Some Modeling and Estimation Issues in Control of Heterogenous - PowerPoint PPT Presentation

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 Automatic Control 1

Overview Focus of our group: Network Link • Model based estimation. control control • Making wireless links friendlier to TCP. Automatic Control Estimation Congestion control 2

Model Based Estimation Window-based flow-control objective: w ≈ b · RTT • Estimation of round-trip time (RTT). Automatic Control • Estimation of available bandwidth ( b ). • Trade-off between noise reduction and tracking performance. • Model-based estimation. Systematic way to make that trade-off. 3

RTT Estimation Model: • Piecewise constant “average RTT” x k . • Occasional step changes due to rerouting, bottlenecks appearing. . . Automatic Control x k +1 = x k + δ k v k δ k ∈ { 0 , 1 } y k = x k + e k Measured RTT Proposed estimator: • Kalman filter to suppress noise. • Change detection to track δ k . 4

Evaluation of RTT Estimators Input: RTT samples KTH ↔ Caida, ≈ 20 hops, interval 30 ms. caida20040119ii.log: Round Trip Time caida20040119iii.log: Round Trip Time 0.21 0.4 Sample Sample srtt, α = 0.9 srtt, α = 0.9 0.35 CK filter CK filter 0.2 RTT [sec] RTT [sec] 0.3 0.19 0.25 0.2 0.18 Automatic Control 1230.5 1231 1231.5 1232 1232.5 1233 1233.5 1234 1234.5 1235 1235.5 1626 1626.2 1626.4 1626.6 1626.8 1627 1627.2 1627.4 1627.6 1627.8 Time [sec] Time [sec] 0.06 0.25 0.2 0.04 0.15 g t g t 0.1 0.02 0.05 0 0 1230.5 1231 1231.5 1232 1232.5 1233 1233.5 1234 1234.5 1235 1235.5 1626 1626.2 1626.4 1626.6 1626.8 1627 1627.2 1627.4 1627.6 1627.8 Time [sec] Time [sec] Bottom: Output from the change detection. 5

Bandwidth Estimation Measurements: ACK inter-arrival times ∆ k . Nm m b N = = Constant packet size m 1 � k ∆ k � k ∆ k N Model: ∆ k = b + e k , zero-mean noise e k . Use a low-pass filter: Automatic Control → ˆ m ∆ k − → Filter − → − b k · Alternative structure (used in TCP-Westwood): → ˆ m ∆ k − → − → Filter − b k · Results in bias independent of filter design. 6

Evaluation of Bandwidth Estimators Input: TCP simulation in ns-2 , 5 Mbps bottleneck. Available bandwidth estimation 25 westwood exponential on bw sample, α = 0.99 exponential on time sample, α = 0.99 20 Should filter before the non- Bandwidth [Mbps] linearity. 15 Automatic Control 10 → ˆ m ∆ k − → Filter − → − b k · 5 → ˆ m ∆ k − → − → Filter − b k · 0 0 5 10 15 20 25 30 Time [sec] At 10 ms: 1 Mbps cross-traffic in forward direction. At 20 ms: 1 Mbps cross-traffic in reverse direction. 7

Influence of Wireless Links on TCP ACK (4) P [%] 80.6 TCP Trans. Recv. TCP Network Power µ + 4 σ SIR (1) Block − 9.3 8.8 + error (2) 0.6 0.6 0.03 0.03 SIR ref 0 40 60 100 120 160 180 Delay [ms] Automatic Control PC ARQ RRQ (3) 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. 8

A Measure of TCP-friendliness Let X be the stochastic link delay. P TO ( X ) := P( X > E( X ) + 4 σ ( X )) P( Timeout ) for TCP • Uniform distribution: P TO = 0 . Automatic Control • Normal distribution: P TO ≈ 0 . 006% . • General distribution: P TO ≤ 6 . 25% . • Wireless link: P TO ≈ 0 . 7% . 9

Tweaking the delay Original: P( X = d i ) = p i . P [%] 80.6 Tweaked: P( ˜ X = d i + x i ) = p i . µ + 4 σ min E( ˜ X ) 8.8 9.3 0.6 0.6 0.03 0.03 Automatic Control 0 40 60 100 120 160 180 Delay [ms] P TO ( ˜ X ) < ǫ P [%] 80.6 x i ≥ 0 µ + 4 σ Decreased P TO , from 0.68% to 0.06%. 9.3 8.8 Mean delay increased by only 2.5 ms. 1.2 0.03 0.03 0 40 86 120 160 180 Delay [ms] Eliminates most spurious timeouts. 10

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. Automatic Control • 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. 11