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

TL;DR

This paper introduces a fluid limit approach to analyze long-term flow rates in a stochastic multiclass queuing network with ingress discarding, demonstrating how threshold-based control can achieve target flow rates.

Contribution

The paper develops a fluid model framework for analyzing a rate control scheme in multiclass networks, showing how high thresholds ensure flow rates approach targets.

Findings

Flow rates can be made arbitrarily close to target rates with high thresholds.

Fluid model stability implies stochastic network performance convergence.

Application to a network switch demonstrates practical relevance.

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.