Title:
   On the Gap between the Stability of
     Fluid and Queueing Networks

Authors:
    J. G. "Jim" Dai (speaker)
    School of Industrial and Systems Engineering
      and School of Mathematics
    Georgia Institute of Technology
    Atlanta, GA 30332

    John Hasenbein
    Operations Research Group
    Department of Mechanical Engineering
    University of Texas at Austin

    John Vande Vate
    School of Industrial and Systems Engineering
    Georgia Institute of Technology
    Atlanta, GA 30332

Dai-Vande Vate (1997) showed that virtual station and push start
conditions characterize the global stability region for 2-station
multi-type fluid networks.  It is known that these conditions are
sufficient for the global stability of the corresponding queueing
networks, and the virtual station conditions are also 
necessary for the global stability of the queueing networks.

We present a 2-station 5-class reentrant queueing network that is
globally stable; yet its corresponding fluid model is not globally
stable. A variant of our network shows that the stability region under
a static buffer priority service discipline depends on the 
distributions of interarrival and service times, not just first
moments. Thus, fluid model can _never_ sharply detect the stability
region for the queueing network.