简介:ThispaperstudiestheoperatingcharacteristicsofanM/G/1queuingsystemwitharandomizedcontrolpolicyandatmostJvacations.Afterallthecustomersareservedinthequeueexhaustively,theserverimmediatelytakesatmostJvacationsrepeatedlyuntilatleastNcustomersarewaitingforserviceinthequeueuponreturningfromavacation.IfthenumberofarrivalsdoesnotreachNbytheendoftheJ~(th)vacation,theserverremainsidleinthesystemuntilthenumberofarrivalsinthequeuereachesN.IfthenumberofcustomersinthequeueisexactlyaccumulatedNsincetheserverremainsidleorreturnsfromvacation,theserverisactivatedforserviceswithprobabilitypanddeactivatedwithprobability(1-p).Forsuchvariantvacationmodel,otherimportantsystemcharacteristicsarederived,suchastheexpectednumberofcustomers,theexpectedlengthofthebusyandidleperiod,andetc.Followingtheconstructionoftheexpectedcostfunctionperunittime,anefficientandfastprocedureisdevelopedforsearchingthejointoptimumthresholds(N~*,J~*)thatminimizethecostfunction.Somenumericalexamplesarealsopresented.