AMC-SS: Measure Valued Processes and Stochastic Systems

PI提出研究四个扩散尺度限制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。扩散限制对于捕获重负载系统的随机波动是理想的，这使它们成为研究带宽共享网络（如Internet）中拥塞变化的自然工具。类似的考虑表明，扩散限制是研究在现代web服务器中实现的最短剩余处理时间（SRPT）策略行为的合适工具。对于这样的系统，队列长度的可变性是最重要的，因为它经常接近容量运行。PI还将研究连续双重拍卖的模型，如计算机化金融市场中使用的模型，并确定该模型无套利的条件。

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.