The Last Buuer First Serve Priority Policy Is Stable for Stochastic Re{entrant Lines

In this paper, the stability of the Last Buuer First Serve (LBFS) buuer priority policy, in the sense of positive Harris recurrence, is shown under fairly general assumptions on the interarrival and service time distributions, whenever the nominal load at each machine is less than one. This is done by rst describing the uid limits, and then showing that the uid limits empty in nite time from all suitable initial conditions, which Dai 1] has recently shown to be suucient for positive Harris recurrence.