AMC-SS: Measure Valued Processes and Stochastic Systems

PI建议研究扩散比例限制的四个问题及其在互联网拥塞控制模型、排队论和金融数学中的应用。扩散极限是捕捉重载系统随机波动的理想工具，这使其成为研究带宽共享网络(如互联网)中拥塞变量的自然工具。类似的考虑表明，扩散限制是研究在现代Web服务器中实施的最短剩余处理时间(SRPT)策略的行为的合适工具。队列长度的可变性对这样的系统至关重要，这些系统经常在接近容量的情况下运行。投资促进局还将研究连续双向拍卖的模型，例如计算机化金融市场中使用的模型，并确定该模型在哪些条件下是无套利的。

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.