.Figure2 AsimplequeuingsystemPopulationsourceTheapproachtouseinanalyzingaqueuingproblemdependsonwhetherthepotentialnumberofcustomersislimited.Therearetwopossibilities:infinite-sourceandfinitesourcepopulations.Inaninfinite-sourcesituation,thepotentialnumberofcustomersgreatlyexceedssystemcapacity.Infinite-sourcesituationsexistwheneverserviceisunrestricted.Examplesaresupermarkets,drugstores,banks,restaurants,theaters,amusementcenters,andtollbridges.Theoretically,largenumbersofcustomersfromthe“callingpopulation”canrequestserviceatanytime.Whenthepotentialnumberofmachinesthatmightneedrepairsatanyonetimecannotexceedthenumberofmachinesthatmightneedrepairsatanyonetimecannotexceedthenumberofmachinesassignedtotherepairer.Similarly,anoperatormayberesponsibleforloadingandunloadingabankoffourmachines,anursemayberesponsibleforloadingandunloadingabedward,asecretarymayberesponsiblefortakingdictationfromthreeexecutives,andacompanyshopmayperformrepairsasneededonthefirm’s20trucks.Numberofservers(channels)Thecapacityofqueuingsystemisfunctionofthecapacityofeachserverandthenumberofserversbeingused.Thetermsserverandchannelaresynonymous,anditisgenerallyassumedthateachchannelcanhandleonecustomeratatime.Systemscanbeeithersingle-ormultiple-channel.(Agroupofserversworkingtogetherasateam,suchasasurgicalteam,istreatedasasingle-channelsystem.)Examplesofsingle-channelsystemsaresmallgrocerystoreswithonecheckoutcounter,sometheaters,single-baycarwashes,anddrive-inbankswithoneteller.Multiple-channelsystems(thosewithmorethanoneserver)arecommonlyfoundinbanks,atairlineticketcounters,atautoservicecenters,andatgasstations.Arelateddistinctionisthenumberofstepsorphasesinaqueuingsystem.Forexample,atthemeparks,peoplegofromoneattractiontoanother.Eachattractionconstitutesaseparatephasewherequeuescan(andusuallydo)from.Figure3illustratessomeofthemostcommonqueuingsystems.Becauseitwouldnotbepossibletocoverallofthesecasesinsufficientdetailinthelimitedamountofspaceavailablehere,ourdiscussionwillfocusonsingle-phasesystems.Figure3 FourcommonvariationsofqueuingsystemsArrivalandservicepatternsWaitinglinesareadirectresultofarrivalandservicevariability.Theyoccurbecauserandom,highlyvariablearrivalandservicepatternscausesystemstobetemporarilyoverloaded.Inmanyinstances,thevariabilitiescanbedescribedbytheoreticaldistributions.Infact,themostcommonlyusedmodelsassumethatthecustomerarrivalratecanbedescribedbyaPossiondistributionandthattheservicetimecanbedescribdebyanegativeexponentialdistribution.Figure4illustratesthesedistributions.ThePoissondistributionoftenprovidesareasonablygooddescriptionofcustomerarrivalsperunitoftime(e.g.,perhour).Figure5Aillustrateshowpoisson-distributedarrivals(e.g.,accidents)mightoccurduringathree-dayperiod.Insomehours,therearethreeorfourarrivals,inotherhoursoneortwoarrivals,andinsomehoursnoarrivals.Thenegativeexponentialdistributionoftenprovidesareasonablygooddescriptionofcustomerservicetimes(e.g.,firstaidcareforaccidentvictims).Figure5BillustrateshowexponentialservicetimesmightappearforthecustomerswhosearrivalsareillustratedinFigure5A.Notethatmostservicetimesareveryshort—someareclosetozero—butafewrequirearelativelylongservicetime.Thatistypicalofanegativeexponentialdistribution.Waitinglinesaremostlikelytooccurwhenarrivalsarebunchedorwhenservicetimesareparticularlylengthy,andtheyareverylikelytooccurwhenbothfactorsarepresent.Forinstance,notethelongservicetimeofcustomer7onday1,inFigure5B.InFigure5A,theseventhcustomerarrivedjustafter10o’clockandthenexttwocustomersarrivedshortlyafterthat,makingitverylikelythatawaitinglineformed.Asimilarsituationoccurredonday3withthelastthreecustomers:Therelativelylongservicetimeforcustomer13(Figure5B),andtheshorttimebeforethenexttwoarrivals(Figure5A,day3)wouldcreate(orincreasethelengthof)awaitingline.ItisinterestingtonotethatthePoissonandnegativeexponentialdistributionsarealternatewaysofpresentingthesamebasicinformation.Thatis,ifservicetimeisexponential,thentheservicerateisPoisson..Similarly,ifthecustomerarrivalrateisPoisson,thentheinterarrivaltime(i.e.,thetimebetweenarrivals)isexponential.Forexample,ifaservicefacilitycanprocess12customersperhour(rate),averageservicetimeisfiveminutes.andifthearrivalrateis10perhour,thentheaveragetimebetweenarrivalsissixminutes.ThemodelsdescribedheregenerallyrequirethatarrivalandservicerateslendthemselvestodescriptionusingaPoissondistributionof,equivalently,thatinterarrivalandservicetimeslendthemselvestodescriptionusinganegativeexponentialdistribution.Inpractice,itisnecessarytoverifythattheseassumptionsaremet.Sometimesthisisdonebycollectingdataandplottingthem,althoughthepreferredapproachistouseachi-squaregoodness-of-fittestforthatpurpose.Adiscussionofthechi-squaretestisbeyondthescopeofthistext,butmostbasicstatisticstextbookscoverthetopic.Researchhasshownthattheseassumptionsareoftenappropriateforcustomerarrivalsbutlesslikelytobeappropriateforservice.Insituationswheretheassumptionsarenotreasonablysatisfied,thealternativeswouldbeto(1)developamoresuitalbemodel,(2)searchforabetter(andusuallymorecomplex)existingmodel,or(3)resorttocomputersimulation.Eachofthesealternativesrequiresmoreeffortorcostthantheonespresentedhere.Figure4PoissonandnegativeexponentialdistributionsFigure5PoissonarrivalsandexponentialservicetimesQueuedisciplineQueuedisciplinereferstotheorderinwhichcustomersareprocessed.Allbutoneofthemodelstobedescribedshortlyassumethatserviceisprovidedonfirst-come,first-servedbasis.Thisisperhapsthemostcommonlyencounteredrule.Thereisfrist-comeserviceatbanks,store,theaters,restaurants,four-waystopsigns,registrationlines,andsoon.Examplesofsystemsthatdonotserveonafirst-comebasisincludehospitalemergencyrooms,rushordersinafactory,andmainframecomputerprocessingofjobs.Intheseandsimilarsituations,customersdonotallrepresentthesamewaitingcosts;thosewiththehighestcosts(e.g.,themostseriouslyill)areprocessedfirst,eventhoughothercustomersmayhavearrivedearlier.MeasuresofsystemperformanceTheoperationsmanagertypicallylooksatfivemeasureswhenevaluatingexistingorproposedservicesystems.Thosemeasuresare:1.Theaveragenumberofcustomerswaiting,eitherinlineorinthesystem.2.Thearveragetimecustomerswait,eitherinlineofinthesystem.3.Systemutilization,whichreferstothepercentageofcapacityutiliaed.4.Theimpliedcostofagivenlevelofcapacityanditsrelatedwaitingline.5.Theprobabilitythatanarrivalwillhavetowaitforservice.Ofthesemeasures,systemutilizationbearssomeelaboration.Itreflectstheextenttowhichtheserversarebusyratherthanidle.Onthesurface,itmightseemthattheoperationsmanagerwouldwantgoseek100percentutilization.However,asFigure6illustrates,increasesinsystemutilizationareachievedattheexpenseofincreasesinboththelengthofthewaitinglineandtheaveragewaitingtime.Infact,thesevaluesbecomeexceedinglylargeasutilizationapproaches100percent.Theimplicationisthatundernormalcircumstances,100percentutilizationisnotarealisticgoal.Evenifitwere,100percentutilizationofservicepersonnelisnotgood;theyneedsomeslacktime.Thus,instead,theoperationsmanagershouldtrytoachieveasystemthatminimizesthesumofwaitingcostsandcapacitycosts.Figure6TheaveragenumberwaitinginlineandtheaveragetimecustomerswaitinlineincreaseceponentiallyasthesystemutilizationincreasesQueuingmodels:infinite-sourceManyqueuingmodelsareavailableforamanageroranalysttochoosefrom.Thediscussionhereincludesfourofthemostbasicandmostwidelyusedmodels.Thepurposeistoprovideanexposuretoarangeofmodelsratherthananextensivecoverageofthefield.AllassumeaPoissonarrivalrate.Moreover,themodelspertaintoasystemoperatingundersteadystateconditions;thatis,theyassumetheaveragearrivalandserviceratesarestable.Thefourmodelsdescribedare:1.Singlechannel,exponentialservicetime.2.Singlechannel,constantservicetime.3.Multiplechannel,exponentialservicetime.4.Multiplepriorityservice,exponentialservicetime.Tofacilitateyouruseofqueuingmodels,Table1providesalistofthesymbolsusedfortheinfinite-sourcemodels.Tabel1Infinite-sourcesymbolsSymbolRepresentsλCustomerarrivalrateμServicerateL1ThearveragenumberofcustomerswaitingforserviceL2TheaveragenumberofcustomersinthesystemThesystemutilizationW1TheaveragetimecustomerwaitinlineW2Theaveragetimecustomerspendinthesystem1/μServicetimeP0TheprobabilityofzerounitsinthesystemPnTheprobabilityofnunitsinthesystemMThenumberofservers(channels)LmaxThemaxmumexpectednumberwaitinginlineBasicrelationshipsTherearecertainbasicrelationshipsthatholdforallinfinite-sourcemodels.Knowledgeofthesecanbeveryhelpfulinderivingdesiredperformancemeasures,givenafewkeyvalues.Herearethebasicrelationships:Systemutilization:Thisreflectstheratioofdemand(asmeasuredbythearrivalrate)tosupplyorcapacity(asmeasuredbytheproductofthenumberofservers,M,andtheservicerate,μ)···········(1)Theaveragenumberofcustomersbeingserved:···········(2)Theaveragenumberofcustomers:Waitinginlineforservice:L1(Modeldependent.Obtainusingatableorformula.)Inthesystem(lineplusbeingserved): L2=L1+r  ···········（3）Theaveragetimecustomersare:Waitinginline:W1=············（4）Inthesystem:W2=W1+···········（5）Allinfinite-sourcemodelsrequirethatsystemutilizationbelessthan1.0;themodelsapplyonlytounderloadedsystems.Theaveragenumberwaitinginline,L1,isakeyvaluebecauseitisadeterminantofsomeoftheothermeasuresofsystemperformance,suchastheaveragenumberinthesystem,theaveragetimeinline,andtheaveragetimeinthesystem.Hence,L1willusuallybeoneofthefirstvaluesyouwillwanttodetermineinproblemsolving.ExampleCustomersarriveatabakeryatanaveragerateof18perhouronweekdaymornings.ThearrivaldistributioncanbedescribedbyaPoissondistributionwithameanof18.eachclerkcanserveacustomerinanaverageofrourminutes;thistimecanbedescribedbyanexponetialdistributionwithameanof4.0minutes.a.Whatarethearrivalandservicerates?b.Computetheaveragenumberofcustomersbeingseredatanytime.c.Supposeithasbeendeterminedthattheaveragenumberofcustomerswaitinginlineis      3.6. Computetheaveragenumberofcustomersinthesystem(i.e.,waitinginlineorbeingserved),theaveragetimecustomerswaitinline,andtheaveragetimeinthesystem.d.DeterminethesystemutilizationforM=2,3and4servers.Solutiona. Thearrivalrateisgivenintheproblem:customersperhour.Changetheservicetimetoacomparablehourlyratebyfirstrestatingthetimeinhoursandthentakingitsreciprocal.Thus,(4minutesprecustomer)/(60minutesperhour)=1/15=1/μ.Itsreciprocalisμ=15customersperhour.b.      =  =1.2customers.c.  Given:L1=3.6customers.L2=L1+r=3.6+1.2=4.8customershourspercustomer,or0.2hours*60minutes/hour=12minutesW2  =waitinginlineplusservice=W1+=0.2+ =0.267hour,orapproximately16minutesd. SystemutilizationisForM=2,     =0.6ForM=3,     =0.4ForM=4,     =0.3Hence,asthesystemcapacityasmeasuredasmeasuredbyMμincreases,thesystemutilizationforagivenarrivalratedecreases.Referenceliterature:OperationsManagement WilliamJ.Stevenson  SeventhEdition中文等待队列与模式“MissManners”文章嘲笑一种生活现实：必须在队里等待。毫无疑问，在队里等待的人都同意得到问题的解答：增加更多服务器或者提高服务速度。尽管这两种方法都能解决问题，但一些敏锐的问题必然得以解决。首先，多数系统从长远的角度来看，它能提供比实际要处理的服务还要多，因此顾客等待问题是一种短期现象。另外，有些机器处于等待顾客的服务，因此要是采取通过增加系统的服务能力并不能解决这类问题，这样只会增加服务系统的闲置时间。因此，在设计系统时，设计者要衡量成本与提供服务容量水平，要考虑潜在客户的需求的同时减少多余服务的浪费。对服务能力分析与计划是基于数学方法中的对等候行列分析的排队理论。现代排队理论是在20世纪早期丹麦电话工程师A.K.Erlang研究自动拨号设备的基础上发展而成的。第二次世界大战之前，排队理论好少应用于处理商业业务所碰到的问题，二次大战后，排队理论被广泛应用于各种各样的问题。数学排队问题可以是很复杂，因此，这里重点不在于数学，而是强调使用排队理论在分析等待线问题的概念。我们将依靠使用数学公式和 表格 关于规范使用各类表格的通知入职表格免费下载关于主播时间做一个表格详细英语字母大小写表格下载简历表格模板下载 图来分析。排队等候经常见到，尽管顾客所需的服务是随机的。如在我们日常生活所出现的排队现象：离开超市时的结算、快餐店、飞机售票台、电影院、邮局和所有收费通行的服务等。在很多情况下，等待的“顾客”并不是人员而是等待其他。如卡车等待卸载，工作等待处理、或者设备等待维修。还有其他例子，如船等待停泊、飞机等待登陆、医院的病人等待护士，汽车等待通行证等等。排队问题分析的一个重要原因是顾客认为等待不能创造价值。等待会影响服务质量，尤其是过久的等待会使顾客产生服务质量差的印象。类似的，在组织设置时，要工作或雇员等待都是非增值活动――JIT系统所努力减少的浪费。关于排队理论的讨论源于一个问题或者说是等候线的基本问题：那儿为什么要等候？为什么要等候？很多市民很惊讶去知道等候线的形成原因，即使系统未负荷。例如，快餐馆有能力每小时处理200份菜单，但等候现象还是会产生，即使每小时只有150份菜单。关键问题是“平均”，顾客的到来是随机的，而不是平均间隔到来；同时菜单所花费的时间不一致，有些会比其他的要长。换句话说，到来的随机性以及服务时间是不确定的。因此系统随时面临超载，增加了队伍的长度。而其他没有顾客时间，系统无所事事。因此，尽管系统在宏观立场上看是未超载，但由于顾客到来的随机性以及服务时间的不一致，在微观立场上来，系统出现超载现象。因此，可以说，在变化性很少的系统（到来的时间可以预测和服务时间是恒定）一般不存在排队等候的现象。管理人员需要掌握充分的有关排队等候的资料，主要包括以下几点：1、提供等候排队的空间所花费的成本。2、顾客离开而造成的可能存在的商业损失。3、信誉可能损失。4、顾客满意度可能降低。5、发生的阻塞可能会打乱商业活动运作和（或）顾客。等候线分析的目标排队理论的本质是使总成本达到最小。在排队过程存在着两种基本费用：与顾客等待有关以及与系统容量有关。系统容量成本是维护所提供的服务、稳定服务水平所支出的成本。如汽车服务中的汽车道的多少、超级市场付账服务台数量、维修机器的人员数量、在高速公路上车道的数量等。由于这些容量是不能储存的，故当设施、设备等处于空闲的状态时，容量就会消失。有关顾客等待的成本包括支付给等待服务的雇员的薪金（如等待维修用的工具或设备、等待卡车卸载的司机）和等待所占用空间所花费的成本（候诊室的大小、洗车位的多少、在飞机着落前所要消耗原料所占的空间）以及由于顾客拒绝等候或由于等候过长而将来失去顾客所造成的商业损失。常常遇到一些实实在在的困难，不得不采取花费顾客等待时间，尤其是大部分费用不是可数的数据。应对这类问题，常用的方法就是把等待的时间和队列的长度看作是可变的，管理人员确定顾客可接受的等候时间以及队列长度，并建立一个服务水平达到这一要求的系统。排队理论的传统分析目标在于平衡系统提供一定服务水平所花的费用与顾客排队所支付的成本。图1充分 说明 关于失联党员情况说明岗位说明总经理岗位说明书会计岗位说明书行政主管岗位说明书 了这一原理。注意到，当容量增加会伴随着费用的增加，明显它们间的关系是线性关系。在实际情况下，阶梯函数比直线更适当应用。当容量增量，倾向于减少等待的顾客的数量和时间，从而减少等待成本。在典型的交易关系中，总成本可以用Ｕ形曲线代表。分析的目标是在获得一定服务能力水平的情况下如何使总成本最小。(它不同于在存货EOQ模型的情况，在总成本曲线的极小的点通常不是两条成本线相交的地方。)在队伍内等候的外部顾客（与雇员即内部顾客相对）通常会对组织的质量存在着消极的影响。结果很多组织把注意力放在如何提供更快的服务速度——快速服务并不是仅仅增加服务器的数量。减少顾客等待比提供更快的服务速度能总成本曲线向下滑移更多。图1排列理论分析的目标在于寻找最低成本时的最佳容量系统特征有许多排队理论模型可供选择分析。显然，能否分析成功很大程序取决于是否选择了合适的模型。模型的选择受系统特征的影响，主要特征如下：1、人口来源2、服务器（渠道）的数量3、到来和服务的方式4、队列的制度（服务命令）如图2描述了一个简单的排队系统。图2一个简单的队列系统人口来源在这方面分析排队问题在于潜在顾客来源是否有限制。有两种可能情况：无限制的顾客来源与有限制的顾客来源。在无限制来源情况下，顾客的潜在的数量很大地超出系统容量。无限制顾客来源存在于服务是无限制的情况下，如超级市场、药房、银行、餐馆、剧院、娱乐中心和收费桥。理论上，在“号召顾客群”中的大量顾客的服务请求能得以实现。某一时候可能出现需要修理的机器超过预计修理的数量而得不到修理，或者超出于应分配给每个维修工的数量。同样，一个操作工可能同时要负责四台机器的操作，护士同时接收病人入院和退房的要求，秘书要负责 记录 混凝土 养护记录下载土方回填监理旁站记录免费下载集备记录下载集备记录下载集备记录下载 三个董事长的工作指令，一个公司的销售店可能要求需要20辆卡车。服务器（渠道）的数量排队系统容量是指每台服务器的功能与能提供服务需求的数量。服务器和渠道是同义的。通常假设，每一种渠道在每一次几乎只处理一名顾客。系统可以是单一或多渠道的（一组服务人员组成服务团体，如一个外科医疗小组共同处理一个单一系统）。单一系统的例子还有只有一个结算台的小杂货店，某些剧院，只有一条汽车道的服务和只有一位出纳的银行。多渠道系统（拥有多台服务器）常见于银行系统、售飞机票系统、自动服务系统、加油站等。它们的分别联系在于服务层次的数量或一个排队系统的所处的阶段。例如，人们往往从一种吸引力转移到另一种吸引力，每个阶段解释了队伍的形成的一般理由。图3说明一些最常见的的排队系统。由于在有限的空间，不可能包括所有的细节，在这里也不能一一述说，因此我们集中讨论单阶系统。