Reflected Brownian Motions, Stochastic Networks, and their Applications

Stochastic network models are the subject of a rich and varied mathematical theory, with a long tradition and a vibrant body of applications. This special workshop will bring together mathematicians and applied researchers who share an interest in stochastic network models and will highlight areas of greatest current activity. The workshop will also provide an opportunity to honor Ruth J. Williams, Distinguished Professor of Mathematics at the University of California, San Diego, who has been one of the most important contributors to the targeted research area.

Stochastic networks have been used to model manufacturing systems, call centers, health care systems, and most notably, a wide variety of electronic communication systems, including the Internet, wireless and wireline networks, sensor networks, and ad hoc networks. There have been many important developments associated with stochastic networks in recent decades, specifically, semimartingale reflected Brownian motions (SRBMs) in polyhedral state spaces have enjoyed extensive study. Such diffusion processes arise as heavy traffic approximations for multiclass queueing networks, as well as more complex networks. Advances have also taken place in stability theory based on fluid limit models, fixed point theory for networks, large deviations theory for networks, self-similarity in networks, stochastic geometry of networks, gossip based information dissemination, and network information theory.

These topics are well represented in the recent work of the invited speakers. The workshop will also include discussions in related areas, such as the  exciting new applications of stochastic networks in molecular biology.