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1 Network Simulation and Testing Polly Huang EE NTU http://cc.ee.ntu.edu.tw/~phuang phuang@cc.ee.ntu.edu.tw
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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
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3 Paper Selection (Pre-lecture) InterestingBoringEasyDifficult Failure of Poisson SS in Ethernet SS in WWW IP Dynamics
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4 Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model
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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
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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
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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
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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
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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
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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
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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
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12 Inter-Arrival Process: A Little Exercise Beginning SYN ACK&SYN ACK&Segment 1 End FIN ACK&FIN ACK Beginning ? ?
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13 TCP Connection Arrival Poisson? Depends
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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
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15 Independent and Poisson? Y/N TELNET FTP FTPDATA FTPDATA burst SMTP NNTP
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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
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17 Before One Can Explain Human-initiated process –Independent and Poisson Non-human-initiated process –Well, who knows
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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
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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
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20 TELNET Packets Poisson? No, heavy-tailed!
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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
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22 Full TELNET model? Poisson connection arrival Heavy-tailed packet arrival within a connection
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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
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24 OK. We know it’s not Poisson. But what?
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25 Going Self-Similar Well, since other evidences suggest so And it’s the next good thing Go straight into producing self-similar traffic
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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
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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
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28 The Real Message Poisson is no longer sufficient!
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29 Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model
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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
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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
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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
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33 Same Distribution? Same autocorrelation function –r(k) = E[(X t - )(X t+k - )]/ 2 –Look familiar? r(k) ~ k - –k –0 < < 1 Think variance
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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
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35 Just FYI The Hurst parameter: 1- /2
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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
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37 Pareto Review Exponential –f(x) = ce -cx Heavy-tailed –F(x) ~ x -c, 0 < c < 2 –Hyperbolic Pareto –f(x) = ck c x -c-1 –F(x) = 1- (k/x) c –A line at the log-log scale of F(x) plot
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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!
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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
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40 Physical Cause Heavy-tailed transmission time –Heavy-tailed file sizes –Magic of the nature –E.g., book size in library
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41 Identifying Internet Traffic Failure of Poisson Self-similar Traffic Practical Model
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42 So, enough Math. Just tell me what to do! It depends!
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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
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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
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45 Remember Wavelet Analysis? FFT –Frequency decomposition –f j, Fourier coefficient –Amount of the signal in frequency j WT: wavelet transform –Frequency (scale) and time decomposition –d j,k, wavelet coefficient –Amount of the signal in frequency j, time k
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46 Self-similarity Energy function –E j = Σ(d j,k ) 2 /N j –Weighted average of the signal strength at scale j Self-similar process –E j = 2 j(2H-1) C <- the magic!! –log 2 E j = (2H-1) j + log 2 C –linear relationship between log 2 E j and j
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47 ‘Shape’ of Self-Similarity Self-similar ?? RTT
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48 Wavelet Example 0 1 00 00 00 00 11 11 11 11 s1s2s3s4s1s2s3s4 d1d2d3d4d1d2d3d4 0 0 0 0 2 2 2 20 0 0 0 0 0 4 40 0 0 8 0 88
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49 Adding Periodicity packets arrive periodically, 1 pkt/2 3 msec coefficients cancel out at scale 4 10 00 00 00 s1s2s3s4s1s2s3s4 d1d2d3d4d1d2d3d4 1 0 0 0 1 0 1 20
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50 Visualization J=4 Adding Periodicity
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51 ’Shape' of self-similarity Self-similar Yes RTT!
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52 Large Scale Heavy-tailed connection duration
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53 Medium Scale TCP close-loop control RTT
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54 TCP Flow Control sourcesink RTT Time
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55 Variability Delay and congestion (bandwidth & load) SimulationMeasurement
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56 Internet Traffic is Weird! Different properties at different time scales –Large scales: self-similarity –Medium scale: periodicity –Small scale: ??? (possibly multifractal)
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57 New Queuing Theory? For chaotic Internet traffic Only pen and paper
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58 NO! Probably not in the near future Confirmed by experts
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59 A Few Reasons Not exactly self-similar (FGN - big no no) ’Shape' of self-similarity changes with the network conditions Don't know what self-similar processes add up to (mathematically intractable) Don ’ t know what those strange small-scale behavior is exactly
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60 Therefore 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
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61 Paper Selection (Post-lecture) InterestingBoringEasyDifficult Failure of Poisson SS in Ethernet SS in WWW IP Dynamics
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62 Paper Review #1 Dues 13:59:59, Friday, 3/12
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63 On the Review Forms Novelty –New idea Clarity –The problem Reality (practicality) –Evaluation Importance, significance, relevance –How much impact? –Would things change?
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64 OK for Beginners Clarity –Easiest –Judging the writing Evaluation –Easy –Judging the experiments and technical content
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65 Challenging for the Advanced Novelty –Hard –Need to follow/read enough papers in the area Importance –Hardest –Need to have breadth and know enough development in the area
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