HOTELLING LECTURES
UNIVERSITY OF NORTH CAROLINA, CHAPEL HILL
NOVEMBER 1-5, 2004
The Hotelling Lectures are an annual event at the University of North Carolina, Chapel Hill, featuring three talks by a guest speaker. The first lectures were given by David R. Cox in 1980, and in subsequent years by Herman Chernoff, Ole Barndorff-Nielsen, Frank Hampel, David Brillinger, David Kendall, Persi Diaconis, Pal Revesz, Willem van Zwet, C.R. Rao, Bradley Efron, Lucien LeCam, Peter Bickel, Ulf Grenander, Larry Shepp, David Donoho, David Siegmund, Herbert Robbins, Lawrence D. Brown, Nancy Reid, S.R.S. Varadhan, Stuart Geman, Iain Johnstone and Peter Hall. The 2004 Hotelling Lectures will be given by Professor Ruth Williams of the University of California at San Diego.
STOCHASTIC PROCESSING NETWORKS
R. J. Williams, Professor of Mathematics, UCSD

Stochastic processing networks arise as models in manufacturing, telecommunications, computer systems and the service industry. Common characteristics of these networks are that they have entities, such as jobs, customers or packets, that move along routes, wait in buffers, receive processing from various resources, and are subject to the effects of stochastic variability through such quantities as arrival times, processing times, and routing protocols. Networks arising in modern applications are often highly complex and heterogeneous. Typically, their analysis and control present challenging mathematical problems. One approach to these challenges is to consider more approximate models.

In the last 15 years, significant progress has been made on using approximate models to understand the stability and performance of a class of stochastic processing networks called open multiclass queueing networks. First order (functional law of large numbers) approximations called fluid models have been used to study the stability of these networks, and second order (functional central limit theorem) approximations which are diffusion models, have been used to analyze the performance of heavily congested networks. The interplay between these two levels of approximation has been an important theme in this work.

In contrast to this progress, optimal control of multiclass queueing networks is an active area of research, and performance analysis and optimal control of more general stochastic processing networks are still in their early stages of development.

These three Hotelling lectures will progress from motivating the study of stochastic processing networks, through describing some significant developments of the last 15 years, and will end with some current research on the control of these networks. The three lectures will be as follows. (Click on the titles to find the talks. Copyright Ruth Williams 2004. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams@math.ucsd.edu for this.)

  • Stochastic Processing Networks: What, Why and How? This lecture will explain what a stochastic processing network is, why such networks models are of interest in applications, and outline some approaches to the analysis and control of these networks.
  • Multiclass Queueing Networks: Progress and Surprises of the Past 15 Years. This lecture will review developments of the last 15 years which have resulted in a useful approach to analyzing the stability and performance of open multiclass queueing networks.
  • Control of Stochastic Processing Networks: More Questions than Answers. This lecture will describe some of the theory that has been developed concerning the control of stochastic processing networks. Illustrative examples will be used throughout. A variety of open problems will be described.