Time-varying tandem queues with blocking: modeling, analysis, and operational insights via ?uid models with re?ection

Abstract In this paper, we develop time-varying ?uid models for tandem networks withblocking.Beyondhavingtheirownintrinsicvalue,thesemathematicalmodelsare also limits of corresponding many-server stochastic systems. We begin by analyzing atwo-stationtandemnetworkwithageneraltime-varyingarrivalrate,a?nitewaiting roombeforethe?rststation,andnowaitingroombetweenthestations.Inthismodel, customers that are referred from the ?rst station to the second when the latter is saturated(blocked)areforcedtowaitinthe?rststationwhileoccupyingaserverthere. The ?nite waiting room before the ?rst station causes customer loss and, therefore, requires re?ection analysis. We then specialize our model to a single station (manyserver?uidlimitoftheGt/M/N/(N+H)queue),generalizeittokstationsintandem, and allow ?nite internal waiting rooms. Our models yield operational insights into network performance, speci?cally on the effects of line length, bottleneck location, waiting room size, and the interaction among these effects