**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**