[Paper Review] Convergence and Optimal Buffer Sizing for Window Based AIMD Congestion Control

Konstantin Avrachenkov, Urtzi Ayesta+1 more|ArXiv.org|Mar 13, 2007

Network Traffic and Congestion Control16 references3 citations

TL;DR

This paper analyzes window-based AIMD congestion control in conjunction with a Drop Tail bottleneck router using a deterministic hybrid model, proving convergence to cyclic behavior and deriving conditions for single-packet-loss cycles. It formulates optimal buffer sizing as a multi-criteria optimization problem balancing goodput and queue delay, showing that buffer size should be reduced under traffic aggregation, with analytical results confirmed by Simulink and NS simulations.

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.

Motivation & Objective

• To analyze the convergence behavior of window-based AIMD congestion control interacting with a bottleneck router using a deterministic hybrid model.
• To characterize the cyclic behavior of the system and derive necessary and sufficient conditions for the absence of multiple packet losses in a single cycle.
• To formulate the optimal buffer size selection as a multi-criteria optimization problem balancing average goodput and average queue delay.
• To provide analytical evidence that buffer size should be reduced in the presence of traffic aggregation, challenging traditional BDP-based rules.

Proposed method

• Models the interaction between AIMD congestion control and a Drop Tail router as a deterministic hybrid system, capturing both continuous window growth and discrete window reductions upon loss.
• Uses implicit differentiation and asymptotic analysis to study the behavior of buffer size and window dynamics, particularly in the limit of small or large buffer sizes.
• Derives conditions under which the system avoids multiple losses per cycle by analyzing the evolution of the congestion window and buffer occupancy.
• Applies Lagrangian relaxation to the multi-criteria optimization problem, expressing the objective as a linear combination of average goodput and average queue delay.
• Performs asymptotic analysis of the system’s behavior as the buffer size approaches zero or infinity, deriving limiting expressions for key performance metrics.
• Validates analytical findings through simulations using Simulink and the NS simulator, confirming theoretical predictions.

Experimental results

Research questions

• RQ1 Does the hybrid model of AIMD congestion control and a Drop Tail router always converge to a cyclic behavior, and what are the characteristics of these cycles?
• RQ2 What are the necessary and sufficient conditions for the absence of multiple packet losses within a single cycle in the AIMD window evolution?
• RQ3 How can the optimal buffer size be selected to balance competing performance metrics such as goodput and queue delay?
• RQ4 How does traffic aggregation influence the optimal buffer size, and does it contradict the traditional BDP-based rule of thumb?
• RQ5 To what extent do analytical predictions on buffer size optimization align with simulation results using Simulink and NS?

Key findings

• The system governed by AIMD and a Drop Tail router always converges to a cyclic behavior, with two distinct limiting regimes possible depending on initial conditions.
• Necessary and sufficient conditions for the absence of multiple losses per cycle are derived, improving upon prior sufficient-only conditions.
• The optimal buffer size problem is formulated as a multi-criteria optimization with a Lagrangian combining average goodput and average queue delay.
• The solution to the optimization problem provides strong evidence that buffer size should be reduced when traffic aggregation is present, contradicting the BDP rule.
• As the buffer size approaches zero, the derivative of the buffer occupancy with respect to the window size tends to zero from below, indicating diminishing returns on buffer expansion.
• Simulation results using Simulink and NS confirm the analytical predictions, particularly the convergence behavior and the optimal buffer size trade-offs.