A Control-Theoretic Approach to Flow Control in Communication Networks

1. A Control-Theoretic Approach to Flow Control in Communication Networks May 17, 2005. Network Systems Lab., KAIST Jeong-woo Cho

2. Presentation Layout • Introduction & Related Works • Part I : Network-Performance Oriented Flow Control • Part II : Application-Performance Oriented Flow Control • Summary • Further Works

3. Introduction : Need for Flow Control • TCP Becomes Inefficient. • Loss-based congestion detection and recovery • Inefficient for high-speed networks and wireless networks • Unfair : flows with shorter RTT achieve higher throughput. • Nonlinear Dynamics of TCP Incur Bifurcations. [Ranjan02] • Bifurcation : emergence of oscillatory and chaotic behavior. • Nonlinear dynamics ignored in many works [Misra00, Hollot01] should be reconsidered. • TCP should be Replaced by a New Transport Protocol. • FAST TCP [Jin04], which originates from proportionally fair flow control algorithms, is to be used in near future. • XCP [Katabi02] (eXplicit Control Protocol) is also considered to be a sincere candidate to achieve max-min fairness in the Internet. • Equations describing the macroscopic behavior of XCP areidentical to those used in the existing flow control algorithm [Chong01]. • Equation-based flow control algorithms are gaining considerable support.

4. Introduction : Fairness Objectives • Proportional Fairness • Max-Min Fairness (Informal Def.) [Raduno02] Proportional fairness is achieved. Concavity of utility function is assumed. Proportionally Fair Flow Control Formulation I Formulation II + log function assumption

5. Introduction : Which Is Better? • Which Is Better? • (Bandwidth) Max-Min Fairness • S1=S2=S3=5Mbps • Sum=S1+S2+S3=15Mbps • Equality (Socialism) Preferred • (Bandwidth) Proportional Fairness • S1=3.3Mbps, S2=S3=6.7Mbps • Sum=S1+S2+S3=16.7Mbps • Equality & Efficiency (Capitalism) - But, authors in [Tang04] showed that “max-min fairness achieves higher throughput than proportional fairness in some cases.” - Thus, no one can say that “one is better than the other.” at present.

6. Related Works • Max-Min Flow Control • [Benmoh93] proposed max-min flow control algorithms that can place the poles of the closed-loop system at arbitrary position in complex plane. (too general!) • [Chong01] proposed max-min flow control algorithms with PI controllers in continuous-time domain and provided explicit stability region for controller gains. • We propose max-min flow control algorithms with PID and PII2 controllers in continuous-time domain and provide explicit stability region for controller gains. • Utility Max-Min Flow Control • [Cao99] showed that mostapplications have nonlinear utility functions in general and introduced the concept of utility max-min flow control. • [Cao99] and [Raduno02] presented algorithms to achieve utility max-min fairness assuming that each link knows the utility functions of all flows sharing the link. • We present distributed algorithms to achieve utility max-min fairness without using any kind of per-flow operations and provide stability results of the algorithms. In Part I In Part II

7. Goal : To Enhance the Performance of Networks Theoretical Contribution : Generalized Stability Condition for 3-term Link Controllers Practical Contribution : Fast Convergence, Fast Bandwidth Distribution Network-Performance Oriented Flow Control Goal : To Enhance the Performance of Applications Theoretical Contribution : Stability Condition for Nonlinear Flow Control Algorithms Practical Contribution : Allowing More General Shapes of Utility Functions Application-Performance Oriented Flow Control Introduction : A Control-Theoretic Approach Tools used for stability analysis : Linear control Robust control Fairness Extended Tools used for stability analysis : Nonlinear control

8. Part I : Network-Performance Oriented Flow Control

9. Link Algorithm Source Algorithm Part I : Network Architecture for Max-Min Fairness • Proposed Network Architecture

10. 2 PII Link Controller Part I : Flow Control Algorithms for Max-Min Fairness • Source Algorithm • Link Algorithms PID Link Controller

11. Part I : Stability Condition for Homogeneous Delay • Assumption • Theorem 1 (Homogeneous-Delay Case) • Remarks

12. Part I : Explicit Stability Conditionfor Homogeneous Delay • Corollary 1 Fig. 1. Stability Region • Remarks

13. Part I : Stability Condition for Heterogeneous Delay • Theorem 2 (Heterogeneous-Delay Case) • Remarks • Optimal Controller Gains

14. PID PII2 Part I : Simulation – Scenario 1 • Simulation Tool : NS-2 • Scenario 1 : Multiple Bottleneck Network At t=-∞ At t=5s At t=10s At t=15s At t=20s

15. Part I : Simulation – Scenario 1 (Contd.) Max-min fairness is achieved.

16. 10 flows 15 on-off flows Part I : Simulation – Scenario 2 • Scenario 2 : Simple Network with Short-lived Flows • Parameter Setting

17. Part I : Simulation – Scenario 2 (Contd.) Max-min fairness is achieved.

18. Part II : Application-Performance Oriented Flow Control

19. Part II : Motivation • What Is Utility? : • User-perceived application-specific satisfaction • Nonlinear Utility Necessitates Nonlinear Analysis. • It should be a delayednonlinearanalysis. • Moreover, the algorithm should work in a distributed manner such that the network doesn’t know users’ utility functions. • Analyzing a linearized model [Wydrow03] fails to guarantee global stability. Piecewise Linear Nonlinear Nonlinear Nonlinear

20. Part II : Motivation (Contd.) • Bandwidth Max-Min vs. Utility Max-Min in a Single Link Case Equal Bandwidth Allocation Equal Utility Allocation

21. Link Algorithm Source Algorithm Part II : Network Architecture for Utility Max-Min Fairness • Proposed Network Architecture Inverses of Utility Functions Feedback Utility

22. 2 PII Link Controller Part II : Flow Control Algorithms for Utility Max-Min • Source Algorithm • Link Algorithms PID Link Controller

23. Part II : Theoretical Backgrounds • What Is Absolute Stability Theory? • Attempts to deduce the stability of a family of nonlinear systems by examining only all linear systems within that family. • We may be relieved of burdens to analyze the stability of nonlinear feedback systems. • Famous incorrect conjectures: - Aizerman’s conjecture [Aizerm49] - Kalman’s conjecture [Kalman57]

24. Part II : Theoretical Backgrounds (Contd.) • Theoretical Obstacles • Famous absolute stability criterions, including Circle criterion and Popov criterion, are based on Lyapunov function method and assume that target systems have no delay. • Many criteria are quite restrictive, meaning that the shape of feedback is quite limited. • Many criteria assume that the open-loop function without nonlinear feedback is stable, which is not the case for our systems. • We Solves These Problems. • To the best of our knowledge, this is the first work providing distributed utility max-min architecture and its stability.

25. Part II : Stability Condition for Homogeneous Delay • Assumption • Theorem 1 (Homogeneous-Delay Case) • Remarks

26. Part II : Practical Stability Conditionfor Homogeneous Delay • Corollary 1 • Remarks • Inevitable Limitation small slope

27. Part II : Approximating Various Utility Functions • Approximating Utility Functions With Minimum Slope Requirement

28. Part II : Simulation – Scenario 1 • Simulation Tool : NS-2 • Scenario 1 : Simple Network with Heterogeneous Delays At t=-∞ At t=5s At t=10s At t=15s At t=25s At t=40s

29. Part II : Simulation – Scenario 1 (Contd.) Utility max-min is achieved. PII2 model achieves zero queue length at steady state and converges much faster than PID model. Real-time flows achieve larger data rates than elastic flows. Multi-layer streaming flows achieve base-layer rate before t=40s and achieve enhancement-layer rate after t=40s

30. Part II : Simulation – Scenario 2 • Scenario 2 : Multiple Bottleneck Network with Heterogeneous Delays At t=10s At t=20s At t=-∞ At t=40s

31. Part II : Simulation – Scenario 2 (Contd.) entry of S5, S6 entry of S7~S11 Bottleneck of S1 changes. entry of S12~S14

32. Part II : Simulation – Scenario 2 (Contd.) Utility max-min is achieved.

33. Part II : Simulation – Scenario 2 (Contd.) Real-time and stepwise flows achieve larger data rates than elastic flows if they share a common bottleneck. (e.g. S12~S14 and S4 after t=40s)

34. Summary • Network-Performance Oriented Flow Control • Generalized and explicit stability conditions for PID and PII2 models are provided. • Stability conditions for heterogeneous-delay case are provided. • PID model achieves the target queue length as well as the full utilization of each link. • PII2 model rapidly achieves fair rates and absorbs the fluctuation induced by short-lived flows, sacrificing link utilization. • Application-Performance Oriented Flow Control • Premiere distributed algorithms for application-performance oriented flow control are provided. • Utility max-min flow control algorithms with guaranteed stability are provided. • A unified flow control scheme that simultaneously serves not only elastic flows but also nonelastic flows.

35. Practical Implication • It Dispenses with Per-Flow Operation in Routers • Routers neither need to store nor need to process any kind of per-flow information. • That is, the proposed link algorithm is O(1) with respect to number of flows traversing the link. • A Distributed Algorithm Suitable for High-Speed Routers • It Is Stable in the Presence of Various Delays. • Routers need to know only one upper bound of round-trip delays even though flows experience heterogeneous round-trip delays. • A Distributed Algorithm Suitable for High-Speed Routers • It Accommodates Various Kinds of Application-Specific QoS. • Flows can express their nonlinear QoS needs since the algorithm accommodates nonlinear utility functions.  A Unifying Algorithm Suitable for Users’ Various Needs

36. Further Works • Obtaining Stronger Stability Conditions for Utility Max-Min Flow Control • Consideration of heterogeneous-delay case • Consideration of a multiple bottleneck network • Stability analysis when link controller gains are normalized by the sum of utility functions’ slopes

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