A repairablequeueingmodelwithtwo-phaseservice,start-uptimesandretrial customers

A repairablequeueingmodelwithatwo-phaseserviceinsuccession,providedbyasingleserver,isinves- tigated. Customersarriveinasingleordinaryqueueandafterthecompletionofthefirstphaseservice, either proceedtothesecondphaseorjoinaretrialboxfromwheretheyretry,afterarandomamountof time andindependentlyoftheothercustomersinorbit,tofindapositionforserviceinthesecondphase. Moreover, theserverissubjecttobreakdownsandrepairsinbothphases,whileastart-uptimeisneeded in ordertostartservingaretrialcustomer.Whentheserver,uponaserviceorarepaircompletionfinds no customerswaitingtobeserved,hedepartsforasinglevacationofanarbitrarilydistributedlength. The arrivalprocessisassumedtobePoissonandallserviceandrepairtimesarearbitrarilydistributed. For suchasystemthestabilityconditionsandsteadystateanalysisareinvestigated.Numericalresults are finallyobtainedandusedtoinvestigatesystemperformance.