Fluid limits to analyze long-term flow rates of a stochastic network with ingress discarding

Abstract

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.