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Stability of Congestion Control Algorithms Using Control Theory with an application to XCP

Stability of Congestion Control Algorithms Using Control Theory with an application to XCP. Ioannis Papadimitriou ( jpg@stanford.edu ) George Mavromatis ( gmavr@stanford.edu ). Outline. Previous Work Motivation behind applying control theory on congestion control protocols

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Stability of Congestion Control Algorithms Using Control Theory with an application to XCP

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  1. Stability of Congestion Control Algorithms Using Control Theory with an application to XCP Ioannis Papadimitriou (jpg@stanford.edu) George Mavromatis (gmavr@stanford.edu)

  2. Outline • Previous Work • Motivation behind applying control theory on congestion control protocols • eXplicit Control Protocol (XCP) • Stability proof for users with common RTT • Stability • Stability conditions for heterogeneous users • Simulations • NS-2 implementation of XCP and tests

  3. Previous Work • In 1998, F.P. Kelly proposes a fluid-flow description of a network and proves stability • Soon, conditions for stability of this model are established for homo/heterogeneous users • Application of these results to TCP and AQM protocols • TCP unstable for long RTTs and high capacities • RED tradeoffs • Guidelines for AQM implementations • Proposal of new AQM protocols

  4. Survey – Open Issues • Under all these assumptions, are systems really locally stable? • Does local stability imply network stability? • Can we find new fair/efficient algorithms with known stability behavior? • This is a hot research area

  5. XCP – Main Features • Descriptive feedback of congestion levels • Decoupling between efficiency control and fairness control • Congestion header carried by each packet • Stability proof for a single link and N users having the same RTT • Simulations with varying traffic requests and RTTs

  6. XCP stability for different RTTs • Standard assumptions • Constant number of users • One bottleneck link • Local stability around equilibrium point • Negligible queuing delays • Under these assumptions • Average RTT becomes constant (d) • Positive and negative feedback is equally divided among the users around equilibrium • Dynamics become linearized • Our proof: XCP stability conditions for heterogeneous users

  7. Stability Proof • New linearized differential equations with arbitrary delay for each user • Transform to A• x = 0 • System stable when all roots of det[A] = 0 have negative real part • We describe the stability conditions that must be satisfied for N users. • Now the problem purely algebraic although difficult

  8. Our solution for N = 2 • Padé approximation for exp(-d·s) factors • Code in Matlab to find the roots of det[A] = 0 for different values of parameters a, b and different delays. • Plot of the stability region

  9. Stability Region Plot for N = 2

  10. Simulink Model

  11. XCP simulation • We have implemented XCP in ns-2 • Study XCP behavior under adversarial network events: • Large differences in RTT • Number of users variable in time • Try different values for XCP parameters

  12. Questions ?

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