Fluid limits to analyze long-term flow rates of a stochastic network with ingress discarding (Q363845)

The main purpose of the paper is to help to predict the behaviour of systems by means of a fluid model in order to avoid the loss of customers. One considers a multiclass queueing network where the customers are partitioned into \(F\) distinct flows. The customers of a flow arrive according to an independent renewal process and pass a fixed acyclic sequence of stations. Each flow has a weight and each station serves a flow in proportion to its weight using the round-robin or a similar queueing discipline. If any of a flow's queues exceed a threshold \(h\), the flow's customers are discarded at the network ingress. The paper gives a methodology to prove that the long-term average flow rates in this case can be made arbitrarily close to the prognosis of a fluid model if the discarding thresholds are high enough.