Mx/G/1 retrial vacation queue for multi-optional services, phase repair and reneging

摘要

Thepresentpaperdealswithabatcharrivalgeneralretrialqueuewithmulti-optionalservices,vacationandimpatientcustomersundergoingreneging.Theincomingcustomer(orabatchofcustomers)onfindingtheserverinbusyorinnon-workingconditionformsavirtualpoolofcustomerscalledorbitotherwiseundergoesserviceiftheserverisfree.Theserviceisprovidedattwolevels;firstessentialserviceorsecondoptionalservicedependinguponcustomer’schoicetooptforitornot.Moreover,theservermaygoforvacationifhefindsnocustomerwaitingforserviceandreturnsbacktotheservicecenteragainassoonasthecustomerapproachesfortheservice.Theserverisunreliableassuchsubjecttobreakdownduringtheservice;assoonastheserverfails,itisimmediatelysentforrepairsoastorestoreitsfunctionalityasbeforefailure.Therepairmanassignedfortherepairoftheserveralsotakessomesetuptimebeforecommencingtherepairprocess.Byusingsupplementaryvariablestechniqueandprobabilitygeneratingfunctionmethod,theexplicitexpressionsforthequeuesizedistributionandotherperformancemeasureshavebeenderived.Thesensitivityofdifferentparametersonvariousperformanceindiceshasbeenexaminednumericallybytakinganillustration.Also,theneurofuzzyapproachhasbeenusedtoapproximatetheanalyticalresults.