Ruth J. Williams

University of California, San Diego

Election Year: 2012
Primary Section: 32, Applied Mathematical Sciences
Secondary Section: 11, Mathematics
Membership Type: Member

Research Interests

Ruth Williams' current research concerns mathematical problems stemming from the challenges of analyzing and controlling the dynamics of stochastic models of complex networks. Such "stochastic networks" arise in a variety of applications in science and engineering, e.g., in systems biology, high-tech manufacturing, computer systems, telecommunications, transportation, and business service systems. Modern networks, such as the Internet, are often highly complex and heterogeneous, presenting interesting mathematical challenges for their analysis and control. Some aspects of Williams' work involve the development of general theory for broad classes of networks, while others focus on mathematical problems directly motivated by specific applications. As examples of the latter, Williams has recently analyzed models of the Internet to understand the effects of using fair bandwidth-sharing policies, and has developed theory to study coupled enzymatic processing in protein networks, in collaboration with researchers in synthetic biology. Some stochastic process aspects of her research include justifying the approximation of density dependent Markov chains by reflected diffusion processes, analyzing measure-valued processes used to track residual job sizes or ages of jobs in stochastic network models with resource sharing, solving singular diffusion control problems, and addressing foundational questions for reflected diffusion processes in non-smooth domains.

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