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Automatic Control

Some Modeling and Estimation Issues in Control of Heterogenous Networks

Krister Jacobsson, Niels Möller, Karl Henrik Johansson and Håkan Hjalmarsson Department of Signals, Sensors and Systems, KTH

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Overview

Congestion control Estimation Network control Link control Focus of our group:

• Model based estimation.
• Making

wireless links friendlier to TCP.

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Model Based Estimation

Window-based flow-control objective: w ≈ b · RTT

• Estimation of round-trip time (RTT).
• Estimation of available bandwidth (b).
• Trade-off between noise reduction and tracking performance.
• Model-based estimation. Systematic way to make that trade-off.

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RTT Estimation

Model:

• Piecewise constant “average RTT” xk.
• Occasional step changes due to rerouting, bottlenecks
• appearing. . .

xk+1 = xk + δkvk δk ∈ {0, 1} yk = xk + ek Measured RTT Proposed estimator:

• Kalman filter to suppress noise.
• Change detection to track δk.

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Evaluation of RTT Estimators

Input: RTT samples KTH ↔ Caida, ≈ 20 hops, interval 30 ms.

1230.5 1231 1231.5 1232 1232.5 1233 1233.5 1234 1234.5 1235 1235.5 0.18 0.19 0.2 0.21

caida20040119ii.log: Round Trip Time

Time [sec] RTT [sec] 1230.5 1231 1231.5 1232 1232.5 1233 1233.5 1234 1234.5 1235 1235.5 0.02 0.04 0.06 Time [sec] gt Sample srtt, α = 0.9 CK filter 1626 1626.2 1626.4 1626.6 1626.8 1627 1627.2 1627.4 1627.6 1627.8 0.2 0.25 0.3 0.35 0.4

caida20040119iii.log: Round Trip Time

Time [sec] RTT [sec] 1626 1626.2 1626.4 1626.6 1626.8 1627 1627.2 1627.4 1627.6 1627.8 0.05 0.1 0.15 0.2 0.25 Time [sec] gt Sample srtt, α = 0.9 CK filter

Bottom: Output from the change detection.

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Bandwidth Estimation

Measurements: ACK inter-arrival times ∆k. bN = Nm

• k ∆k

= m

1 N

• k ∆k

Constant packet size m Model: ∆k = b + ek, zero-mean noise ek. Use a low-pass filter: ∆k − → Filter − →

m ·

− → ˆ bk Alternative structure (used in TCP-Westwood): ∆k − →

m ·

− → Filter − → ˆ bk Results in bias independent of filter design.

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Evaluation of Bandwidth Estimators

Input: TCP simulation in ns-2, 5 Mbps bottleneck.

5 10 15 20 25 30 5 10 15 20 25

Available bandwidth estimation Time [sec] Bandwidth [Mbps] westwood exponential on bw sample, α = 0.99 exponential on time sample, α = 0.99

Should filter before the non- linearity. ∆k − → Filter − →

m ·

− → ˆ bk ∆k − →

m ·

− → Filter − → ˆ bk At 10 ms: 1 Mbps cross-traffic in forward direction. At 20 ms: 1 Mbps cross-traffic in reverse direction.

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Influence of Wireless Links on TCP

PC SIRref + Power Trans. Recv. SIR (1) − Block error (2) ARQ RRQ (3) Network TCP TCP ACK (4) P [%] Delay [ms] 80.6 8.8 40 9.3 60 0.6 100 0.6 120 0.03 160 0.03 180 µ + 4σ

Without link-layer retransmissions: Constant delay, high loss-rate. With link-layer retransmissions: Random delay, small loss-rate. Link delay distribution influences TCP. Spurious timeouts.

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A Measure of TCP-friendliness

Let X be the stochastic link delay. PTO(X) := P(X > E(X) + 4σ(X)) P(Timeout) for TCP

• Uniform distribution: PTO = 0.
• Normal distribution: PTO ≈ 0.006%.
• General distribution: PTO ≤ 6.25%.
• Wireless link: PTO ≈ 0.7%.

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Tweaking the delay

Original: P(X = di) = pi. Tweaked: P( ˜ X = di + xi) = pi. min E( ˜ X) PTO( ˜ X) < ǫ xi ≥ 0 Decreased PTO, from 0.68% to 0.06%. Mean delay increased by only 2.5 ms. Eliminates most spurious timeouts.

P [%] Delay [ms] 80.6 8.8 40 9.3 60 0.6 100 0.6 120 0.03 160 0.03 180 µ + 4σ P [%] Delay [ms] 80.6 8.8 40 9.3 86 1.2 120 0.03 160 0.03 180 µ + 4σ

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Conclusions

• RTT estimation: Promising model based approach.
• Bandwidth estimation: Average inter-arrival times, not

“bandwidth samples”.

• Artificial delays at the link-layer improve TCP performance.
• For wireless links: Use engineering freedom in the link layer.

Vision: Systematic design of network control mechanisms:

• End-to-end congestion control.
• Network-layer control in intermediate routers.
• Link-layer control loops.

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