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 C i 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: A i = C i (1-u i ) u i : 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  Larger timescale, lower variance Variation range: Range between, say, 10 th to 90 th 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 u i (t): either 0 or 1 Link utilization in (t, t+  ) Averaging timescale:  Available bandwidth in (t, t+  ) End-to-end available bandwidth in (t, t+  )

10. Problem statement Avail-bw random process, measured in timescale   A  (t) Assuming stationarity, marginal distribution of A  : F  (R) = Prob [A  ≤ R] A p :p th percentile of A , such that p = F  (A p ) Objective: Estimate variation range [A L, A H ] for given averaging timescale  A L  and A H are p L and p H percentiles of A  Typically, p L =0.10 and p H =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) = t arv (k) - t snd (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 R left = 97Mbps, R right =34Mbps

15. Percentile sampling & estimation algorithms

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

17. Percentile sampling (cont’) Send N packet streams, and classify each packet stream as Type-G if A  ≤ R: I(R)= 1 with probability F  (R) Type-L if A  > R: I(R)= 0 with probability 1-F  (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 F  (R) ±    maximum percentile error P[N(p-  ) 1-  where p= F  (R) and  small I(R,N) ~ Binomial (N, p) assuming independent sampling With N=40-50 streams, the maximum percentile error  for 10 th -90 th 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 R n Use percentile sampling to estimate percentile rank of R n To estimate the upper percentile A H with p H = F  (A H ): f n = I(R n,N)/N If f n is between p H ±  report A H = R n Otherwise, If f n > p H + , set R n+1 < R n If f n R n Similarly, estimate the lower percentile A L

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  and standard deviation   p th percentile of Gaussian distribution A p =  +    -1 (p) Sender transmits N probing streams of rates R 1 and R 2 Receiver determines percentiles ranks corresponding to R 1 and R 2  and   can be then estimated by solving R 1 =  +    -1 (p 1 ) R 2 =  +    -1 (p 2 ) Variation range is then calculated from: A H =  +    -1 (p H ) A L =  +    -1 (p L )

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 trafficnon-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 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 Non-parametric:  = 40msecParametric:  = 250msec

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: 1. Load at tight link 2. Degree of multiplexing at tight link 3. Averaging time scale Single-hop simulation topology with TCP traffic Monitore load at tight link Examine variation range width V V = A  H - A  L Compare V with Coefficient of Variation (CoV) CoV : standard deviation (at time scale  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 1. Capacity Scaling 1. Increase capacity of tight link and proportionally increase number of flows 2. Average flow rate remains constant 2. Flow Scaling 1. Increase number of flows and proportionally decrease average flow rate 2. 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