Lecture 6: Scaling and Dynamic Randomness; Poisson Processes

Handouts

Whitt’s Slides (PDF-600KB)
The Failure of Poisson Modeling, By Paxson and Floyd (PDF-2MB)
Internet Traffic Tends Toward Poisson and Independent as the Load Increases, By Cao, Cleveland, Lin and Sun (PDF-244KB)
A Nonstationary Poisson View of Internet Traffic, By Karagiannis, Molle, Faloutsos and Broido (PDF-3MB)
How Competition Can Generate Poisson Arrivals, By Lariviere and Van-Mieghem (PDF-320KB)
Traffic Delays at Toll Booths, By Leslie C. Edie (PDF-1.09MB)
The Best Linear Unbiased Estimator for Continuation of a Function, By Goldberg, Ritov and Mandelbaum (PDF-363KB)
Characterizing Normal Operation of a Web Server: Application to Workload Forecasting and Problem Detection, By Hellerstein, Zhang and Shahabuddin (PDF-273KB)
Reading Packet for Dynamic Randomness:
- Hall, Chapter 3: The Arrival Process. (PDF-1.5MB) The chapter covers properties of the Poisson process, as a model for random arrivals at a constant rate, as well as goodness-of-fit tests and parameter estimation. (Time-varying rates are covered later, in Chapter 6: Nonstationary Arrivals (PDF-1.5MB).)
- Whitt’s book: Stochastic Process Limits, Springer 2002. An Internet copy of the book. Chapter 1 is the most relevant: we shall cover parts of it in class. (I recommend a review through Whitt’s very nice slides, from an IEOR course at Columbia University (PDF-600KB)).