CARNEGIE MELLON UNIVERSITY

Department of Mathematical Sciences

Mathematical Sciences Colloquium

Ruth Williams

Mathematics Department

University of California, San Diego

Friday, April 16, 2004

4:30 P.M., Wean Hall 7500

Refreshments at 4:00, Wean 6220

From Queueing Networks to

Reflecting Diffusions

ABSTRACT:

Multiclass queueing networks are used as models for complex manufacturing, telecommunications and computer systems. 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 that are subject to the effects of stochastic variability through such variables as arrival times, processing times, and routing protocols. These networks can be highly complex and heterogeneous. They often cannot be analyzed exactly and one is naturally led to consider approximate models for their analysis. In the past 15 years, a extensive mathematical theory has been developed for using fluid (functional law of large numbers) and diffusion (functional central limit theorem) approximations to analyze the stability and performance of a

large category of open multiclass queueing networks, namely those operating under head-of-the-line (HL) service disciplines. This talk will describe some highlights and surprises in the development of this theory.

BIOSKETCH:

Ruth Williams is a Professor of Mathematics at the University of California at San Diego (UCSD). Her research interests are in probability, stochastic processes and their applications. She is a Fellow of the American Association for the Advancement of Science and the Institute of Mathematical Statistics. Ruth Williams has been a U.S. National Science Foundation (NSF) Presidential Young Investigator (1987-93), an Alfred P. Sloan Fellow (1988-92), a Guggenheim Fellow (2001-2002) and was an invited speaker at the International Congress of Mathematicians held in Berlin in 1998.

Ruth Williams received her Bachelor of Science (Honors) and Master of Science degrees at the University of Melbourne, Australia, in 1977 and 1979, respectively, and she earned her Ph.D. degree in Mathematics from Stanford University in 1983.