Network Simulation and Testing

1. Network Simulation and Testing Polly Huang EE NTU http://cc.ee.ntu.edu.tw/~phuang phuang@cc.ee.ntu.edu.tw

2. Traffic Papers • V. Paxson, and S. Floyd, Wide-Area Traffic: The Failure of Poisson Modeling. IEEE/ACM Transactions on Networking, Vol. 3 No. 3, pp. 226-244, June 1995 • W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, On the Self-Similar Nature of Ethernet Traffic. IEEE/ACM Transactions on Networking, Vol. 2, No. 1, pp. 1-15, Feb. 1995 • M. E. Crovella and A. Bestavros, Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE/ACM Transactions on Networking, Vol 5, No. 6, pp. 835-846, December 1997 • Anja Feldmann; Anna C. Gilbert; Polly Huang; Walter Willinger, Dynamics of IP traffic: A study of the role of variability and the impact of control. In the Proceeding of SIGCOMM '99, Cambridge, Massachusetts, September 1999

3. Paper Selection(Pre-lecture)

4. Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model

5. The Problem • What is the traffic workload like? • Call/packet arrival rate as a process • What kind of process is it? • Very old problem and a lot of work

6. Because • Traces are available • Researchers care about • The validness of their assumption • The network traffic being independent Poisson • Operation people care a lot about • The amount of buffer/bandwidth to provision for their networks • The profit comes from satisfying customers with minimum infrastructure cost

7. Telephone Network • Assumptions • Poisson call arrivals • Exponential call duration • Wonderful Property • Poisson mixing with Poisson is still Poisson • Average rate well-characterize a call • The whole queueing theory

8. Data Network? • Wide-Area Traffic: The Failure of Poisson Modeling • V. Paxson, and S. Floyd • IEEE/ACM Transactions on Networking, Vol. 3 No. 3, pp. 226-244, June 1995

9. A Study of the Wide-Area Traffic • Two units of examination • Connections vs. packets • A sizeable number of traces • ~4M connections, ~26M packets • Different location and different time • Inter-arrival processes • TCP connections • Telnet packets • FTPDATA connections • Going self-similar

10. Unit of Observation • Telephone network • Circuit-switched • The unit is circuit, i.e., a call • People picking up the phone and talk for a while • Data network • Packet-switched • The unit is packet • Another unit is connection, comparable to call • People starting up an FTP connection and send data for a while

11. Packet  Connection • Hosts send/receive packets over a channel at the transport layer • Reliable: TCP • Non-reliable: UDP • Packets from various channels multiplex at the the network layer • IP Routers switched on the packets

12. ? ? Inter-Arrival Process: A Little Exercise Beginning SYN ACK&SYN ACK&Segment 1 FIN ACK&FIN ACK End Beginning

13. TCP Connection Arrival Poisson? Depends

14. Application Dependent • TELNET • Users typing ‘telnet cc.ee.ntu.edu.tw’ • FTP • User typing ‘ftp cc.ee.ntu.edu.tw’ • FTPDATA burst • User typing ‘mget net-simtest-*.ppt’ • FTPDATA • Each individual TCP transfer • NNTP & SMTP • Machine initiated and/or timer-driven

15. Independent and Poisson?

16. Quick Summary • TELNET and FTP • Independent and Poisson • Both the 1-hour and 10-min scales • FTPDATA bursts and SMTP • At the 10-min interval • Not ‘terribly far’ from Poisson • SMTP inter-arrival is not independent • FTPDATA, NNTP • Clearly not Poisson

17. Before One Can Explain • Human-initiated process • Independent and Poisson • Non-human-initiated process • Well, who knows

18. Explanations I • TELNET and FTP • User initiated • Users typing ‘telnet cc.ee.ntu.edu.tw’ • User typing ‘ftp cc.ee.ntu.edu.tw’ • FTPDATA bursts • User typing ‘mget net-simtest-*.ppt’ • Closely-spaced connections… (<= 4 sec) • FTPDATA • TCP connections

19. Explanations II • NNTP • Flooding to propagate network news • Arrival of news trigger another • Periodical and implementation/configuration dependent • SMTP • Mailing list • Timer effects from the DNS queries

20. TELNET Packets Poisson? No, heavy-tailed!

21. Show in 4 Ways • Distribution of packet inter-arrival time • Exponential processes ramp up significantly slower • Packet arrival pattern in seconds and 10 seconds • Exponential processes are smoother at the 10sec scale • Variance-time plot • Change of variance to time scale • Var of exponential processes decays quickly • Packet arrival rate process in seconds • By the sole visual effect • Exponential processes are less spiky

22. Full TELNET model? Poisson connection arrival Heavy-tailed packet arrival within a connection

23. FTPDATA • Connection arrival is not Poisson • Clustered in bursts • Burst sizes in bytes is quite heavy-tailed • A 0.5% of bursts contribute to 50% of the traffic volume

24. OK. We know it’s not Poisson. But what?

25. Going Self-Similar • Well, since other evidences suggest so • And it’s the next good thing • Go straight into producing self-similar traffic

26. Producing Self-Similar Traffic • ON/OFF sources • Fix ON period rate • ON/OFF period length heavy-tailed • M/G/ • Customer arrival being Poisson • Service time being heavy-tailed with infinite variance • Authors’ own model • Pseudo-self-similar • Not long-range dependent though

27. Performance Implication • Low-priority traffic starvation • Shall the high-priority traffic being long-range dependent (bursty) • Admission control based on recent traffic failing • ‘Congestions haven’t happened for a long while’ does not mean it won’t happen now

28. The Real Message Poisson is no longer sufficient!

29. Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model

30. Self-Similar What? • On the Self-Similar Nature of Ethernet Traffic • Will E. Leland; Murad S. Taqqu; Walter Willinger; Daniel V. Wilson • IEEE/ACM Transactions on Networking, Vol. 2, No. 1, pp. 1-15, Feb. 1995

31. This One Easier • Self-similarity in World Wide Web Traffic: Evidence and Possible Causes • Mark E. Crovella; Azer Bestavros • IEEE/ACM Transactions on Networking, Vol 5, No. 6, pp. 835-846, December 1997

32. Definition • X: a stationary time series • X(m): the m-aggregates • Summing the time series over non-overlapping blocks of m • X is H-self-similar if • X (m) has the same distribution for all positive m

33. Think variance Same Distribution? • Same autocorrelation function • r(k) = E[(Xt - )(Xt+k - )]/2 • Look familiar? • r(k) ~ k- • k   • 0 <  < 1

34. Significance of k- • Long-range dependence • Just another way of characterizing the same thing • Power-law decay • Slower than exponential decay • Therefore traffic does not smooth up •  < 1 • r(k) does not converge • Sum of r(k) infinite, I.e., variance infinite

35. Just FYI • The Hurst parameter: 1- /2

36. Tests for Self-Similarity • Variance-time plot • A line with slope - > -1 • R/S plot • Rescaled range grows as the number points included • A line with slope H an the log-log scale • Periodogram • Power spectrum to frequency • A line with slope  - 1 at the log-log scale • Whittle estimator • Confidence to a form • FGN or Fractional ARIMA

37. Pareto Review • Exponential • f(x) = ce-cx • Heavy-tailed • F(x) ~ x-c, 0 < c < 2 • Hyperbolic • Pareto • f(x) = ckc x-c-1 • F(x) = 1- (k/x)c • A line at the log-log scale of F(x) plot

38. In Addition to the Theory • A HUGE volume of Ethernet traces • Show consistency of being self-similar in all sorts of tests • Implication to traffic engineering • A bombshell!

39. Why Self-Similar? • Theory suggests • Fix rate ON/OFF process • Heavy-tailed length • Looking into the length • The ON time: transmission time • The OFF time: silent time

40. Physical Cause • Heavy-tailed transmission time • Heavy-tailed file sizes • Magic of the nature • E.g., book size in library

41. Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model

42. So, enough Math. Just tell me what to do! It depends!

43. Cutting to the Chase • The structural model • user level: Poisson arrival and heavy-tailed duration • network level: TCP closed-loop feedback control and ack clocking • Variability: delay and congestion • Let simulators track the complex behavior

44. Why not FGN? • IP Traffic Dynamics: The Role of Variability and Control • Anja Feldmann; Anna C. Gilbert; Polly Huang; Walter Willinger • In the Proceeding of SIGCOMM '99, Cambridge, Massachusetts, September 1999

45. Remember Wavelet Analysis? • FFT • Frequency decomposition • fj, Fourier coefficient • Amount of the signal in frequency j • WT: wavelet transform • Frequency (scale) and time decomposition • dj,k, wavelet coefficient • Amount of the signal in frequency j, time k

46. Self-similarity • Energy function • Ej = Σ(dj,k)2/Nj • Weighted average of the signal strength at scale j • Self-similar process • Ej = 2j(2H-1) C <- the magic!! • log2 Ej = (2H-1)j + log2C • linear relationship between log2 Ej andj

47. ?? RTT ‘Shape’ of Self-Similarity Self-similar

48. 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 8 0 0 8 8 Wavelet Example 1 0 -1 00 00 00 00 11 11 11 11 s1 s2 s3 s4 d1 d2 d3 d4

49. 10 00 00 00 10 00 00 00 s1 s2 s3 s4 d1 d2 d3 d4 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 2 0 Adding Periodicity • packets arrive periodically, 1 pkt/23 msec • coefficients cancel out at scale 4

50. Adding Periodicity Visualization J=4