Lecture 6: Scaling and Dynamic Randomness; Poisson Processes

Handouts

Whitt’s Slides
The Failure of Poisson Modeling, By Paxson and Floyd
Internet Traffic Tends Toward Poisson and Independent as the Load Increases, By Cao, Cleveland, Lin and Sun
A Nonstationary Poisson View of Internet Traffic, By Karagiannis, Molle, Faloutsos and Broido
How Competition Can Generate Poisson Arrivals, By Lariviere and Van-Mieghem
Traffic Delays at Toll Booths, By Leslie C. Edie
The Best Linear Unbiased Estimator for Continuation of a Function, By Goldberg, Ritov and Mandelbaum
Characterizing Normal Operation of a Web Server: Application to Workload Forecasting and Problem Detection, By Hellerstein, Zhang and Shahabuddin
Reading Packet for Dynamic Randomness:
- Hall, Chapter 3: The Arrival Process. 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).
- 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).