stability of congestion control algorithms using control theory with an application to xcp
DESCRIPTION
Stability of Congestion Control Algorithms Using Control Theory with an application to XCP. Ioannis Papadimitriou ( [email protected] ) George Mavromatis ( [email protected] ). Outline. Previous Work Motivation behind applying control theory on congestion control protocols - PowerPoint PPT PresentationTRANSCRIPT
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Stability of Congestion Control Algorithms
Using Control Theory with an application to XCP
Ioannis Papadimitriou ([email protected])
George Mavromatis ([email protected])
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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 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
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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
1 1 2 1
2 1 2 2
( )2
( )2
0.1 0.1
2 2 20.1 0.1
2 2 21 1
r r r
r r r
d s d d s d s
d d s d s d s
a a bs e e e
d d da a b
A e s e ed d d
s
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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
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