The objective of this proposed research is to develop mathematical tools for the analysis and design of complex stochastic networks arising in telecommunications, computer and service systems. These networks are typically too complex to lend themselves to an exact analysis. The primary goal of this research is to develop new techniques for obtaining a variety of asymptotic approximations for these systems. Specifically, these include so-called fluid or first-order approximations that describe the mean behavior of the system, diffusion approximations that capture fluctuations around the mean, and large deviations approximations that provide estimates for the probabilities of rare events that are critical to the working of the system. These techniques will be applied to gain insight into the behavior of several concrete classes of networks. In particular, new admission control algorithms will be developed for so-called ?real-time? systems that process tasks with deadlines such as, for example, telecom systems carrying digitized voice and tracking systems. In addition, estimates of performance measures will be obtained for multi-server systems that arise in call centers. We will also investigate the equilibrium properties of networks with blocking (used to model mobile wireless networks), as well as the stability of networks utilizing so-called bang-bang controls. One of the mathematical challenges in analyzing stochastic networks is that they are often described by constrained processes that exhibit discontinuous transitions, and so much of the classical theory can no longer be applied. If successful, this research would provide a new set of mathematical tools for the analysis of such constrained processes, which could be of broader applicability. The research also has the potential to contribute to improving the design and control of real-time queueing networks, call centers and wireless networks, which could lead to greater economy in the running of these systems.
