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Network Calculus Characterization of Congestion Control for Time-Varying Traffic

Harvinder Lehal, Natchanon Luangsomboon, Jörg Liebeherr

TL;DR

This work addresses congestion control under time-varying, bursty traffic in data centers by applying a modular network-calculus framework that can characterize both rate-based and window-based CCAs. It introduces a path-server model, models congestion events (ACKs, timeouts, retransmissions, ECN, PFC, RTT), and analyzes single- and multi-flow scenarios with coordinate-system shifts to maintain min-plus linearity within intervals. The paper demonstrates close alignment between model predictions and packet-level simulations, including a data-center case study with DCQCN and PFC, and provides algorithms for rate-based and window-based AIMD analyses as well as fairness proofs under FIFO. This approach offers a rigorous, scalable method to study CCA dynamics for intermittent bursts and has practical implications for designing and evaluating data-center congestion control protocols.

Abstract

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method. This is not suitable for studying congestion control of intermittent but bursty traffic sources. In this paper, we present a characterization of congestion control for arbitrary time-varying traffic that applies to rate-based as well as window-based congestion control. We leverage the capability of network calculus to precisely describe the input-output relationship at network elements for arbitrary source traffic. We show that our characterization can closely track the dynamics of even complex congestion control algorithms.

Network Calculus Characterization of Congestion Control for Time-Varying Traffic

TL;DR

This work addresses congestion control under time-varying, bursty traffic in data centers by applying a modular network-calculus framework that can characterize both rate-based and window-based CCAs. It introduces a path-server model, models congestion events (ACKs, timeouts, retransmissions, ECN, PFC, RTT), and analyzes single- and multi-flow scenarios with coordinate-system shifts to maintain min-plus linearity within intervals. The paper demonstrates close alignment between model predictions and packet-level simulations, including a data-center case study with DCQCN and PFC, and provides algorithms for rate-based and window-based AIMD analyses as well as fairness proofs under FIFO. This approach offers a rigorous, scalable method to study CCA dynamics for intermittent bursts and has practical implications for designing and evaluating data-center congestion control protocols.

Abstract

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method. This is not suitable for studying congestion control of intermittent but bursty traffic sources. In this paper, we present a characterization of congestion control for arbitrary time-varying traffic that applies to rate-based as well as window-based congestion control. We leverage the capability of network calculus to precisely describe the input-output relationship at network elements for arbitrary source traffic. We show that our characterization can closely track the dynamics of even complex congestion control algorithms.
Paper Structure (30 sections, 3 theorems, 35 equations, 8 figures, 1 table, 3 algorithms)

This paper contains 30 sections, 3 theorems, 35 equations, 8 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Network Calculus Background
  3. Network Calculus Model for Congestion Control
  4. Single Flow Model
  5. Modelling Congestion Events
  6. Acknowledgments
  7. Timeouts
  8. Retransmissions
  9. Explicit Congestion Notification (ECN)
  10. Priority Flow Control (PFC)
  11. Round-trip Time (RTT)
  12. Rate-Based Congestion Control
  13. Window-Based Congestion Control
  14. Example: TCP Vegas
  15. Multi-flow Analysis
  16. ...and 15 more sections

Key Result

Lemma 1

Given a path server with ${\mathcal{N}}$ flows that satisfies the FIFO property. For any subset $X\subseteq {\mathcal{N}}$ and any flow $i\in {\mathcal{N}}$, every time interval $[t', t]$ satisfies

Figures (8)

  • Figure 1: Path server model with congestion control.
  • Figure 2: Updating the rate-based traffic functions after a timeout event. (Arrival function $A(t)$ in gray, admitted arrival function $\hat{A}$ in blue, departure function $D(t)$ in red, timeout function $\hat{A}(t-\Delta R)$ in cyan, acknowledgement function $D(t-\Delta R)$ in orange).
  • Figure 3: Congestion window (CWND) of TCP Vegas.
  • Figure 4: Backlog produced by TCP Vegas with our traffic scenario.
  • Figure 5: Multi-flow model for congestion control.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Theorem 1