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 Xiaoqing Zhu, Rong Pan, Michael A. Ramalho, Sergio Mena de la Cruz, Paul Jones, Jiantao Fu, Stefano D’Aronco, and Charles Ganzhorn IETF-95 | Buenos Aires, Argentina | 2016-04-06 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): x o = PRIOR MAX x ref r o r i = r i − 1 − κ ∆ x i − x o r i − 1 − κη x i − x i − 1 r i − 1 τ τ τ r i − r i − 1 = − κ τ [ x i − x o + η x i − x i − 1 ] r i − 1 ∆ ∆ τ 5

Feedback Control Loop in Laplace Transform queuing delay δ x 1 X sC i − System at equilibrium: delayed r o = PRIOx ref e − sRT T R max feedback x o For single flow: 1 + η s τ r o τ r o = C 1 + x o κ x o s τ gradual rate update 6

Open Loop Transfer Function e − sRT T 1 + η s τ G ( s ) = − r o 1 + C κ x o s τ τ sx o At low frequency, s → 0 s → j ∞ At high frequency, e − sRT T G ( s ) ≈ − κη r o RTT G ( s ) ≈ − r o RTT C sRTT τ C x o Guarantees stability for Bandwidth sharing proportional to PRIOR max κη RTT < π ητ >> 1 and 2 τ 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 propagation delay = 50ms bottleneck BW = 1Mbps feedback interval feedback interval @ 100ms @ 1s 9

Bode Diagram with Gain/Phase Margins propagation delay = 50ms bottleneck BW = 1Mbps feedback interval feedback interval @ 100ms @ 1s 10

Step Response of Closed-Loop System propagation delay = 50ms bottleneck BW = 1Mbps 11

Step Response with Feedback Interval @ 100ms propagation delay = 50ms bottleneck BW = 1Mbps 12

Step Response with Feedback Interval @ 200ms propagation delay = 50ms bottleneck BW = 1Mbps 13

Step Response with Feedback Interval @ 500ms propagation delay = 50ms bottleneck BW = 1Mbps 14

Settling Time vs. Feedback Interval propagation delay = 50ms 15

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 NS2: physical link rate change NS3: time-varying background UDP flow 17

Propagation Delay @ 50ms, Feedback Interval = 50ms NS2: physical link rate change NS3: time-varying background UDP flow 18

Propagation Delay @ 50ms, Feedback Interval = 100ms NS2: physical link rate change NS3: time-varying background UDP flow 19

Propagation Delay @ 50ms, Feedback Interval = 200ms NS2: physical link rate change NS3: time-varying background UDP flow 20

Propagation Delay @ 50ms, Feedback Interval = 500ms NS2: physical link rate change NS3: time-varying background UDP flow 21

Propagation Delay @ 50ms, Feedback Interval = 1s NS2: physical link rate change NS3: time-varying background UDP flow 22

Propagation Delay @ 50ms, Feedback Interval = 2s NS2: physical link rate change NS3: time-varying background UDP flow instable instable 23

Propagation Delay @ 150ms, Feedback Interval = 20ms NS2: physical link rate change NS3: time-varying background UDP flow 24

Propagation Delay @ 150ms, Feedback Interval = 200ms NS2: physical link rate change NS3: time-varying background UDP flow 25

Propagation Delay @ 150ms, Feedback Interval = 2s NS2: physical link rate change NS3: time-varying background UDP flow instable instable 26

Convergence Time vs. Feedback Interval NS2: Transition after t=120s NS3: Transition after t=120s Overhead ~ 1.6 % @ 1Mbps 27

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 δ x = x i − x o , δ r = r i − r o Consider small perturbation around equilibrium: r = − κ τ [ δ xr o + x o δ r κ x o r = − κ r o τ [ δ x δ ˙ + ηδ ˙ xr o ] τ 2 δ r + δ ˙ τ + ητδ ˙ x ] τ τ In Laplace domain: R ( s ) 1 + ητ s X ( s ) = − r o τ 2 ( R ( s ) + τ 2 κ x o sR ( s )) = − κ r o τ 2 ( X ( s ) + ητ sX ( s )) 1 + τ x o κ x o s τ κ x o 30