Muticlass queueing networks model semiconductor wafer fabrication lines. For a network operating under a non-idling operational policy, it is important to determine if the network is stable under a given offered load. Fluid models have become a primary tool to study the stability of such a network.
We present a queueing network example whose stability region depends on the distribution of inter-arrival and service times. The network is a 2-station re-entrant line operating under a static buffer priority service policy. When the distribution is exponential, we prove that the total number of jobs in the network goes to infinity as time goes to infinity. When the distribution is deterministic, we prove that the system goes to a limit cycle from any initial state. When the distribution is uniform, simulations show that the network can be stable or unstable, depending on the spread of the distribution.
The traditional fluid model of a queueing network is defined through a set of equations that employ the means of inter-arrival and service time distributions. Our example shows that such a fluid model cannot be used to determine the stability of our queueing network.
The talk is based on joint works with John Hasenbein at University of Texas at Austin and John Vande Vate at Georgia Tech.