1. On the Constancy of Internet Path Properties Yin Zhang, Nick Duffield AT&T Labs Vern Paxson, Scott Shenker ACIRI Internet Measurement Workshop 2001 Presented by Ryan

2. Outline Motivation Three Notions of Constancy Mathematical, Operational and Predictive Analysis Methodology Measurement Methodology Constancy of Internet Path Properties Packet Loss and Throughput Conclusion

3. Motivation There has been a surge of interest in network measurements Mathematical Traffic Models Operational Procedures Adaptive Algorithms Measurements are inherently bound to the “present” state of the network

4. Motivation Measurements are valuable when network properties exhibit constancy Constancy like “stationarity” More general rather then a specific mathematical view “Hold steady and does not change”

5. Notions of Constancy Mathematical Constancy Operational Constancy Predictive Constancy

6. Mathematical Constancy A dataset is mathematically steady if it can be described with a single time-invariant mathematical model Key : To find the appropriate model Simplest Example A single independent and identically distributed (IID) random variable

7. Operational Constancy A dataset is operationally steady if the quantities of interest remain within bounds considered operationally equivalent Key : Whether an application care about the changes

8. Operational Constancy Operational but not Mathematical Loss rate remains constant at 10% for first thirty minutes, abruptly changes to 10.1% for next thirty minutes Mathematical but not Operational Loss process is a bimodal process with a high degree of correlation An application will see sharp transitions from low-loss to high-loss regimes

9. Predictive Constancy A dataset is predictively steady if past measurements allow one to reasonably predict future characteristics Key : How well changes can be tracked

10. Predictive Constancy Mathematical but not Predictive IID process (no correlations in the process) Predictive but neither Mathematical nor Operational Examples will be shown later

11. Analysis Methodology Mathematical Constancy To find change-points CP/Bootstrap CP/RankOrder To partition a time series into change free regions (CFR) To test for IID within each CFR Box-Ljung test (based on autocorrelation, r)

12. Analysis Methodology Operational Constancy To define operational categories based on requirements of real applications Predictive Constancy To evaluate the performance of commonly used estimators Moving Average (MA) Exponentially-Weighted Moving Average (EWMA)

13. Measurement Methodology Measurement Infrastructure NIMI (National Internet Measurement Infrastructure) During Winter 1999-2000 (W1)  31 hosts, 80% located in US During Winter 2000-2001 (W2)  49 hosts, 73% located in US

14. Measurement Methodology Losses Poisson packet streams Duration – 1 hour Mean rate – 10Hz (W1) and 20Hz (W2) Payloads – 256 bytes (W1) and 64 bytes (W2) Throughput TCP transfers Duration – 5 hours 1 MB transfer every minute

15. Summary of Datasets Dataset # NIMI sites # packet traces # packets # thruput traces # transfers W1W1 312,375140M5816,900 W2W2 491,602113M11131,700 W 1 + W 2 493,977253M16948,600

16. Loss Constancy Previous Works by Mukherjee Individual loss High correlation in packet loss for packets with a spacing of <= 200ms In this paper Much of correlation from back-to-back losses rather than from “nearby” losses Loss episode A series of consecutive packets that are lost

17. Loss Constancy Individual Loss VS Loss Episode Time scale Traces consistent with IID Individual Loss Loss Episode Up to 0.5-1 sec27%64% Up to 5-10 sec25%55%

18. Loss Constancy Poisson nature of loss episode Loss episode inter-arrivals with exponential distributions

19. Loss Constancy Mathematical Constancy All traces – more than half over the full hour Lossy traces – half less than 20 - 30 minutes Overall loss rate exceeded 1%

20. Loss Constancy Mathematical Constancy 88-92% of CFR are consistent with an absence of lag 1 correlation 77-86% are consistent with no correlation up to lag 100

21. Loss Constancy Operational Constancy Loss rate categories (total 6) 0-0.5%, 0.5-2%, 2-5%, 5-10%, 10-20% and 20+% Short Period of Constancy Long Period of Constancy

22. Loss Constancy Shorter period of Constancy (lasting 50 minutes or less) No significant difference between 10 seconds average and 1 minutes average results

23. Loss Constancy Longer period of Constancy (lasting 50 minutes or more) Take only a single 10 sec change in loss rate is much likely than a singe 1 min change IntervalTypeProb. 1 min Episode71% Loss57% 10 sec Episode25% Loss22%

24. Loss Constancy Mathematical VS Operational 20 mins steady region – categorizing as “steady” Set Interval 1 min10 sec 6-9%11% 6-15%37-45% 2-5%0.1% 74-83%44-52% M : Mathematical Steady O : Operational Steady

25. Loss Constancy Predictive Constancy Mean Prediction Error E[ | log( predicted value / actual value ) | ] Estimation Scheme and Parameters Don’t matter Computed over entire tracesComputed over CFR

26. Loss Constancy Prediction performance is the worst for the traces are Mathematical and Operational steady Using EWMA (α = 0.25) estimator

27. Throughput Constancy Mathematical Constancy Around 60%, the largest CFR is less than 2.5 hrs But only 10%, the CFR is under 20 min Weighted average – the average length of CFR if you pick a random point in the traces  E.g. 5 hrs trace  2 hrs CFR + 3hrs CFR  Weighted average = 2/5 * 2 + 3/5 * 3 = 2.6hrs

28. Throughput Constancy Mathematical Constancy 92% passes the independence test for autocorrelation up to 6 lags

29. Throughput Constancy Operational Constancy The ratio between MAX and MIN throughput, ρ

30. Throughput Constancy Predictive Constancy Almost all estimators perform well Estimators with long memory are worse EWMA with α=0.01 MA with windows of 128

31. Conclusion This paper raised the concepts and tools to understand three different notions of constancy Mathematical, Operational, Predictive The degree of constancy found in the Internet path properties is under study The relationships between three constancy are discussed

33. Loss Constancy Binary loss series T i is the time of ith observation E i is an indicator, value = 1 if there is a loss original packet loss series (0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0) (0, 0, 1, 1, 0, 1, 0, 0) loss episode series

34. Appendix (CP Detection) A set of n value x i, i = 1, 2, … n Rank r i of each x i with 1 for the smallest If there is a change point, s i ’ will climb to a max before decreasing to 0 at i = n