Analysis of Large-Scale Stochastic Systems

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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.