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

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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. 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.