1. Traffic (1993-2000) Heavy tails (HT) in net traffic??? Careful measurements Appropriate statistics Connecting traffic to application behavior “optimal” web layout  HT files  HT traffic Traffic Verbal Data/stat Mod/sim Analysis Synthesis

2. Is streamed out on the net. Creating fractal Gaussian internet traffic (Willinger,…) Heavy tailed files time log(file size)  > 1.0 log(> size) p  s - 

3. Traffic (1993) Traffic is “bursty”? Traffic Verbal

4. Traffic (1993-2000) Bursty??? Careful measurements Appropriate statistics Traffic Verbal Data/stat Why?

5. Heavy tailed files time Long space Becomes long time Why? Traffic Verbal Data/stat Mod/sim

6. Heavy tailed files time log(file size)  > 1.0 log(> size) p  s -  Traffic Verbal Data/stat Mod/sim Analysis

7. Heavy tailed files time log(file size)  > 1.0 log(> size) p  s -  What?

8. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Decimated data Log (base 10) Forest fires 1000 km 2 (Malamud) WWW files Mbytes (Crovella) Data compression (Huffman) Cumulative

9. Probability that a file is bigger than x. Probability that a packet is in a file bigger than x.

10. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Fires Web files Codewords Cumulative Log (base 10) -1/2

11. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Forest fires 1000 km 2 WWW files Mbytes Data compression Cumulative -1/2 exponential

12. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Forest fires 1000 km 2 WWW files Mbytes Data compression Cumulative exponential All events are close in size.

13. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Forest fires 1000 km 2 WWW files Mbytes Data compression Cumulative -1/2 Most events are small But the large events are huge

14. -6-5-4-3-2012 0 1 2 3 4 5 6 FF WWW DC Data + Model/Theory

15. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Decimated data Log (base 10) WWW files Mbytes (Crovella) CumulativeMost files are small (mice) Most packets are in large files (elephants)

16. Network Sources Mice Elephants Router queues Delay sensitive Bandwidth sensitive Unfortunate interaction of files with congestion control

17. Heavy tailed files time log(file size)  > 1.0 log(> size) p  s -  Why?

18. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency WWW files Mbytes Data compression Cumulative exponential All events are close in size.

19. Source coding for data compression Based on frequencies of source word occurrences, Select code words. To minimize message length.

20. 012 0 1 2 3 4 5 6 DC Data How well does the model predict the data?

21. 012 0 1 2 3 4 5 6 DC Data + Model How well does the model predict the data? Not surprising, because the file was compressed using Shannon theory. Small discrepancy due to integer lengths.

22. Generalized “coding” problems Minimize avg file transfer No feedback Discrete (0-d) topology Minimize avg file transfer Feedback 1-d topology Web Data compression

23. document split into N files to minimize download time A toy website model (= 1-d grid HOT design) Traffic Verbal Data/stat Mod/sim Analysis Synthesis

24. Probability of user access Wasteful Hard to navigate.

25. Wasteful Hard to navigate. Just right

26. More complete website models (Zhu, Yu) Detailed models –user behavior –content and hyperlinks Necessary for real web layout optimization Statistics consistent with simpler models Improved protocol design (TCP) Commercial implications still unclear

27. Traffic (1993-2000) Heavy tails (HT) in net traffic??? Careful measurements Appropriate statistics Connecting traffic to application behavior “optimal” web layout  HT files  HT traffic Traffic Verbal Data/stat Mod/sim Analysis Synthesis

28. -6-5-4-3-2012 0 1 2 3 4 5 6 WWW DC Data

29. -6-5-4-3-2012 0 1 2 3 4 5 6 WWW DC Data + Model/Theory

30. -6-5-4-3-2012 0 1 2 3 4 5 6 WWW Data + Model/Theory Are individual websites distributed like this? Roughly, yes.

31. -6-5-4-3-2012 0 1 2 3 4 5 6 WWW DC Data + Model/Theory How has the data changed since 1995?

32. Traffic (1993-2000) Traffic TopologyLayeringC&D Verbal Data/stat Mod/sim Analysis Synthesis

33. Theory and the Internet TrafficTopologyC&DLayering Verbal Data/stat Mod/sim Analysis Synthesis

34. Network Sources Mice Elephants Router queues

35. Network Sources Mice Elephants Router queues Delay sensitive Bandwidth sensitive Unfortunate interaction of files with congestion control

36. Network Sources Mice Elephants Router queues Delay sensitive Bandwidth sensitive Better Control Fortunate interaction of files with improved congestion control

37. High variability in context More high variability Heterogeneity Human behavior Actuating Today: Simplify/broaden Look back/sideways Extend Optimization Layer/distribute Dynamics/control Develop Delays Actuation