A RED function design targeting link utilization and stable queue size behavior

In this article we introduce a derivation method for the Random Early Detection (RED) drop function, drawing on heuristics and control theory. This way the negative effects experienced by deploying the original linear RED drop probability function are improved so that link under-utilization and heavy oscillations are avoided and the function is applicable to a wide load range. As it is impossible to include all of these requirements in one approach, we show two separate approaches and combine them at the end.The first approach aims at avoiding link under-utilization and is achieved heuristically. Therefore we provide a few examples from simulations to illustrate that the original linear RED drop function fails to avoid under-utilization and is not applicable to a wide load range. We use these examples to define conditions a proper drop function has to meet in order for under-utilization to be avoided. Bearing these conditions in mind, we propose a heuristic approach, where even a class of non-linear drop functions originates, with, apart from the usual RED parameters, one parameter free to define. Simple simulations show that such a non-linearity in the drop function should be preferred concerning the metric of under-utilization.According to the second approach the drop function is derived analytically based on the condition to achieve system stability, i.e. to avoid heavy oscillations. Here, we use a mathematical model for the TCP window queue size behavior of a router operating with TCP and apply control theory for the derivation process. The term stability refers to the oscillation amplitude of the steady state queue size, whereas heavy oscillations indicate an unstable state. The analytically derived function is polynomial and can be approximated by using the findings of the first approach. The derived function thus avoids both under-utilization and heavy oscillations. The applicability to an arbitrary load range is included automatically in the derivation process. The impacts of parameter variations are investigated. Simulative comparisons of the derived function with ARED and with GRED (parameter variation included) with both FTP and Web traffic clearly attest to the advantage of the derivation process and to an improvement in RED performance, especially in metrics, such as link utilization, forced drops and queue size variation.