Analysis and control of large-scale stochastic systems in queueing and finance

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。通常，对这些系统的精确分析是困难的，但有价值的见解通常可以通过适当的渐近近似来获得。在这个节目中，我们考虑三类问题。第一类是服务时间呈指数分布的多服务台排队网络的控制问题。我们研究了现有的渐近最优控制理论没有涵盖的情况。例如，这包括具有在代理数量上显著不同的服务站的网络。第二类研究服务时间为非指数分布的排队。我们计划将在指数设置下开发的现有控制框架扩展到一般分布的情况。我们还将讨论具有相关服务和耐心时间的队列的渐近性能分析，以及不在先到先服务原则下操作的队列。第三类问题出现在金融市场微观结构的研究中。我们将把流体和扩散近似应用到库存控制模型中，并研究存在极限订货簿的最优交易问题。

This proposal concerns the analysis of large-scale stochastic systems that arise in manufacturing and service systems, computer data systems and financial engineering. Typically, an exact analysis of these systems is intractable, but valuable insight can often be obtained via suitable asymptotic approximations. In this program we consider three classes of problems. The first deals with control of multi-server queueing networks with exponentially distributed service times. We investigate cases, which are not covered by the existing theory of asymptotically optimal control. This includes, for example, networks with service stations that significantly differ by the number of agents. Second class studies queues with non-exponential service time distribution. We plan to extend the existing control framework, developed in the exponential setting, to the case of general distribution. We will also address asymptotic performance analysis of queues with correlated service and patience times; and queues, which are not operated under first-come-first-served discipline. The third class of problems arises in the study of market microstructure in finance. We will apply fluid and diffusion approximations to models of inventory control; and also investigate a problem of optimal trading in a presence of limit order book.