STOCHASTIC PROCESSING NETWORKS
R. J. WILLIAMS, PROFESSOR OF MATHEMATICS
UNIVERSITY OF CALIFORNIA, SAN DIEGO
This series of lectures will be held at the University of Melbourne, 4.15-6.15 P.M. on September 4, 5,6, 2006. The first lecture is in Redmond Barry Building, Lowe Theatre. THe second lecture is in Latham Theatre, Redmond Barry Building. The series is jointly sponsored by the Maurice H. Belz fund and the Center of Excellence for Mathematics and Statistics of Complex Systems (MASCOS).
ABSTRACT

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 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 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 topics.

  • Some notes to accompany the presentations. These notes include some exercises for students.

    Powerpoint Slides:

  • Stochastic Processing Networks: What, Why and How? For a black and white printable copy, click here.
  • Open Multiclass HL Queueing Networks: Progress and Surprises of the Past 15 Years. For a black and white printable copy, click here.
  • Control of Stochastic Processing Networks: Some Theory and Examples. For a black and white printable copy, click here.

    For a review of Stochastic Processing Networks, click here.

    Copyright R. J. Williams 2006. All print and electronic rights and use rights reserved. Personal, non-commerical use only, for individuals with permission from author --- write to williams at math dot ucsd dot edu for this.)

    Last updated September 28, 2006.