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Adaptive Virtual Queue

This review discusses rate allocation formulation and explores adaptive virtual queue algorithms for congestion control in computer networks. It covers various perspectives, stability analysis, performance evaluation, and alternative approaches such as ARED, FRED, SRED, BLUE, and SFB.

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Adaptive Virtual Queue

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  1. Adaptive Virtual Queue Yang Richard Yang 10/31/2001

  2. Review: Rate Allocation • Rate allocation formulation [Kelly ‘97]

  3. Rate Allocation: Primal-Dual [LL00] • Define • Then the dual problem is to solve xi User i chooses xi such that

  4. Rate Allocation • Recall: • The derivative of D(p) is:

  5. End Hosts and the Network pj(t) xi(t) To control the value of p, the routers observe congestion measures and adjust p Example congestion measure pj(t) • queue length • queueing delay • arrival rate • delay jitter • others Example adaptation algorithms • TCP/Reno (loss) • TCP/SACK (loss) • TCP/Vegas (queueing delay) • TCP-Friendly congestion (loss)

  6. Three Perspectives • Efficiency and fairness • Stability and robustness • Reality

  7. Active Queue Management (AQM) • Objective • generate signal p to users • control queue size • improve utilization • influence loss rate • Issues • how to measure congestion? • queue length at a link • arrival rate at a link • how about combine them?? • how to map from congestion measure to marking (dropping) probability? • why do we need the mapping? • generally, the higher the congestion measure, the higher the mark rate

  8. Previous Work

  9. marking 1 Avg queue RED (Floyd & Jacobson 1993) • Congestion measure: average queue length qj(t+1) = [qj(t) + xj(t) - cj]+ • Mapping: p-linear probability function • Feedback: dropping or ECN marking • Performance • de-synchronization works well • extremely sensitive to parameter setting • fail to prevent buffer overflow as #sources increases

  10. REM (Athuraliya & Low 2000) • Congestion measure: price uj(t+1) = [uj(t) + g(aj (qj(t)-qref)+ xj(t) - cj )]+ • Mapping: exponential probability function • Feedback: dropping or ECN marking

  11. Adaptive Virtual Queue (AQM)

  12. Adaptive Virtual Queue (AVQ) • Based on GKVQ [Gibbens and Kelly ‘99] • Measure congestion by arrival rate At each packet arrival If (VQ+b > B) Mark or drop packet in real queueElseEndif

  13. AVQ System Model queue dynamics

  14. Equilibrium State

  15. Using  to Replace xi

  16. How to Check Whether a System is Stable? • Example 1: • Example 2:

  17. Laplace Transform • Some simple rules • Check the stability of Example 1 characteristic equation

  18. Linearization: User Behavior

  19. Linearization: Router Behavior

  20. Laplace-Transform

  21. Characteristic Equation where

  22. Stability of AVQ

  23. Performance: Queue Length and VQ Queue length Virtual capacity

  24. Experiment 2: FTP Only Loss Queue length

  25. Experiment 5: Dropping Loss Queue length

  26. Backup Slides

  27. Variant: ARED (Feng, Kandlur, Saha, Shin 1999) • Motivation: RED extremely sensitive to #sources • Idea: adapt maxp to load • If avg. queue < minth, decrease maxp • If avg. queue > maxth, increase maxp • No per-flow information needed

  28. Variant: FRED (Lin & Morris 1997) • Motivation: marking packets in proportion to flow rate is unfair (e.g., adaptive vs. unadaptive flows) • Idea • a flow can buffer up to minq packets without being marked • a flow that frequently buffers more than maxq packets gets penalized • all flows with backlogs in between are marked according to RED • no flow can buffer more than avgcq packets persistently • Need per-active-flow accounting

  29. Variant: SRED (Ott, Lakshman & Wong 1999) • Motivation: wild oscillation of queue in RED when load changes • Idea: • estimate number N of active flows • an arrival packet is compared with a randomly chosen active flows • N ~ prob(Hit)-1 • cwnd~p-1/2 and Np-1/2 = Q0implies p = (N/Q0)2 • marking prob = m(q) min(1, p) • No per-flow information needed

  30. Variant: BLUE (Feng, Kandlur, Saha, Shin 1999) • Motivation: wild oscillation of RED leads to cyclic overflow & underutilization • Algorithm • on buffer overflow, increment marking prob • on link idle, decrement marking prob

  31. 1 1 1 1 Variant: SFB • Motivation: protection against nonadaptive flows • Algorithm • L hash functions map a packet to L bins (out of NxL ) • marking probability associated with each bin is • Incremented if bin occupancy exceeds threshold • Decremented if bin occupancy is 0 • packets marked with min {p1, …, pL} h1 h2 hL-1 hL nonadaptive adaptive

  32. Variant: SFB • Idea • a nonadaptive flow drives marking prob to 1 at allL bins it is mapped to • an adaptive flow may share some of its L bins with nonadaptive flows • nonadaptive flows can be identified and penalized

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