A tandemretrialqueueingsystemwithtwoMarkovianflowsandreservationof channels

he inputflowatStation1isdescribedbythe BMAP (batch Markovianarrivalprocess).Customersfrom this flowareconsideredasnon-prioritycustomers.Customersofanarrivinggroup,whichmeetabusy server, gototheorbitofinfinitesize.Fromtheorbit,theytrytheirluckinexponentiallydistributed random time.ServicetimesatStation1areindependentidenticallydistributedrandomvariableshaving an arbitrarydistribution.AfterserviceatStation1anon-prioritycustomerproceedstoStation2. The servicetimebyaserverofStation2isexponentiallydistributed.Besidescustomersproceedingfrom Station 1,anadditional MAP flow ofprioritycustomersarrivesatStation2directly,notenteringStation1. If aprioritycustomermeetsafreeserveruponarrival,itstartsserviceimmediately.Else,itleavesthesys- tem forever.ItisassumedthatafewserversofStation2arereservedtoservetheprioritycustomersonly. We calculatethestationarydistributionandthemainperformancemeasuresofthesystem.Theproblem of optimaldesignisnumericallyinvestigated.