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# Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions

## November 19 @ 4:00 pm - 5:00 pm

Ruth J Williams (University of California, San Diego)

E18-304

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**Abstract**:

Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network’s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions.

This talk is based on joint work with Yingjia Fu.

**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.