/i Dewey Working Paper Alfred P. Sloan School of Management Some Badly Behaved Closed Queueing Networks Some Badly Behaved Closed Queueing Networks Received Some Badly Behaved Closed Queueing Networks

We study several variations of a multiclass closed queueinp network model, all closely related to the open priority network of Lu and Kumar. Foi each of our examples it is shown that, as the population size n —• oo, the long-run utilization rate of each server approaches a limit strictly less than one. Thus no "bottleneck station" emerges in the heavy traffic limit. This is analogous to the "bad behavio' ' of open network examples developed by Bramson and by Lu and Kumar, among others, in which queue sizes grow without bound even though each service static^.; has a traffic intensity parameter less than one. Two of the three examples considered here have preemptive-resume priority service disciplines at each station, as in the Lu-Kumar open network example, and one has FIFO service at each station, as in Bramson's open network examples.