简介：Thispaperdealswithadiscrete-timeGeo/Geo/1queueingsystemwithworkingbreakdownsinwhichcustomersarriveatthesysteminvariableinputratesaccordingtothestatesoftheserver.Theservermaybesubjecttobreakdownsatrandomwhenitisinoperation.Assoonastheserverfails,arepairprocessimmediatelybegins.Duringtherepairperiod,thedefectiveserverstillprovidesserviceforthewaitingcustomersatalowerservicerateratherthancompletelystoppingservice.Weanalyzethestabilityconditionfortheconsideredsystem.Usingtheprobabilitygeneratingfunctiontechnique,weobtaintheprobabilitygeneratingfunctionofthesteady-statequeuesizedistribution.Also,variousimportantperformancemeasuresarederivedexplicitly.Furthermore,somenumericalresultsareprovidedtocarryoutthesensitivityanalysissoastoillustratetheeffectofdifferentparametersonthesystemperformancemeasures.Finally,anoperatingcostfunctionisformulatedtomodelacomputersystemandtheparabolicmethodisemployedtonumericallyfindtheoptimumservicerateinworkingbreakdownperiod.

简介：在这篇论文，我们与工作假期和假期打断学习M/M/1队列。工作假期最近被介绍，在哪个期间服务者能仍然以更低的率在原来的进行中的工作上提供服务。同时，我们介绍一个新policy:the服务器罐头一旦系统的一些索引例如顾客的数字，在假期时期完成某个值，从假期回到正常工作水平。没有完成假期，服务者可以从假期回来。如此的政策被称为假期打断。我们连接提及的上面二条政策并且假设如果在假期时期期间在在服务结束以后的系统有顾客，服务器将回到正常工作水平，嗨伪出生和死亡过程和矩阵几何的解决方案方法称为，我们为顾客和等待的时间的数字获得分布和随机的分解结构并且提供系统的一些索引。

简介：WestudyanM/PH/1queuewithphasetypeworkingvacationandvacationinterruptionwherethevacationtimefollowsaphasetypedistribution.Theserverservesthecustomersatalowerrateinavacationperiod.Theservercomesbacktotheregularbusyperiodataservicecompletionwithoutcompletingthevacation.Suchpolicyiscalledvacationinterruption.Intermsofquasibirthanddeathprocessandmatrix-geometricsolutionmethod,weobtainthestationaryqueuelengthdistribution.Moreoverweobtaintheconditionalstochasticdecompositionstructuresofqueuelengthandwaitingtimewhentheservicetimedistributionintheregularbusyperiodisexponential.

简介：Inthispaper,weanalyzeabulkinputM[X]/M/1queuewithmultipleworkingvacations.Aquasiuppertriangletransitionprobabilitymatrixoftwo-dimensionalMarkovchaininthismodelisobtained,andwiththematrixanalysismethod,highlycomplicatedprobabilitygeneratingfunction(PGF)ofthestationaryqueuelengthisfirstlyderived,fromwhichwegotthestochasticdecompositionresultforthestationaryqueuelengthwhichindicatestheevidentrelationshipwiththatoftheclassicalM[X]/M/1queuewithoutvacation.ItisimportantthatwefindtheupperandthelowerboundsofthestationarywaitingtimeintheLaplacetransformorderusingthepropertiesoftheconditionalErlangdistribution.Furthermore,wegainthemeanqueuelengthandtheupperandthelowerboundsofthemeanwaitingtime.

简介：Thispaperanalyzesafinite-bufferrenewalinputsingleserverdiscrete-timequeueingsystemwithmultipleworkingvacations.Theserverworksatadifferentrateratherthancompletelystoppingworkingduringthemultipleworkingvacations.Theservicetimesduringaserviceperiod,servicetimeduringavacationperiodandvacationtimesaregeometricallydistributed.ThequeueisanalyzedusingthesupplementaryvariableandtheimbeddedMarkov-chaintechniques.Weobtainsteady-statesystemlengthdistributionsatpre-arrival,arbitraryandoutsideobserver'sobservationepochs.Theanalysisofactualwaiting-timedistributionandsomeperformancemeasuresarecarriedout.Wepresentsomenumericalresultsanddiscussspecialcasesofthemodel.