1 / 35

End-to-End Estimation of Available Bandwidth Variation Range

This document explores the methodologies for estimating available bandwidth variation in network paths, crucial for applications reliant on accurate network parameters such as delay and loss rate. It details the distinction between bandwidth capacity and available bandwidth, discusses the significance of bandwidth estimation for TCP transfers, streaming multimedia, and intelligent routing, and highlights the challenges of measuring bandwidth due to cross-traffic. The use of statistical methods and proactive probing techniques to assess bandwidth estimates and their variability is emphasized, with practical examples provided.

tyler
Télécharger la présentation

End-to-End Estimation of Available Bandwidth Variation Range

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. End-to-End Estimation of Available Bandwidth Variation Range Constantine Dovrolis Joint work with Manish Jain & Ravi Prasad College of Computing Georgia Institute of Technology

  2. Probing the Internet • Several network parameters are important for applications and transport protocols: • Delay, loss rate, capacity, congestion, load, etc • Internet routers do not provide direct feedback to end-hosts • Due to scalability, simplicity & administrative issues • Except SNMP, ICMP • Alternatively: • Infer network state through end-to-end measurements

  3. End-to-end bandwidth estimation • “Bandwidth” in data networks refers to throughput(bits/sec) • Capacity: maximum possible throughput w/o cross traffic • Available bandwidth (or residual capacity): capacity – cross traffic • Bandwidth estimation: measurement techniques & statistical analysis to infer bandwidth-related metrics of individual links and end-to-end network paths • Objectives: • Accuracy: application-specific but typically within 10-20% • Estimation latency: within a few seconds • Non-intrusiveness: cross traffic should not be affected • Scalability: important when monitoring many paths (not covered in this talk)

  4. Why to measure bandwidth? • Large TCP transfers and congestion control • Bandwidth-delay product estimation • TCP socket buffer sizing • Streaming multimedia • Adjust encoding rate based on avail-bw • Intelligent routing systems • Overlay networks and p2p networks • Intelligent routing control & multihoming • Content Distribution Networks (CDNs) • Choose server based on least-loaded path • SLA verification & interdomain problem diagnosis • Monitor path load and allocated capacity • End-to-end admission control • Network spectroscopy • Several more..

  5. Definitions and problem statement

  6. Capacity • Maximum possible end-to-end throughput at IP layer • In the absence of any cross traffic • For maximum-sized packets • If Ci is capacity of link i, end-to-end capacity C defined as: • Capacity determined by narrow link

  7. Average available bandwidth • Per-hop average avail-bw: • Ai = Ci (1-ui) • ui: average utilization • A.k.a. residual capacity • End-to-end avg avail-bw A: • Determined by tight link • ISPs measure average per-hop avail-bw passively • 5-min averaging intervals

  8. Avail-bw variability • Avail-bw has significant variability • Variability depends on averaging timescale t • Larger timescale, lower variance • Variation range: • Range between, say, 10th to 90th percentiles • Example: • Path-1: variation range [10Mbps, 90Mbps] • Path-2: variation range [20Mbps, 20Mbps] • Which path would you prefer?

  9. The avail-bw as a random process • Instantaneous utilization ui(t): either 0 or 1 • Link utilization in (t, t+t) • Averaging timescale: t • Available bandwidth in (t, t+t) • End-to-end available bandwidth in (t, t+t)

  10. Problem statement • Avail-bw random process, measured in timescale t: At(t) • Assuming stationarity, marginal distribution of At: • Ft(R) = Prob [At ≤ R] • Ap :pth percentile of At, such that p = Ft(Ap) • Objective: Estimate variation range [AL, AH] for given averaging timescale t • ALand AH are pL and pH percentiles of At • Typically, pL =0.10 and pH =0.90

  11. Probing methodology

  12. Probing a network path • Sender transmits periodic packet stream of rate R • K packets, packet size L, interarrival T = L/R • Receiver measures One-Way Delay (OWD) for each packet • D(k) = tarv(k) - tsnd(k) • OWD variations: Δ(k) = D(k+1) – D(k) • Independent of clock offset between sender/receiver • With stationary & fluid-modeled cross traffic: • If R > A, then Δ(k) > 0 for all k • Else, Δ(k) = 0 for all k

  13. Self-loading periodic streams • Increasing OWDs means R>A • Non-increasing OWDs means R<A

  14. Example of OWD variations • 12-hop path from U-Delaware to U-Oregon • K=100 packets, A=74Mbps, T=100μsec • Rleft = 97Mbps, Rright=34Mbps

  15. Percentile sampling & estimation algorithms

  16. Percentile sampling • Given R and t, estimate Ft(R) • Ft(R) is also referred to as the rank of rate R • Assume that Ft(R) is inversible • Sender transmits a periodic packet stream of rate R • Length of stream: measurement timescale t • Receiver classifies the stream, based on measured one-way delay trends, as: • Type-G if At ≤ R: • I(R)= 1 with probability Ft(R) • Type-L if At > R: • I(R)= 0 with probability 1-Ft(R)

  17. Percentile sampling (cont’) • Send N packet streams, and classify each packet stream as • Type-G if At ≤ R: • I(R)= 1 with probability Ft(R) • Type-L if At > R: • I(R)= 0 with probability 1-Ft(R) • Number of type-G streams: • Unbiased estimator for the rank of rate R:

  18. How many streams do we need? • Larger N  longer estimation duration • Smaller N  larger variance in estimator I(R,N)/N • Choose N so that: • I(R,N)/N within Ft(R)± r • r:maximum percentile error • P[N(p-r) < I(R,N) < N(p+r)] > 1-e • where p= Ft(R) and e small • I(R,N) ~ Binomial (N, p) assuming independent sampling • With N=40-50 streams, the maximum percentile error r for 10th-90th variation range is about 0.05

  19. Non-parametric estimation • It does not assume specific avail-bw distribution • Iterative algorithm • Stationarity requirement across iterations • N-th iteration: probing rate Rn • Use percentile sampling to estimate percentile rank of Rn • To estimate the upper percentile AH with pH = Ft(AH): • fn = I(Rn,N)/N • If fn is between pH±r, report AH = Rn • Otherwise, • If fn > pH +r, set Rn+1 < Rn • If fn < pH -r, set Rn+1 > Rn • Similarly, estimate the lower percentile AL

  20. Non-parametric algorithm • Parameter b • Upper bound on rate variation in successive iterations • Tradeoff between accuracy and responsiveness • Larger b: • Faster convergence • Larger oscillations

  21. Validation example (non-parametric) • Testbed experiments using real Internet traffic traces b=0.05 b=0.15 • Non-parametric estimator tracks variation range within 10-20% • Optimal selection of b depends on traffic • Traffic spikes/dips may not be detected if b is too small • But larger b causes larger MSRE

  22. Parametric estimation • Assume Gaussian avail-bw distribution • Justified assumption for large degree of traffic multiplexing • And/or for long averaging timescale (>200msec) • Gaussian distribution completely specified by • Mean m and standard deviation st • pth percentile of Gaussian distribution • Ap = m + st f-1(p) • Sender transmits N probing streams of rates R1 and R2 • Receiver determines percentiles ranks corresponding to R1 and R2 • m and st can be then estimated by solving • R1 = m + st f-1(p1) • R2 = m + st f-1(p2) • Variation range is then calculated from: • AH = m + st f-1(pH) • AL = m + st f-1(pL)

  23. Parametric algorithm • Variation range estimate • Non-iterative algorithm • More appropriate under non-stationary conditions • Probing rates do not need to follow variation range • Less intrusive probing

  24. Validation example (parametric) Gaussian traffic non-Gaussian traffic • Parametric algorithm is more accurate than non-parametric algorithm, when • traffic is good match to Gaussian model • in non-stationary conditions

  25. Comparison of the two algorithms Non-parametric: t = 40msec Parametric: t = 250msec • Non-parametric algorithm • Stationarity assumption is more critical (iterative algorithm) • Can be used with any cross traffic distribution • Parametric algorithm • Provides variation range estimate at end of each round • Accurate when underlying traffic close to Gaussian

  26. Avail-bw variability factors

  27. A sample measurement from the Internet • Path from Georgia Tech to University of Ioannina, Greece • Average avail-bw increases over this 2-hour period • Variation range decreases as average avail-bw increases

  28. Objectives and methodology • Examine effect of following factors on avail-bw variability: • Load at tight link • Degree of multiplexing at tight link • Averaging time scale • Single-hop simulation topology with TCP traffic • Monitore load at tight link • Examine variation range width V • V = AtH - AtL • Compare V with Coefficient of Variation (CoV) • CoV : standard deviation (at time scalet) over average avail-bw • V : Absolute variability metric • CoV : Relative variability metric

  29. Tight Link Utilization • Variation range width V shows non-monotonic behavior • V increases in low/medium load, due to increasing variance in input traffic (tight link rarely saturated) • V decreases in heavy load due to “clamping” by tight link capacity • CoV increases monotonically with load

  30. Statistical Multiplexing • Conventional wisdom: • Keeping the load constant, higher degree of multiplexing makes the traffic smoother • Two models for increasing degree of multiplexing • Capacity Scaling • Increase capacity of tight link and proportionally increase number of flows • Average flow rate remains constant • Flow Scaling • Increase number of flows and proportionally decrease average flow rate • Capacity of tight link remains constant

  31. Capacity Scaling • Variation range width V increases with capacity scaling • CoV decreases with capacity scaling • Conventional wisdom true for relative variability (CoV) but not for absolute variation range (V)

  32. Flow Scaling • Variation range decreases in both absolute and relative terms

  33. Measurement Timescale • Avail-bw variability decreases with averaging time scale • Rate of decrease depends on correlation structure of avail-bw process • Observed decrease rate consistent with scaling process in the 50-500ms (Hurst parameter=0.7)

  34. Summary and future work

  35. Future work • Applications of bandwidth estimation: • Overlay routing and multihoming: path selection algorithms, avoidance of oscillations, provisioning • Interdomain performance problem diagnosis • TCP throughput prediction (see ACM Sigcomm’05) • Internet traffic analysis: • Use of bw-estimation to explain traffic burstiness in short time scales (see ACM Sigmetrics’05) • Examine validity of single-bottleneck assumption • Examine congestion responsiveness of Internet traffic • New estimation problems: • Detect maximum possible shared available bandwidth among set of network paths

More Related