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

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

• Ioannis Papadimitriou (jpg_at_stanford.edu)
• George Mavromatis (gmavr_at_stanford.edu)

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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

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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

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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

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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

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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

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Stability Proof

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

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Our solution for N 2

• Padé approximation for exp(-ds) factors
• Code in Matlab to find the roots of detA 0
  for different values of parameters a, b and
  different delays.
• Plot of the stability region

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Stability Region Plot for N 2
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Simulink Model
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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

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Questions
?