1. 1 A State Feedback Control Approach to Stabilizing Queues for ECN- Enabled TCP Connections Yuan Gao and Jennifer Hou IEEE INFOCOM 2003, San Francisco, April 2003 Presented by Bob Kinicki

2. Advanced Computer Networks : (SFC) State Feedback Controller 2 Outline Introduction Enhanced TCP model Analyze the Interaction between TCP and AQM Details of the State Feedback Controlled AQM Related Work Simulations Conclusions

3. Advanced Computer Networks : (SFC) State Feedback Controller 3 Introduction Authors put their research in the category where network behavior is modeled with AQM routers as controllers and TCP traffic as plants in an automatic control theory scheme. Analytic models can then be used to provide insight on designing better AQM controllers.

4. Advanced Computer Networks : (SFC) State Feedback Controller 4 Introduction Generally, these models describe the main dynamics of TCP in congestion avoidance phase where AIMD is used to adjust cwnd. Rate of change in size of cwnd is expressed as: (1-p)/ τ – ω 2 p/ 2 τ where ω current cwnd size and τ is the round-trip time (RTT).

5. Advanced Computer Networks : (SFC) State Feedback Controller 5 Introduction They claim other models only model gradual decrease in ω 2 p/ 2 instead of sudden halving of cwnd. Their model is more realistic in that cwnd decreases faster. Paper analyzes the stability of its linearized model with the use of state feedback control theory. Hence their AQM controller is called the state feedback controller (SFC).

6. Advanced Computer Networks : (SFC) State Feedback Controller 6 Outline Introduction Enhanced TCP model Analyze the Interaction between TCP and AQM Details of the State Feedback Controlled AQM Related Work Simulations Conclusions

7. Advanced Computer Networks : (SFC) State Feedback Controller 7 Enhanced TCP model Assumptions (A1) TCP connections only operate in congestion avoidance phase. (A2) The change in packet dropping/marking probability is insignificant in one RTT. (A3) All packets are marked independently.

8. Advanced Computer Networks : (SFC) State Feedback Controller 8 Enhanced TCP model Big deal claim :: the expected cwnd change is calculated over one RTT and not over the interval between two ACKs. Namely, E (Δ ω) / τ is used as the cwnd rate change.

9. Advanced Computer Networks : (SFC) State Feedback Controller 9 Enhanced TCP model TCP behavior is modeled in terms of “cycles” that are approximately one RTT to yield equation 1 E (Δ ω) = fcn (ω, ω’, b, p) [1] where b allows for modeling of delayed ACKs ω’ is the size of cwnd one RTT in past.

10. Advanced Computer Networks : (SFC) State Feedback Controller 10 Enhanced TCP model Using the assumption, p is small and that ωp << 1, yields equation 4: d E(ω) / dt = … [4] The important idea being :: this model (when compared to others) has the congestion window size decreasing faster  the impact of the dropping/marking probability on cwnd change is larger than other models predict.

11. Advanced Computer Networks : (SFC) State Feedback Controller 11 Analysis of the Interaction between TCP and AQM The authors use partial differential equations to describe the dynamic system used to analyze the interaction between TCP and an AQM. The system consists of N homogeneous TCP connections traversing a single bottleneck link with bandwidth C.

12. Advanced Computer Networks : (SFC) State Feedback Controller 12 Analysis of the Interaction between TCP and AQM Homogeneous :: All TCP connections are assumed to have the same RTT. q - the queue length on the bottleneck link ω – Each connection has the same connection window size.

13. Advanced Computer Networks : (SFC) State Feedback Controller 13 Dynamic System Equations dq/dt = g(ω(t), q) = Nω/ τ - C dω/dt = f(ω(t), ω(t - τ), p) The first differential equation states that the queue length is an integral of the difference between the packet arrival rate and the link capacity. The second differential equation describes the dynamic behavior of the TCP window developed in the enhanced TCP model.

14. Advanced Computer Networks : (SFC) State Feedback Controller 14 Linear Differential Approximation Since the system model is non-linear, the system is approximated with its small- deviation linearized model around an operating point (ω 0,p 0 ) to analyze its local stability. This yields the following set of differential equations: δq/dt = Nδω/ τ δω/dt = - (p 0 + 2bω 0 p 0 )δω/ 2bτ - δp(t-τ)/bτp 0

15. Advanced Computer Networks : (SFC) State Feedback Controller 15 Utilizing Control Theory The authors convert the linear differential equations to a matrix form where the matrix [D AD] is full ranked. This implies this system is controllable and by using the proper control law, the system’s state (i.e., characterized by q and ω), can be taken to a desirable equilibrium point.

16. Advanced Computer Networks : (SFC) State Feedback Controller 16 State Feedback Controller Based on state feedback control theory, the authors design an AQM controller under the linearized model. Stabilize (in this context) makes δq and δω as close to zero as possible!

17. Advanced Computer Networks : (SFC) State Feedback Controller 17 State Feedback Controller Reasons for state feedback controller: 1. Using average queue length brings “sluggishness” into a delay system. 2. A state feedback controller can be easily implemented and it can respond quickly to system dynamics.

18. Advanced Computer Networks : (SFC) State Feedback Controller 18 Block Diagram Letting p(t) = K x(t) allows parameter characterization in terms of k 1 and k 2. The control theory then permits determination of the stable region for k 1 and k 2.

19. Advanced Computer Networks : (SFC) State Feedback Controller 19 Stable Regions The stable region for k 2 is bounded by N/ τC. Based on Figure 2, the stable region is characterized in terms of N min and τ max. After the value of k 2 is determined, k 1 can be determined and the relationship is graphed in Figure 3.

20. Advanced Computer Networks : (SFC) State Feedback Controller 20 Sample Settings Given: C = 10Mbps; average packet size =1000 bytes; N min = 300; τ max = 0.6 sec.; b = 2; Then k 2 = 0.2 and k 1 = 0.0005

21. Advanced Computer Networks : (SFC) State Feedback Controller 21 SFC Algorithm

22. Advanced Computer Networks : (SFC) State Feedback Controller 22 AQM Taxonomy

23. Advanced Computer Networks : (SFC) State Feedback Controller 23 Schemes that aim to achieve fairness FRED – monitors both global average queue length and also average queue length for queue for each flow. – Requires two min and max thresholds BRED – Extends FRED and imposes three thresholds.

24. Advanced Computer Networks : (SFC) State Feedback Controller 24 Schemes that decouple congestion index from the performance index. These AQM schemes aim for high utilization and low delay. The decoupling accomplished by calculating p using an additional measure than queue length. BLUE – Uses instantaneous queue length and link utilization as traffic load indices.

25. Advanced Computer Networks : (SFC) State Feedback Controller 25 Schemes that decouple congestion index from the performance index. REM – Defines a “price function” in terms of rate difference and queue mismatch. AVQ – Only uses input rate and maintains a virtual queue.

26. Advanced Computer Networks : (SFC) State Feedback Controller 26 Schemes that stabilize the instantaneous queue length SRED – Estimates value of N and uses estimate in determining p. PI – aims to stabilize instantaneous queue size using fluid model. Scalable control scheme – Uses link price and virtual capacity.

27. Advanced Computer Networks : (SFC) State Feedback Controller 27 Single Bottleneck Simulations router 10 Mbps, 40 ms 10 Mbps, 20 ms

28. Advanced Computer Networks : (SFC) State Feedback Controller 28 200 TCP flows

29. Advanced Computer Networks : (SFC) State Feedback Controller 29 200 TCP flows

30. Advanced Computer Networks : (SFC) State Feedback Controller 30 200 TCP flows

31. Advanced Computer Networks : (SFC) State Feedback Controller 31 System Response

32. Advanced Computer Networks : (SFC) State Feedback Controller 32 Dynamic Traffic Changes

33. Advanced Computer Networks : (SFC) State Feedback Controller 33 Throughput Robustness

34. Advanced Computer Networks : (SFC) State Feedback Controller 34 Loss Rate Robustness

35. Advanced Computer Networks : (SFC) State Feedback Controller 35 Multiple Bottleneck Simulations

36. Advanced Computer Networks : (SFC) State Feedback Controller 36 Instantaneous Queue Length

37. Advanced Computer Networks : (SFC) State Feedback Controller 37 Link Utilization

38. Advanced Computer Networks : (SFC) State Feedback Controller 38 Packet Loss Rate

39. Advanced Computer Networks : (SFC) State Feedback Controller 39 Conclusions Paper developed enhanced model to characterize TCP. Designed SFC as AQM controller designed to stabilize the queue at the router. Simulations show SFC outperforms other schemes with respect to queue length, utilization, and packet loss.

40. Advanced Computer Networks : (SFC) State Feedback Controller 40 Criticisms What did they not do? Other issues?