  We study a simple rate control scheme for a multiclass queuing network for
which customers are partitioned into distinct flows that are queued separately
at each station. The control scheme discards customers that arrive to the
network ingress whenever any one of the flow's queues throughout the network
holds more than a specified threshold number of customers. We prove that if the
state of a corresponding fluid model tends to a set where the flow rates are
equal to target rates, then there exist sufficiently high thresholds that make
the long-term average flow rates of the stochastic network arbitrarily close to
these target rates. The same techniques could be used to study other control
schemes. To illustrate the application of our results, we analyze a network
resembling a 2-input, 2-output communications network switch.
