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Queuing Analysis of Tree-Based LRD Traffic Models

Queuing Analysis of Tree-Based LRD Traffic Models. Vinay J. Ribeiro R. Riedi, M. Crouse, R. Baraniuk. Research Topics. LRD traffic queuing Internet path modeling: probing for cross-traffic estimation Open-loop vs. closed-loop traffic modeling (AT&T labs)

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Queuing Analysis of Tree-Based LRD Traffic Models

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  1. Queuing Analysis of Tree-Based LRD Traffic Models Vinay J. Ribeiro R. Riedi, M. Crouse, R. Baraniuk

  2. Research Topics • LRD traffic queuing • Internet path modeling: probing for cross-traffic estimation • Open-loop vs. closed-loop traffic modeling (AT&T labs) • Sub-second scaling of Internet backbone traffic (Sprint Labs)

  3. Long-range dependence (LRD) Variance LRD Poisson Scale (T) • Process X is LRD if 4 ms 2 ms 1 ms

  4. Multiscale Tree Models Model relationship between dyadic scales

  5. Additive and Multiplicative Models Gaussian non-Gaussian (asymp. Lognormal)

  6. Queuing

  7. Multiscale Queuing • Exploit tree for queuing

  8. Restriction to Dyadic Scales Only dyadic scales: Approximate queuing formulas: Multiscale queuing formula (MSQ) Critical dyadic time scale (CDTSQ)

  9. Multiscale Queuing Formula: Intuition independence • Assumption: dyadic scales far enough apart to allow • independence

  10. Simulation: Accuracy of Formula Berkeley Traffic Multiplicative model log P(Q>b) Additive model Queue size b

  11. Issues • Restriction to dyadic scales • Convergence of MSQ • Non-stationarity of models

  12. How good is the dyadic restriction? • Compare CDTSQ to well known critical time scale approximation • Equality if critical time scale is a dyadic scale • fractional Gaussian noise: equality at b=const.

  13. Convergence of MSQ Tree depth • For infinite terms is MSQ(b)=1? • Result: There exists N such that

  14. Non-Stationarity of Models • Tree models are non-stationary • Queue distribution changes with time • Formulas for edge of tree (t=0) How is queue at t=0 related to the queue at other times t? How is does the models’ queuing compare with that of the stationary modeled traffic? No common parent Common parent

  15. Non-Stationarity Stationary traffic: Non-stationary model: Theorem: If the autocorrelation of X is positive and non-increasing, Implication: The model captures the variance of traffic best at the edge (t=0) of the tree => best location to study queuing

  16. Asymptotic Queuing Conjecture: Note: The conjecture is true for fGn (Sheng Ma et al)

  17. Conclusions • Developed queuing formulas for multiscale traffic models • Studied the impact of using only dyadic scales, tree depth and non-stationarity of the models • Ongoing work: accuracy of formulas for non-asymptotic buffer sizes

  18. End-to-End Path Modeling Abstract the network dynamics into a single bottleneck queue driven by `effective’ crosstraffic • Goal: Estimate volume of cross-traffic

  19. Probing delay spread of packet pair correlates with cross-traffic volume

  20. Probing Uncertainty Principle • Small T for accuracy • But probe traffic disturbs cross-traffic (overflow buffer!) • Larger T leads to uncertainties • queue could empty between probes • To the rescue: model-based inference

  21. Multifractal Cross-Traffic Inference • Model bursty cross-traffic using the multiplicative multiscale model

  22. Efficient Probing: Packet Chirps • Tree inspires geometric chirp probe • MLE estimates of cross-traffic at multiple scales

  23. Chirp Cross-Traffic Inference

  24. ns-2 Simulation • Inference improves with increased utilization Low utilization (39%) High utilization (65%)

  25. Conclusion • Efficient chirp probing scheme for cross-traffic estimation

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