Analysis of Large-Scale Stochastic Systems

这项建议涉及大规模随机系统的分析，这些系统出现在制造和服务系统、计算机数据系统和金融工程中。我们将考虑三大类问题。第一类是服务时间一般分布的多服务器系统网络的设计、控制和性能分析。这些系统中客户放弃的影响也将被考虑。第二个问题出现在金融微观结构的研究中。提案中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指令账簿动态的洞察。最后一个主题是关于时变随机网络的研究。虽然在齐次系统的研究中已经开展了大量的工作，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，对这些系统的控制的理论分析相对较少。该提案旨在朝着建立严格的条件迈出初步的一步，在这种条件下，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线选择和人员配备提供指导，并有助于评估计算机数据系统的性能。对限价指令账簿的研究可能有助于更好地理解监管交易所的协议对买卖价差等重要金融数量的影响。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算法来为更复杂的系统构造接近最优的控制。此外，这项提议中的工作可能需要在不同领域发展数学技术，从测量值过程和随机偏微分方程式到大偏差和随机博弈，这些都将引起更广泛的兴趣。

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.