Delayed Stability and Performance of Distributed Congestion Control

1
Delayed Stability and Performance ofDistributed
Congestion Control

• TCPs congestion control is inadequate for
• High speed networks
• Fluctuation sensitive real-time multimedia
• Asymptotic Stability
• Avoid oscillations in the steady-state and
  properly respond to external perturbations
• Stability proofs become complicated as feedback
  delays are taken into account
• Special case heterogeneous delays

2
Paper Goal

• Design discrete congestion control algorithm
• Asymptotically stable under heterogeneous
  feedback delay
• Control equations not explicitly dependent on
  RTTs of endflows
• Smooth sending rate
• Fast convergence to efficiency
• Fast convergence to fairness

3
MKC

• Discrete system
• Stable and fair under heterogeneously delayed
  feedback
• Fixed control parameters
• Low implementation overhead inside routers
• Main Result Any max-min fair system with a
  stable symmetric Jacobian remains asymptotically
  stable under arbitrary feedback delay

4
Classic Kelly Control

• Linear end-flow equation (rate)
• Depends on last rate and the delayed feedback
• Effect of Delay
• Sending rate oscillates as delay increases
  (diverges after D 4 time units)
• Solution
• Adaptively update the control parameters
• Glitch Introduces unfairness between flows with
  different RTTs (due to reliable estimation
  problem)

5
Kelly Control
6
Kelly Control - Insights

• Uses proportional fairness
• Stationary rates are constrained by the capacity
  of all resources
• Real networks are constrained by the slowest
  resource (bottleneck)
• Leads to over/under utilization of resources
  (example)

7
Kelly Control - Insights
8
Kelly Control - Insights

• Real Problem
• The control uses conflicting information from
  slow and fast resources
• Combining the conflicting information into the
  rate determining summation leads to a middle
  ground
• The middle ground utilizes none efficiently
  (fastest or the slowest resources)

9
MKC

• Solution
• Do not charge any price at the routers that do
  not experience packet loss
• For proportional fairness as implemented in Kelly
  control this implies AIMD like probing ? Slow
  convergence
• Use Max-min fairness

10
MKC

• Do not involve the last sending rate in the rate
  calculations ? reduce unstability
• Fix the control parameters among end users and
  establish a uniform set of equations ? end
  unfairness
• Use max-min fairness ? Only the feedback from the
  congested routers matter

11
MKC Involved Analysis

• Show that class of systems with symmetric
  Jacobians are stable
• Show that the Jacobian is symmetric for MKC
• Show that MKC achieves smooth sending rates
• Show that MKC convergence to efficiency is
  exponential
• Show that convergence to fairness is
• Exponential if number of flows scales as capacity
  
• Linear otherwise
• Show that the burden on routers is minimal