Wednesday, October 24, 2018 - 4:00pm to Thursday, October 25, 2018 - 4:55pm
Event Calendar Category
Other LIDS Events
Speaker Name
Ruth J. Williams
Affiliation
University of California, San Diego
Building and Room Number
32-D677
Abstract
Host: Devavrat Shah (LIDS)
Random order of service (ROS) is a natural scheduling policy for queueing systems where there is no implicit ordering of jobs. Applications in which ROS arises include the processing of biological molecules in a cell with limited resources. Indeed, multiclass queues with ROS and reneging have been used to gain insights into correlations between different types of proteins processed by a common enzyme in E. Coli cells. To date, this analysis has relied on exact results that assume exponential distributions for processing and patience times. It is desirable to have methods for analyzing such systems when these distributions are more general, especially to accommodate lengthy biological operations such as binding/unbinding, folding, transcription and translation.
In this talk we will consider a multi-class queueing model with reneging operating under ROS and with generally distributed interarrival, processing and patience times. We will use measure-valued processes to describe the dynamic evolution of the model, and establish a fluid approximation for this representation. Obtaining a fluid limit for this network requires a multi-scale analysis of its fast and slow components. We further study the asymptotic behavior of fluid model solutions as time goes to infinity.
Biography
Ruth Williams holds the Charles Lee Powell Chair in Mathematics I at the University of California, San Diego (UCSD). She is a mathematician who works in probability theory, especially on stochastic processes and their applications. She is particularly known for her foundational work on reflecting diffusion processes in domains with corners, for co-development with Maury Bramson of a systematic approach to proving heavy traffic limit theorems for multiclass queueing networks, and for the development of fluid and diffusion approximations for the analysis and control of more general stochastic networks, including those described by measure-valued processes. Her current research includes the study of stochastic models of complex networks, for example, those arising in Internet congestion control and systems biology.
Williams studied mathematics at the University of Melbourne where she earned her Bachelor of Science (Honours) and Master of Science degrees. She then studied at Stanford University where she earned her Ph.D. degree in Mathematics. She had a postdoc at the Courant Institute of Mathematical Sciences in New York before taking up a position as an Assistant Professor at the University of California, San Diego (UCSD). She has remained at UCSD during her career, where she is now a Distinguished Professor of Mathematics.
Ruth Williams is an Elected Member of the US National Academy of Sciences, an Elected Fellow of the American Academy of Arts and Sciences, an inaugural Fellow of the American Mathematical Society, a Fellow of the Institute for Operations Research and the Management Sciences, a Fellow of the American Association for the Advancement of Sciences, and a Fellow of the Institute of Mathematical Statistics. She is also a Fellow of St. Hilda's College at the University of Melbourne, and received an honorary Doctor of Science degree from La Trobe University in Australia. Williams has been a Guggenheim Fellow, an Alfred P. Sloan Fellow and a National Science Foundation Presidential Young Investigator. She delivered a 45-minute invited address at the International Congress of Mathematicians in 1998. In 2007, Williams received the Best Publication Award of the INFORMS Applied Probability Society, jointly with Amber Puha and H. Christian Gromoll. In 2012, Williams served as President of the Institute of Mathematical Statistics, a major international professional society for the development and dissemination of the theory and applications of probability and statistics. In 2016, Williams was awarded the John von Neumann Theory Prize by the Institute for Operations Research and the Management Sciences, jointly with Martin I. Reiman. At the annual INFORMS meeting in 2017, she was awarded the 2017 Award for the Advancement of Women in Operations Research and the Management Sciences. In 2018, Williams was elected as a Corresponding Member of the Australian Academy of Science.