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On the Benefits of Traffic "Reprofiling" -- The Multiple Hops Case -- Part I

Jiaming Qiu, Jiayi Son, Roch Guerin, Henry Sariowan

TL;DR

The paper addresses meeting hard end-to-end delay bounds under deterministic traffic profiles by exploring traffic reprofiling at ingress. It develops a tractable two-part service-curve model (DESC plus 2SRC) within SCED scheduling and formulates an optimization (OPT) to minimize total bandwidth, showing that an optimal reprofiler can be realized with a per-flow delay D and a minimum-reprofiler 2SRC. It proposes an exact NLP-based solution (OPT−) and a scalable Greedy reprofiling algorithm, demonstrating via TSN-like and inter-datacenter evaluations that reprofiling yields significant bandwidth savings and allows more flows to be accommodated, at the cost of upfront reprofiling delay. The results reveal a fundamental trade-off between smoothing benefits and scheduling flexibility, and show that reprofiling can improve efficiency even with strong schedulers, providing a practical approach for predictable networks. The work lays a foundation for extending reprofiling to simpler schedulers, statistical guarantees, and broader deployment scenarios.

Abstract

This paper considers networks where user traffic is regulated through deterministic traffic profiles, e.g., token buckets, and requires hard delay bounds. The network's goal is to minimize the resources it needs to meet those bounds. The paper explores how reprofiling, i.e., proactively modifying how user traffic enters the network, can be of benefit. Reprofiling produces ``smoother'' flows but introduces an up-front access delay that forces tighter network delays. The paper explores this trade-off and demonstrates that, unlike what holds in the single-hop case, reprofiling can be of benefit} even when ``optimal'' schedulers are available at each hop.

On the Benefits of Traffic "Reprofiling" -- The Multiple Hops Case -- Part I

TL;DR

The paper addresses meeting hard end-to-end delay bounds under deterministic traffic profiles by exploring traffic reprofiling at ingress. It develops a tractable two-part service-curve model (DESC plus 2SRC) within SCED scheduling and formulates an optimization (OPT) to minimize total bandwidth, showing that an optimal reprofiler can be realized with a per-flow delay D and a minimum-reprofiler 2SRC. It proposes an exact NLP-based solution (OPT−) and a scalable Greedy reprofiling algorithm, demonstrating via TSN-like and inter-datacenter evaluations that reprofiling yields significant bandwidth savings and allows more flows to be accommodated, at the cost of upfront reprofiling delay. The results reveal a fundamental trade-off between smoothing benefits and scheduling flexibility, and show that reprofiling can improve efficiency even with strong schedulers, providing a practical approach for predictable networks. The work lays a foundation for extending reprofiling to simpler schedulers, statistical guarantees, and broader deployment scenarios.

Abstract

This paper considers networks where user traffic is regulated through deterministic traffic profiles, e.g., token buckets, and requires hard delay bounds. The network's goal is to minimize the resources it needs to meet those bounds. The paper explores how reprofiling, i.e., proactively modifying how user traffic enters the network, can be of benefit. Reprofiling produces ``smoother'' flows but introduces an up-front access delay that forces tighter network delays. The paper explores this trade-off and demonstrates that, unlike what holds in the single-hop case, reprofiling can be of benefit} even when ``optimal'' schedulers are available at each hop.
Paper Structure (72 sections, 16 theorems, 67 equations, 41 figures, 2 tables, 2 algorithms)

This paper contains 72 sections, 16 theorems, 67 equations, 41 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Network Calculus
  4. Arrival Curves
  5. Service Curves
  6. Delay and Buffer Bounds
  7. Traffic Shaping and Greedy Shaper
  8. SCED Scheduling Policy
  9. Two-Slope Rate-Latency Service Curve
  10. Delay Element Service Curve
  11. Two-Slope Reprofiling Curve
  12. Problem Formulation
  13. Problem Setting
  14. Optimization Framework
  15. Inputs
  16. ...and 57 more sections

Key Result

Lemma 1

Given a set of service curves $\beta_i(t), i=1,\ldots,m$, any scheduling mechanism requires a link bandwidth of at least: to guarantee those service curves. SCED realizes those service curves with a link bandwidth of exactly $C^*$.

Figures (41)

  • Figure 1: 2SRLSC and its two components.
  • Figure 2: Optimal reprofiler given reprofiling delay.
  • Figure 3: Optimal reprofiler given reprofiling delay.
  • Figure 4: Network with $m$ flows and $n$ links.
  • Figure 5: Overview of Greedy.
  • ...and 36 more figures

Theorems & Definitions (21)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • Lemma 8
  • Lemma 9
  • Lemma 10
  • ...and 11 more