Updates on NADA: Stability Analysis and Impact of Feedback Intervals - - PowerPoint PPT Presentation

Updates on NADA: Stability Analysis and Impact of Feedback Intervals

draft-ietf-rmcat-nada-02

IETF-95 | Buenos Aires, Argentina | 2016-04-06 Xiaoqing Zhu, Rong Pan, Michael A. Ramalho, Sergio Mena de la Cruz, Paul Jones, Jiantao Fu, Stefano D’Aronco, and Charles Ganzhorn

1

Outline

• Update on draft -02
• Stability analysis of NADA feedback control loop
• Numerical results on NADA with varying feedback intervals
• Simulation results on NADA with varying feedback intervals
• Summary and next steps

2

Changes in Draft -02

• No algorithm changes
• Added a section on feedback requirements of NADA in Sec. 5.3
• Addressed review comments from Stefan and Zahed (Thanks!)
• Minor adjustment in notations, fixed various errors and typos.

3

Outline

• Update on draft -02
• Stability analysis of NADA feedback control loop
• Numerical results on NADA with varying feedback intervals
• Simulation results on NADA with varying feedback intervals
• Summary and next steps

4

Simplifying Assumptions for Stability Analysis

• Considers only gradual rate update mode, w/o packet losses or

marking: x_curr = d_queue

• Ignores effect of 15-tap minimum filtering
• Rate update equation reduces to (see Eq(5)-(7) in draft):

ri = ri−1 − κ∆ τ xi − xo τ ri−1 − κη xi − xi−1 τ ri−1

xo = PRIORMAX ro xref ri − ri−1 ∆ = −κ τ [xi − xo τ + η xi − xi−1 ∆ ]ri−1

5

ro = C

Feedback Control Loop in Laplace Transform

1 sC

e−sRT T

queuing delay

ro xo 1 + ηsτ 1 +

τ κxo sτ

δx

delayed feedback gradual rate update

X

i −

ro = PRIOxref xo Rmax

System at equilibrium: For single flow:

6

Open Loop Transfer Function

G(s) = −ro C 1 + ηsτ 1 +

τ κxo sτ

e−sRT T sxo

G(s) ≈ −ro C RTT xo G(s) ≈ −κη ro C RTT τ e−sRT T sRTT

At low frequency, At high frequency, s → 0 Bandwidth sharing proportional to Guarantees stability for κη RTT τ < π 2 ητ >> 1

and

s → j∞ PRIORmax

7

Outline

• Update on draft -02
• Stability analysis of NADA feedback control loop
• Numerical results on NADA with varying feedback intervals
• Simulation results on NADA with varying feedback intervals
• Open Issues and next steps

8

Bode Diagram with Gain/Phase Margins

9

propagation delay = 50ms bottleneck BW = 1Mbps feedback interval @ 100ms feedback interval @ 1s

Bode Diagram with Gain/Phase Margins

10

feedback interval @ 100ms feedback interval @ 1s propagation delay = 50ms bottleneck BW = 1Mbps

Step Response of Closed-Loop System

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propagation delay = 50ms bottleneck BW = 1Mbps

Step Response with Feedback Interval @ 100ms

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propagation delay = 50ms bottleneck BW = 1Mbps

Step Response with Feedback Interval @ 200ms

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propagation delay = 50ms bottleneck BW = 1Mbps

Step Response with Feedback Interval @ 500ms

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propagation delay = 50ms bottleneck BW = 1Mbps

Settling Time vs. Feedback Interval

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propagation delay = 50ms

Outline

• Update on draft -02
• Stability analysis of NADA feedback control loop
• Numerical results on NADA with varying feedback intervals
• Simulation results on NADA with varying feedback intervals
• Open Issues and next steps

16

Propagation Delay @ 50ms, Feedback Interval = 20ms

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NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 50ms

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NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 100ms

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NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 200ms

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NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 500ms

21

NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 1s

22

NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 50ms, Feedback Interval = 2s

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instable instable NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 150ms, Feedback Interval = 20ms

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NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 150ms, Feedback Interval = 200ms

25

NS2: physical link rate change NS3: time-varying background UDP flow

Propagation Delay @ 150ms, Feedback Interval = 2s

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instable instable NS2: physical link rate change NS3: time-varying background UDP flow

Convergence Time vs. Feedback Interval

27

NS2: Transition after t=120s

Overhead ~ 1.6 % @ 1Mbps

NS3: Transition after t=120s

Summary and Next Steps

• Guaranteed stability of NADA feedback control loop for RTT < 500ms
• Qualitatively matching results from numerical analysis and simulation results:
• Remains stable for sub-second feedback intervals
• System response slows down with increasing feedback intervals
• Recommended feedback interval at 100ms — tradeoff between overhead and

response speed

• Next steps:
• Investigate different convergence behavior with different BW changing mechanisms;
• Study system stability with varying parameter choice and network settings

28

Backup Slides

29

Derivation of Laplace Transfer Function for Gradual Rate Update

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δx = xi − xo, δr = ri − ro

Consider small perturbation around equilibrium:

δ ˙ r = −κ τ [δxro τ + xoδr τ + ηδ ˙ xro] κxo τ 2 (R(s) + τ 2 κxo sR(s)) = −κro τ 2 (X(s) + ητsX(s)) R(s) X(s) = − ro xo 1 + ητs 1 +

τ κxo sτ

In Laplace domain:

κxo τ 2 δr + δ ˙ r = −κro τ [δx τ + ητδ ˙ x]