Deficit Round-Robin: A Second Network Calculus Analysis

TL;DR

This paper advances the analysis of Deficit Round-Robin scheduling by deriving improved worst-case delay bounds using network calculus, including non-convex and iterative methods, surpassing previous bounds especially under constrained interfering traffic.

Contribution

It introduces a non-convex strict service curve for DRR and an iterative method to refine delay bounds considering arrival constraints, improving upon prior work.

Findings

Derived a non-convex strict service curve for DRR.

Developed an iterative method to improve delay bounds.

Provided the best-known worst-case delay bounds for DRR.

Abstract

Deficit Round-Robin (DRR) is a widespread scheduling algorithm that provides fair queueing with variable-length packets. Bounds on worst-case delays for DRR were found by Boyer et al., who used a rigorous network calculus approach and characterized the service obtained by one flow of interest by means of a convex strict service curve. These bounds do not make any assumptions on the interfering traffic hence are pessimistic when the interfering traffic is constrained by some arrival curves. For such cases, two improvements were proposed. The former, by Soni et al., uses a correction term derived from a semi-rigorous heuristic; unfortunately, these bounds are incorrect, as we show by exhibiting a counter-example. The latter, by Bouillard, rigorously derive convex strict service curves for DRR that account for the arrival curve constraints of the interfering traffic. In this paper, we improve on these results in two ways. First, we derive a non-convex strict service curve for DRR that improves on Boyer et al. when there is no arrival constraint on the interfering traffic. Second, we provide an iterative method to improve any strict service curve (including Bouillard's) when there are arrival constraints for the interfering traffic. As of today, our results provide the best-known worst-case delay bounds for DRR. They are obtained by using the method of the pseudo-inverse.