1. Dobby@mmlab.snu.ac.kr Measurement, Modeling and Analysis of the Internet Wang Xiaofei Vishal Misra, Columbia University

2. Dobby@mmlab.snu.ac.kr Traffic Modeling 2 TCP Modeling & Congestion Control 3 Conclusion 5 Content Introduction 1 Topology Modeling 4

3. Dobby@mmlab.snu.ac.kr 1.Introduction

4. Dobby@mmlab.snu.ac.kr 1.Introduction  Why?  Impossible to replicate the Internet in our lab and study it as a whole  So…to analyze network measurements and their transformation into models, to help explain the Internet’s functionality and improve its performance.  Traffic Models  TCP Models  Topology Models

5. Dobby@mmlab.snu.ac.kr 2.Traffic Modeling

6. Dobby@mmlab.snu.ac.kr 2.Traffic Modeling  Early Modeling:  “Poisson distribution model” Limited behavior of an aggregate traffic flow created by multiplexing large number of independent flowsLimited behavior of an aggregate traffic flow created by multiplexing large number of independent flows RandomRandom  “Big Bang” in 1993 “On the Self-similar Nature of Ethernet Traffic”  “Self-similar” behavior has serious implications for design, control, analysis of high-speed and large-coverage network…

7. Dobby@mmlab.snu.ac.kr  Self-Similarity  It describes the phenomenon in which the behavior of a process is preserved regardless of scaling in space or time  Long Ranged Dependence  The behavior of a time-dependent process shows significant correlations across large time scales 2.Traffic Modeling

8. Dobby@mmlab.snu.ac.kr “Self-Similarity”

9. Dobby@mmlab.snu.ac.kr  “Self-similar” 2.Traffic Modeling

10. Dobby@mmlab.snu.ac.kr  Open Loop Model Aggregate traffic is made up of many connections randomlyAggregate traffic is made up of many connections randomly Each connection has a “size” and transmits packets at some “rate”Each connection has a “size” and transmits packets at some “rate” Previous traffic has NO impact on following packetsPrevious traffic has NO impact on following packets  “M/G/infinity traffic model”  Problem: Less than 10% of network traffics are open loop.Less than 10% of network traffics are open loop. “always misleading”“always misleading” 2.Traffic Modeling

11. Dobby@mmlab.snu.ac.kr 2.Traffic Modeling  Closed Loop Model 90% network traffics are closed loop90% network traffics are closed loop Future transmission depends on previous packetsFuture transmission depends on previous packets FeedbackFeedback Closed loop behavior induces correlations independently of file size distributionClosed loop behavior induces correlations independently of file size distribution  Chaotic dynamics “Chaos”?“Chaos”? –nonlinearity –unpredictability –order in disorder –"butterfly effect"

12. Dobby@mmlab.snu.ac.kr 2.Traffic Modeling  Combined (structural) Models Internet protocol hierarchy is layeredInternet protocol hierarchy is layered Different layers act at different timescaleDifferent layers act at different timescale Short time scale behavior can be quite different from long time scaleShort time scale behavior can be quite different from long time scale

13. Dobby@mmlab.snu.ac.kr 3.TCP Modeling

14. Dobby@mmlab.snu.ac.kr 3.TCP Modeling  TCP throughput modeling: Hot in 90s  TCP Congestion Control “Window”  Increase window by 1 per RTT if no loss W  W+1W  W+1  Decrease by half on detection of loss W  W / 2W  W / 2

15. Dobby@mmlab.snu.ac.kr 3.TCP Modeling  SDE Model  Stochastic Differential Equation

16. Dobby@mmlab.snu.ac.kr 3.TCP Modeling  RED Model  Random Early Detect  Proactively mark or drop packets Prevent congestion by reacting earlyPrevent congestion by reacting early Probability based on average queue lengthProbability based on average queue length  …

17. Dobby@mmlab.snu.ac.kr 4.Topology Modeling

18. Dobby@mmlab.snu.ac.kr  Why?  Performance of networks critically dependent on topology  Early models  “Erdos-Renyi” random graphs Nodes randomly distributed on 2D planeNodes randomly distributed on 2D plane Connected to each other with probability inversely proportional to distance.Connected to each other with probability inversely proportional to distance.  BUT, random graphs didn’t represent real world networks 4.Topology Modeling

19. Dobby@mmlab.snu.ac.kr  Real World Network Topologies?  Hierarchical structure  Specialized nodes and Connectivity  Redundancy  GT-ITM simulator  “Georgia Tech Inter-network Topology Models”  Real world network topology & traffic…  BUT… 4.Topology Modeling

20. Dobby@mmlab.snu.ac.kr 4.Topology Modeling  “A Huge Bang”  “Power Law” in 1999, by Faloutsos 3 Frequency of websites, whose hit numbers are larger than x, is proportional to X -a Poisson Power Law Visit number of all websites in Internet

21. Dobby@mmlab.snu.ac.kr 4.Topology Modeling  Power Law everywhere!  “High desired degree - Low frequency” Internet websites visit numberInternet websites visit number Frequency of highly-used words in a LanguageFrequency of highly-used words in a Language Salary distribution of the whole countrySalary distribution of the whole country “2 - 8 rule”“2 - 8 rule” Private lands and apartments…Private lands and apartments…  “Unfair” but “Real”  Internet traffic also obey Power law…  GT-ITM didn’t give power law graphs…

22. Dobby@mmlab.snu.ac.kr 4.Topology Modeling  Power Law Graphs  Power Law Random Graph (PLRG) assign degrees to nodes from power law distributionassign degrees to nodes from power law distribution create k copies of node v; k is the degree of vcreate k copies of node v; k is the degree of v randomly match nodes in pool…randomly match nodes in pool…

23. Dobby@mmlab.snu.ac.kr 4.Topology Modeling  “Barabasi Model” New node connect to node i with probabilityNew node connect to node i with probability probability(i  j) = ki / kj

24. Dobby@mmlab.snu.ac.kr  General linear preference Greater flexibility in assigning preferenceGreater flexibility in assigning preference By preference parameterBy preference parameter  Inet...  … 4.Topology Modeling

25. Dobby@mmlab.snu.ac.kr  Topology constraints!  Technology: Processing speedProcessing speed Either a large number of low bandwidth connections, or a small number of high bandwidth connections…Either a large number of low bandwidth connections, or a small number of high bandwidth connections…  Geography Connectivity driven by geographical proximityConnectivity driven by geographical proximity  Economy Capacity of links is constrained by the capacity of nodes.Capacity of links is constrained by the capacity of nodes. “Economization”“Economization” 4.Topology Modeling

26. Dobby@mmlab.snu.ac.kr  Optimization Based Models  HOT-1 Highly Optimized Tolerances Each new node solves the local optimization problem to find a target node to connect to…Each new node solves the local optimization problem to find a target node to connect to…  HOT-2 Heuristically Optimized Tradeoffs  HOT-3: Variant of HOT-2  … 4.Topology Modeling

27. Dobby@mmlab.snu.ac.kr 5.Conclusion

28. Dobby@mmlab.snu.ac.kr  Traffic Model  “Self-similarity” of  “Self-similarity” of Internet traffic  Open Loop, Closed Loop, Combined…  TCP Model  “Window Algorithm”, RED, SDE, …  Topology Model  “Power Law” Power Law Graph Models…Power Law Graph Models…  Topology constraints Optimization…Optimization… 5.Conclution

29. Dobby@mmlab.snu.ac.kr