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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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