Discrete-Time Geo x /G/1 Queue with Geometrically Working Vacations and Vacation Interruption

摘要

Thispapertreatsadiscrete-timebatcharrivalqueuewithgeometricallyworkingvacationsandvacationinterruption.Themainpurposeofthispaperistopresentaperformanceanalysisofthissystem.Forthispurpose,wefirstderivetheprobabilitygeneratingfunction(PGF)ofthestationarysystemlengthatthedepartureepochsbasedontheembeddedMarkovchaintechnique.Next,wepresentthestationarydistributionsofthesystemlengthsaswellassomeperformancemeasuresatrandomepochsbyusingthesupplementaryvariablemethod.Thirdly,stillbasedonthesupplementaryvariablemethodwegiveadistributionforthenumberofthecustomersatthebeginningofabusyperiodandgiveastochasticdecompositionformulaforthePGFofthestationarysystemlengthatthedepartureepochs.Additionally,weinvestigatetherelationbetweenourdiscrete-timesystemanditscontinuouscounterpart.Finally,somenumericalexamplesshowtheinfluenceoftheparametersonsomecrucialperformancecharacteristicsofthesystem.