Probability and Statistics in Complex Systems: Genomics, Networks, and Financial Engineering, September 1, 2003 - June 30, 2004

Organizers:

Christopher L. DeMarco
Department of Electrical and Computer Engineering
University of Wisconsin-Madison
demarco@engr.wisc.edu
http://www.engr.wisc.edu/ece/faculty/demarco_christopher.html

Thomas G. Kurtz
Center for Mathematical Sciences
University of Wisconsin-Madison
kurtz@math.wisc.edu
http://www.math.wisc.edu/~kurtz/

Ruth J. Williams
Department of Mathematics
University of California, San Diego
williams@math.ucsd.edu
http://math.ucsd.edu/~williams/

The tutorial will introduce some of the main issues in the design and operation of communication and power networks and will provide background helpful in understanding the material to be presented during the Workshop. While the connectivity of power and communications networks may be similar, the physics of these networks is very different. The tutorial and the following workshop should provide a better understanding of both the similarities and the differences in these systems.

TUTORIAL SCHEDULE
SUNDAY, MARCH 7, All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30	Coffee and Registration	Reception Room EE/CS 3-176
9:00 AM	Douglas N. Arnold, Scot Adams, and Organizers	Welcome and Introduction
9:15-10:15 AM	Christopher L. DeMarco	Models for the Electric Power Grid Slides:   pdf
10:45-12:00 Noon	R. Srikant	The Architecture of the Internet Slides:   html   pdf    ps    ppt
1:30-2:45 PM	Christopher L. DeMarco	Cascading Failures in Power Networks Slides:   pdf
3:15-4:30 PM	R. Srikant	Pricing and Control of the Internet Slides:   html   pdf    ps    ppt
4:30 PM	Questions and Further Discussion

Abstracts

Network Control, Pricing, and the Role of Cascading Failure Phenomena in Electric Power Grids
Christopher L. DeMarco, University of Wisconsin - Madison

While sharing a number of broad qualitative features with problems in control and resource allocation for other large scale networks such as the internet, electric power grids present a range of unique challenges. Three major technological characteristics distinguish control and pricing problems in electric power: (i) the commodity being delivered is inefficient to store, so production tracks consumption across the entire interconnected grid, nearly instantaneously; (ii) the majority of branches in the delivery network are passive elements, with branch flows dictated by nonlinear relations to nodal boundary conditions, rather than by direct control; (iii) many constraints on operation represent physical limits whose violation can yield costly equipment damage and threats to human safety. Adding to the complexity of analysis is the U.S. electric power system's uneven regulatory policy transition, in which certain physical elements contributing to grid control operate in competitive markets (generators), while the others (e.g., switched capacitor banks, adjustable tap transformers) operate under the authority of regulated regional transmission monopolies.

This tutorial will give an overview of the mathematical models used to predict both dynamic and steady state performance of physical quantities in the electric power grid. Starting from the nonlinear constraints on network power flow, and the nature of financial offers and bids for electric power production and consumption, the relation of so-called "locational marginal prices" to an underlying optimization formulation will be reviewed. Issues in developing effective offer and bid strategies from these locational prices, and related issues for setting regulatory structures to govern these, will be highlighted. The tutorial will conclude with an overview of techniques for predicting cascading failure phenomena. Research to improve these techniques could play a key role in balancing operational strategies that favor efficiency under "normal" conditions, versus strategies that favor mitigation of risk of extremely high cost, low probability failure events such as the eastern U.S. blackout of August 2003.

Pricing and Control for the Internet
R. Srikant, University of Illinois, Urbana-Champaign

In the first part of the tutorial, we will present a general introduction to the architecture of the Internet. Various protocols for scheduling, admission control, routing and congestion control will be introduced. We will then focus our attention on TCP, the widely-used protocol for file transfer in the Internet today. Jacobson's TCP congestion control algorithm has been remarkably successful in regulating file transfers and facilitating the phenomenal growth of the Internet over the last decade. This congestion control mechanism was designed for networks where the required data rate per user is small (less than one Mbps) and the round-trip times are small (of the order of a few milliseconds). However, access speeds, application requirements and file transfer distances continue to increase. Using simple tools from queueing theory and delay-differential equations, we will illustrate the need to redesign the congestion management mechanisms in the Internet to efficiently deliver high data rates over long distances.

In the second part of the tutorial, we will concentrate on pricing and control mechanisms that have recently led to the design of scalable TCP protocols. Starting with Kelly's model of resource allocation in a heterogeneous Internet, it will be shown that congestion management can be viewed as a distributed algorithm for fair resource allocation in the Internet. We will illustrate the use of tools from convex optimization, stochastic processes and control theory in designing congestion control mechanisms at the end users and congestion indication mechanisms at the routers that deliver an efficient loss-free, delay-free service over the Internet.

LIST OF CONFIRMED PARTICIPANTS

NAME	DEPARTMENT	AFFILIATION
Scot Adams	Institute for Mathematics and its Applications	University of Minnesota
Inkyung Ahn	Department of Mathematics	Korea University
Greg Anderson	School of Mathematics	University of Minnesota
Douglas Arnold	Institute for Mathematics and its Applications	University of Minnesota
Donald Aronson	Institute for Mathematics and its Applications	University of Minnesota
Gerard Awanou	Institute for Mathematics and its Applications	University of Minnesota
Karen Ball	Institute for Mathematics and its Applications	University of Minnesota
Antar Bandyopadhyay	Institute for Mathematics and its Applications	University of Minnesota
Maury Bramson	School of Mathematics	University of Minnesota
James Carson		RisQuant Energy
Michael Chen	Coordinated Science Laboratory	University of Illinois at Urbana-Champaign
Wanyang Dai	Department of Mathematics	Nanjing University
Christopher DeMarco	Department of Electrical and Computer Engineering	University of Wisconsin-Madison
Shi-Jie Deng	Department of Industrial and Systems Engineering	Georgia Institute of Technology
Shmuel Friedland	Department of Mathematics, Statistics, and Computer Science	University of Illinois at Chicago
Tim Garoni	Institute for Mathematics and its Applications	University of Minnesota
Art Guetter	Department of Mathematics	Hamlin University
Bruce Hajek	Department of Electrical and Computer Engineering	University of Illinois at Urbana-Champaign
Chuan-Hsiang Han	Institute for Mathematics and its Applications	University of Minnesota
Naresh Jain	School of Mathematics	University of Minnesota
Ramesh Johari	Laboratory for Information and Decision Systems	Massachusetts Institute of Technology
Lili Ju	Institute for Mathematics and its Applications	University of Minnesota
Herve Kerivin	Institute for Mathematics and its Applications	University of Minnesota
Peter Key		Microsoft Research
Mohammad Khan	Department of Mathematics	Kent State University
Hye-Ryoung Kim		Seoul National University
Thomas Kurtz	Department of Mathematics	University of Wisconsin-Madison
Peter Kuznia		Hamline University
Nam Lee	Department of Mathematics	University of California, San Diego
Ioannis Lestas	Department of Engineering	University of Cambridge
David McDonald	Department of Mathematics	University of Ottawa
Richard McGehee	School of Mathematics	University of Minnesota
Sean Meyn	Department of Electrical and Computer Engineering	University of Illinois at Urbana-Champaign
Haewon Nam	Institute of Mathematics and Statistics	University of Minnesota
Amir Niknejad	Department of Mathematics	University of Illinois at Chicago
Asuman Ozdaglar	Department of Electrical Engineering and Computer Science	Massachusetts Institute of Technology
Lea Popovic	Institute for Mathematics and its Applications	University of Minnesota
Kavita Ramanan	Department of Mathematical Sciences	Lucent Technologies Bell Laboratories
Martin Reiman	Bell Laboratories	Lucent Technologies Bell Laboratories
Grzegorz Rempala	Department of Mathematics	University of Louisville
Sara Robinson		SIAM
Fadil Santosa	Institute for Mathematics and its Applications	University of Minnesota
Arnd Scheel	School of Mathematics	University of Minnesota
R. Srikant	Department of Electrical and Computer Engineering	University of Illinois at Urbana-Champaign
Cortin Stelter		Hamline University
Tamon Stephen	Institute of Mathematics and its Application	University of Minnesota
Hui Wang	Division of Applied Mathematics	Brown University
Jing Wang	Institute for Mathematics and its Applications	University of Minnesota
Ruth Williams	Department of Mathematics	University of California, San Diego
Yuhong Yang	Department of Statistics	Iowa State University
William Yurcik	Department of NCSA	University of Illinois at Urbana-Champaign
Ofer Zeitouni	School of Mathematics	University of Minnesota
Jun Zhao	Institute of Mathematics and its Application	University of Minnesota
Ilze Ziedins	Department of Statistics	University of Auckland