Measurement, Modeling, and Analysis of the Internet: Part II

Overview

Part II.a: Traffic modeling

Traffic Modeling

Slide 5

Extract from abstract

Properties of Self-Similarity

What went wrong? What next?

Explanations of LRD

Open loop models

Cox’s construction

M/G/ ¥ traffic model

Where are the heavy tails though…

Crovella dataset

Picture seemed complete..

Problems with open loop models

Closed loop models

Why is closed loop important?

Chaos?

Chaotic dynamics

Chaos continued..

Verification of TCP induced LRD

Another TCP based model

Model

Combined (structural) models

Recent (and not so) thoughts on traffic modeling

From traces to traffic models

Example of web traffic modeling

Consider independent Markov on-off processes

Wavelet plot (PSD) of LRD vs Markovian

Relating layers to traffic generation

The thousand word picture

Part II.b: Fluid modeling of TCP

Outline

Slide 35

TCP Congestion Control: window algorithm

Slide 37

Background:

Loss modeling

Trace analysis

Scatter plot of statistic

Experiment 1

Experiment 2

Experiment 3

Experiment 4

SDE based model

Slide 47

Active Queue Management:RED

The RED mechanism

Loss Model

Slide 51

System of Differential Equations (cont.)

Closed loop

Slide 54

Control theoretic analysis

Block diagram view

Small Signal model

Immediate insights

(Control) Theory based parameter tuning

PI Controller performance

UNC Testbed

Slide 62

Slide 63

Recent fluid limits

Continuous setting

Discrete setting

Srikant et al.

Slide 68

Slide 69

Other applications of fluid models

Part II.c: Topology modeling

Why study topology?

Internet topologies

More on topologies..

Early work

Real world topologies

So…are we done?

Power laws in AS level topology

Power Laws

Power Laws

Power Laws

Power Laws

Power Laws

GT-ITM abandoned..

Generating power law graphs

Power law random graph (PLRG) (Aiello et al)

Inet  (Chen et al)

Barabasi model: fixed exponent

General linear preference

“Scale-free” graphs

Is the router-level Internet graph scale-free?

Topology constraints

Optimization based models for topology

Fabrikant HOT

Modified Fabrikant HOT

Thanks