AMC-SS: Measure Valued Processes and Stochastic Systems

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The PI proposes to study four problems on diffusion scaling limits and their applications to Internet congestion control models, queuing theory, and financial mathematics. Diffusion limits are ideal for capturing the random fluctuations of heavily loaded systems, which makes them a natural tool to study the variabliltiy of congestion in bandwidth sharing networks such as the Internet. Similar considerations suggest that diffusion limits are an appropriate tool for studying the behavior of the Shortest Remaining Processing Time (SRPT) policy being implemented in modern web servers. The variability of the queue length is paramount is such systems, which frequently operate near capacity. The PI will also study a model of continuous double auctions, such as those used in computerized financial markets, and identify conditions under which the model is arbitrage free.