简介：

简介：Thispaperconsidersadiscrete-timeGeo/G/1queueinamulti-phaseserviceenvironment,wherethesystemissubjecttodisastrousbreakdowns,causingallpresentcustomerstoleavethesystemsimultaneously.Atafailureepoch,theserverabandonstheserviceandthesystemundergoesarepairperiod.Afterthesystemisrepaired,itjumpstooperativephaseiwithprobabilityqi,i=1,2···,n.Usingthesupplementaryvariabletechnique,weobtainthedistributionforthestationaryqueuelengthatthearbitraryepoch,whicharethenusedforthecomputationofotherperformancemeasures.Inaddition,wederivetheexpectedlengthofacycletime,thegeneratingfunctionofthesojourntimeofanarbitrarycustomer,andthegeneratingfunctionoftheserver’sworkingtimeinacycle.Wealsogivetherelationshipbetweenthediscrete-timequeueingsystemtoitscontinuous-timecounterpart.Finally,someexamplesandnumericalresultsarepresented.