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

这个建议涉及的分析大规模随机系统中出现的制造和服务系统，计算机数据系统和金融工程。通常，这些系统的精确分析是棘手的，但有价值的见解往往可以通过适当的渐近近似获得。在这个程序中，我们考虑三类问题。第一个问题是服务时间服从指数分布的多服务器排队网络的控制问题。我们调查的情况下，这是不包括由现有的渐近最优控制理论。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服从非指数分布的排队系统。我们计划扩展现有的控制框架，在指数设置，一般分布的情况下。我们还将解决相关的服务和耐心时间的队列的渐近性能分析，和队列，这是不是先到先得的纪律下操作。第三类问题出现在金融市场微观结构的研究中。我们将应用流体和扩散近似的库存控制模型，并探讨了最优交易的问题，在限价订单簿的存在。

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.