Stability and weakly convergent approximations of queuing systems on a circle

Abstract

We rst consider a nongreedy queueing system on a circle We present a new and very simple proof of the stability of this system un der the appropriate condition based on the average travel times between customers Next we show that the same nongreedy system with a restricted number of customers converges weakly to this system when the restricted number goes to innity Finally we consider a polling network with nitely many service stations in which the server has a greedy service strategy Under the appropriate condition we give a new simple proof of the stability of this system