A State Feedback Control Approach to Stabilizing Queues for ECN-Enabled TCP Connections

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. Outline • Introduction • Enhanced TCP model • Analyze the Interaction between TCP and AQM • Details of the State Feedback Controlled AQM • Related Work • Simulations • Conclusions 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. 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 – ω2p/ 2 τ where ω current cwnd size and τ is the round-trip time (RTT). Advanced Computer Networks : (SFC) State Feedback Controller

5. Introduction • They claim other models only model gradual decrease in ω2p/ 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). 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 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. 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. 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. 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. 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. 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. 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. 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 (ω0 ,p0) to analyze its local stability. This yields the following set of differential equations: δq/dt = Nδω/ τ δω/dt = - (p0 + 2bω0p0)δω/2bτ - δp(t-τ)/bτp0 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. 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 andδω as close to zero as possible! Advanced Computer Networks : (SFC) State Feedback Controller

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

18. Block Diagram • Letting p(t) = K x(t) allows parameter characterization in terms of k1 and k2. • The control theory then permits determination of the stable region for k1 and k2. Advanced Computer Networks : (SFC) State Feedback Controller

19. Stable Regions • The stable region for k2 is bounded by N/ τC. • Based on Figure 2 , the stable region is characterized in terms of Nmin and τmax . • After the value of k2 is determined, k1 can be determined and the relationship is graphed in Figure 3. Advanced Computer Networks : (SFC) State Feedback Controller

20. Sample Settings Given: C = 10Mbps; average packet size =1000 bytes; Nmin= 300; τmax = 0.6 sec.; b = 2; Then k2 = 0.2 and k1 = 0.0005 Advanced Computer Networks : (SFC) State Feedback Controller

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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