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A Control-Theoretic Perspective on BBR/CUBIC Congestion-Control Competition

Simon Scherrer, Adrian Perrig, Stefan Schmid

TL;DR

The paper tackles the fairness problem in BBR/CUBIC congestion-control competition by integrating a dynamic fluid model with control-theoretic analysis to obtain executable conditions for oscillation and provable fairness bounds. It shows that steady-state models fail to capture the transient oscillations that dominate fairness in practice, while fluid simulations alone lack general analytical guarantees. By deriving the equilibrium of a joint BBR/CUBIC fluid model, establishing short-term and long-term dynamics, and applying Lyapunov/center-manifold techniques, the authors obtain sufficient conditions for oscillation, quantify worst-case and non-pessimal fairness bounds, and evaluate countermeasures such as smoothed RTT estimates and newer BBR versions. The work provides a rigorous framework to understand, predict, and mitigate oscillations, informing the design of more stable and fair congestion-control algorithms in heterogeneous Internet deployments.

Abstract

To understand the fairness properties of the BBR congestion-control algorithm (CCA), previous research has analyzed BBR behavior with a variety of models. However, previous model-based work suffers from a trade-off between accuracy and interpretability: While dynamic fluid models generate highly accurate predictions through simulation, the causes of their predictions cannot be easily understood. In contrast, steady-state models predict CCA behavior in a manner that is intuitively understandable, but often less accurate. This trade-off is especially consequential when analyzing the competition between BBR and traditional loss-based CCAs, as this competition often suffers from instability, i.e., sending-rate oscillation. Steady-state models cannot predict this instability at all, and fluid-model simulation cannot yield analytical results regarding preconditions and severity of the oscillation. To overcome this trade-off, we extend the recent dynamic fluid model of BBR by means of control theory. Based on this control-theoretic analysis, we derive quantitative conditions for BBR/CUBIC oscillation, identify network settings that are susceptible to instability, and find that these conditions are frequently satisfied by practical networks. Our analysis illuminates the fairness implications of BBR/CUBIC oscillation, namely by deriving and experimentally validating fairness bounds that reflect the extreme rate distributions during oscillation. In summary, our analysis shows that BBR/CUBIC oscillation is frequent and harms BBR fairness, but can be remedied by means of our control-theoretic framework.

A Control-Theoretic Perspective on BBR/CUBIC Congestion-Control Competition

TL;DR

The paper tackles the fairness problem in BBR/CUBIC congestion-control competition by integrating a dynamic fluid model with control-theoretic analysis to obtain executable conditions for oscillation and provable fairness bounds. It shows that steady-state models fail to capture the transient oscillations that dominate fairness in practice, while fluid simulations alone lack general analytical guarantees. By deriving the equilibrium of a joint BBR/CUBIC fluid model, establishing short-term and long-term dynamics, and applying Lyapunov/center-manifold techniques, the authors obtain sufficient conditions for oscillation, quantify worst-case and non-pessimal fairness bounds, and evaluate countermeasures such as smoothed RTT estimates and newer BBR versions. The work provides a rigorous framework to understand, predict, and mitigate oscillations, informing the design of more stable and fair congestion-control algorithms in heterogeneous Internet deployments.

Abstract

To understand the fairness properties of the BBR congestion-control algorithm (CCA), previous research has analyzed BBR behavior with a variety of models. However, previous model-based work suffers from a trade-off between accuracy and interpretability: While dynamic fluid models generate highly accurate predictions through simulation, the causes of their predictions cannot be easily understood. In contrast, steady-state models predict CCA behavior in a manner that is intuitively understandable, but often less accurate. This trade-off is especially consequential when analyzing the competition between BBR and traditional loss-based CCAs, as this competition often suffers from instability, i.e., sending-rate oscillation. Steady-state models cannot predict this instability at all, and fluid-model simulation cannot yield analytical results regarding preconditions and severity of the oscillation. To overcome this trade-off, we extend the recent dynamic fluid model of BBR by means of control theory. Based on this control-theoretic analysis, we derive quantitative conditions for BBR/CUBIC oscillation, identify network settings that are susceptible to instability, and find that these conditions are frequently satisfied by practical networks. Our analysis illuminates the fairness implications of BBR/CUBIC oscillation, namely by deriving and experimentally validating fairness bounds that reflect the extreme rate distributions during oscillation. In summary, our analysis shows that BBR/CUBIC oscillation is frequent and harms BBR fairness, but can be remedied by means of our control-theoretic framework.
Paper Structure (97 sections, 7 theorems, 110 equations, 20 figures, 1 table)

This paper contains 97 sections, 7 theorems, 110 equations, 20 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. BBRv1
  4. Bandwidth probing
  5. RTT probing
  6. CUBIC
  7. Motivation
  8. Comparison of Models
  9. Experiment Setting
  10. Results
  11. The Relevance of Transient Behavior
  12. Conclusion
  13. Fluid-Model Equilibrium
  14. Relevance
  15. Fluid-Model Basics
  16. ...and 82 more sections

Key Result

Lemma 1

CUBIC Equilibrium Conditions:

Figures (20)

  • Figure 1: BBR.
  • Figure 2: CUBIC.
  • Figure 3: Model evaluation for 10 flows (The dotted gray line indicates the proportional share of BBR flows under perfect per-flow fairness).
  • Figure 4: BBR/CUBIC competition over time for different CCA combinations (Aggregate capacity shares).
  • Figure 5: Basic mechanism of BBR/CUBIC oscillation.
  • ...and 15 more figures

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • proof
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4