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Measurement, ModelingMeasurement, Modelingand Analysis of the Internetand Analysis of the Internet
Measurement, ModelingMeasurement, Modelingand Analysis of the Internetand Analysis of the Internet
Wang XiaofeiWang Xiaofei
Vishal Misra, Columbia UniversityVishal Misra, Columbia University
Traffic Modeling2
TCP Modeling & Congestion Control3
Conclusion5
Content
Introduction1
Topology Modeling4
1.Introduction
Why?Why? Impossible to replicate the Internet in our Impossible to replicate the Internet in our
lab and study it as a wholelab and study it as a whole So…to analyze network measurements So…to analyze network measurements
and their transformation into models, to and their transformation into models, to help explain the Internet’s functionality help explain the Internet’s functionality and improve its performance.and improve its performance.
Traffic ModelsTraffic ModelsTCP ModelsTCP ModelsTopology ModelsTopology Models
2.Traffic Modeling
Early Modeling:Early Modeling: ““Poisson distribution model”Poisson distribution model”
• Limited behavior of an aggregate traffic flow created Limited behavior of an aggregate traffic flow created by multiplexing large number of independent flowsby multiplexing large number of independent flows
• RandomRandom
““Big Bang” in 1993Big Bang” in 1993““On the Self-similar Nature of Ethernet Traffic”On the Self-similar Nature of Ethernet Traffic”
““Self-similarSelf-similar” behavior has serious ” behavior has serious implications for design, control, analysis of implications for design, control, analysis of high-speed and large-coverage network…high-speed and large-coverage network…
Self-SimilaritySelf-Similarity It describes the phenomenon in which the It describes the phenomenon in which the
behavior of a process is preserved behavior of a process is preserved regardless of scaling in space or timeregardless of scaling in space or time
Long Ranged Long Ranged DependenceDependence The behavior of a time-dependent process The behavior of a time-dependent process
shows significant correlations across shows significant correlations across large time scaleslarge time scales
2.Traffic Modeling
Open Loop ModelOpen Loop Model• Aggregate traffic is made up of many connections Aggregate traffic is made up of many connections
randomlyrandomly• Each connection has a “size” and transmits Each connection has a “size” and transmits
packets at some “rate”packets at some “rate”• Previous traffic has NO impact on following Previous traffic has NO impact on following
packetspackets
““M/G/infinity traffic model”M/G/infinity traffic model” Problem: 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
2.Traffic Modeling
Closed Loop ModelClosed 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 Closed loop behavior induces correlations
independently of file size distributionindependently of file size distribution
Chaotic dynamicsChaotic dynamics• ““Chaos”?Chaos”?
– nonlinearitynonlinearity– unpredictabilityunpredictability– order in disorderorder in disorder– "butterfly effect""butterfly effect"
2.Traffic Modeling
Combined (structural) ModelsCombined (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 Short time scale behavior can be quite different
from long time scalefrom long time scale
3.TCP Modeling
TCP throughput modeling: Hot in 90sTCP throughput modeling: Hot in 90sTCP Congestion Control “Window”TCP Congestion Control “Window”
Increase window by 1 per RTT if no lossIncrease window by 1 per RTT if no loss• WWW+1W+1
Decrease by half on detection of lossDecrease by half on detection of loss• WWW / 2W / 2
3.TCP Modeling
SDE ModelSDE Model Stochastic Differential EquationStochastic Differential Equation
3.TCP Modeling
RED ModelRED Model Random Early DetectRandom Early Detect Proactively mark or drop packets 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
……
Why?Why? Performance of networks critically Performance of networks critically
dependent on topologydependent on topologyEarly modelsEarly models
““Erdos-Renyi” random graphsErdos-Renyi” random graphs• Nodes randomly distributed on 2D planeNodes randomly distributed on 2D plane• Connected to each other with probability inversely Connected to each other with probability inversely
proportional to distance.proportional to distance.
BUT, random graphs didn’t represent real BUT, random graphs didn’t represent real world networksworld networks
4.Topology Modeling
Real World Network Topologies?Real World Network Topologies? Hierarchical structureHierarchical structure Specialized nodes and ConnectivitySpecialized nodes and Connectivity RedundancyRedundancy
GT-ITM simulatorGT-ITM simulator ““Georgia Tech Inter-network Topology Georgia Tech Inter-network Topology
Models”Models” Real world network topology & traffic…Real world network topology & traffic… BUT…BUT…
4.Topology Modeling
4.Topology Modeling
““ A Huge Bang”A Huge Bang” ““Power Law” in 1999, by Power Law” in 1999, by FaloutsosFaloutsos33
Frequency of websites, whose hit Frequency of websites, whose hit numbers are larger than x, is numbers are larger than x, is
proportional to Xproportional to X-a-a
Poisson Power Law
Visit number Visit number of all websites of all websites in Internetin Internet
4.Topology Modeling
Power Law everywhere!Power Law everywhere! ““High desired degree - Low frequency”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 Salary distribution distribution of the whole countryof the whole country• ““2 - 8 rule”2 - 8 rule”• Private lands and apartments…Private lands and apartments…
““Unfair” Unfair” butbut “Real” “Real”Internet traffic also obey Power law…Internet traffic also obey Power law…
GT-ITM didn’t give power law graphs…GT-ITM didn’t give power law graphs…
4.Topology Modeling
Power Law GraphsPower Law Graphs Power Law Random Graph (PLRG)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…
4.Topology Modeling
““Barabasi Model”Barabasi Model”• New node connect to node i with probabilityNew node connect to node i with probability
probability(iprobability(ij) = ki / kjj) = ki / kj
General linear preferenceGeneral linear preference• Greater flexibility in assigning preferenceGreater flexibility in assigning preference• By preference parameterBy preference parameter
Inet...Inet... ……
4.Topology Modeling
Topology constraints!Topology constraints! Technology:Technology:
• Processing speedProcessing speed• Either a Either a large number of low bandwidthlarge number of low bandwidth
connections, or a connections, or a small number of high small number of high bandwidthbandwidth connections… connections…
GeographyGeography• Connectivity driven by Connectivity driven by geographical proximitygeographical proximity
EconomyEconomy• Capacity of links is constrained by the Capacity of links is constrained by the capacity capacity
of nodesof nodes..• ““EconomizationEconomization””
4.Topology Modeling
Optimization Based Models Optimization Based Models HOT-1 Highly Optimized TolerancesHOT-1 Highly Optimized Tolerances
• Each new node solves the Each new node solves the local optimization local optimization problemproblem to find a target node to connect to…to find a target node to connect to…
HOT-2 Heuristically Optimized TradeoffsHOT-2 Heuristically Optimized Tradeoffs HOT-3: Variant of HOT-2HOT-3: Variant of HOT-2 ……
4.Topology Modeling
Traffic ModelTraffic Model ““Self-similarity” of Self-similarity” of Internet traffic Open Loop, Closed Loop, Combined…Open Loop, Closed Loop, Combined…
TCP ModelTCP Model ““Window Algorithm”, RED, SDE, …Window Algorithm”, RED, SDE, …
Topology ModelTopology Model ““Power Law”Power Law”
• Power Law Graph Power Law Graph Models…Models…
Topology constraintsTopology constraints• Optimization…Optimization…
5.Conclution
