Analysis of Large-Scale Stochastic Systems

大规模随机系统分析

• 批准号: 1052750
• 负责人: Kavita Ramanan
• 金额: $ 32.49万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-02-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1052750&HistoricalAwards=false
• 关键词: Analysis; Large; Scale; Stochastic; Systems

This proposal concerns the analysis of large-scale stochastic systems that arise in manufacturing and service systems, computer data systems and financial engineering. Three broad classes of problems will be considered. The first involves the design, control and performance analysis of networks of multi-server systems with generally distributed service times. The effect of customer abandonement in these systems will also be considered. The second problem arises in the study of microstructure in finance. The research in this part of the proposal aims to introduce a rigorous model that will provide insight into the dynamics of limit order books. The last topic concerns the study of time-varying stochastic networks. Although a lot of work has been carried out in the study of homogeneous systems, most real- world applications exhibit non-negligible time-varying behavior. However, there is relatively little theoretical analysis of the control of these systems.The proposal aims to take a preliminary step towards establishing rigorous conditions under which the study of a simpler system can shed insight into the analysis of the time-varying network.If successful, the analysis on multi- server queues would provide guidelines for routing and staffing in call centers, as well as help assess the performance of computer data systems. The work on limit order books could lead to a better understanding of the effect that protocols governing an exchange have on important financial quantities such as the bid-ask spread. The study on time-varying stochastic systems would identify conditions under which simple heuristics may be used to construct near-optimal controls for more complex systems. In addition, the work in this proposal is likely to require the development of mathematical techniques in diverse areas, ranging from measure-valued processes and stochastic partial differential equations to large deviations and stochastic games, which would be of broader interest.

该提案涉及对制造和服务系统、计算机数据系统和金融工程中出现的大规模随机系统的分析。将考虑三大类问题。第一个涉及具有普遍分布式服务时间的多服务器系统网络的设计、控制和性能分析。还将考虑这些系统中客户放弃的影响。第二个问题出现在金融微观结构的研究中。该提案这一部分的研究旨在引入一个严格的模型，该模型将提供对限价订单簿动态的深入了解。最后一个主题涉及时变随机网络的研究。尽管在同质系统的研究中已经开展了大量工作，但大多数现实世界的应用都表现出不可忽略的时变行为。然而，对这些系统控制的理论分析相对较少。该提案旨在建立严格的条件，在该条件下对更简单的系统的研究可以深入了解时变网络的分析。如果成功，对多服务器队列的分析将为呼叫中心的路由和人员配置提供指导，并帮助评估计算机数据系统的性能。限价订单簿方面的工作可以让人们更好地理解管理交易所的协议对重要金融数量（例如买卖价差）的影响。对时变随机系统的研究将确定在哪些条件下可以使用简单的启发式方法为更复杂的系统构建近乎最优的控制。此外，该提案中的工作可能需要在不同领域发展数学技术，从测值过程和随机偏微分方程到大偏差和随机博弈，这将引起更广泛的兴趣。