Convergence and Optimal Buffer Sizing for Window Based AIMD Congestion Control

TL;DR

This paper analyzes the convergence behavior of AIMD congestion control with Drop Tail buffers and proposes an analytical framework for optimal buffer sizing to balance goodput and delay.

Contribution

It introduces a hybrid model showing convergence to cyclic behavior and develops a multi-criteria optimization for buffer size considering goodput and delay.

Findings

Hybrid model always converges to cyclic behavior

Optimal buffer size reduces with traffic aggregation

Simulation confirms analytical results

Abstract

We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that the hybrid model of the interaction between the AIMD congestion control and bottleneck router always converges to a cyclic behavior. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps of congestion window in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate the problem of the optimal router buffer size as a multi-criteria optimization problem, in which the Lagrange function corresponds to a linear combination of the average goodput and the average delay in the queue. The solution to the optimization problem provides further evidence that the buffer size should be reduced in the presence of traffic aggregation. Our analytical results are confirmed by simulations performed with Simulink and the NS simulator.