ABSTRACT
Stochastic models are widely used to analyze and optimize healthcare, communication, large-scale computing, and transportation systems. Existing theory has tended to focus on easier-to-analyze homogeneous models that assume that service requirements are identical for all users. Recent technological trends have made it possible to collect large amounts of data that show that users' requirements are often heterogeneous. Thus, a theory of nonhomogeneous stochastic models is needed. The goal of this project is develop a theory of "transitory stochastic models" that explicitly incorporates users' inhomogeneity and, concomitantly, considers the optimization and control of these models. If successful, this project will contribute to the theoretical understanding of nonhomogeneous stochastic systems, and the application of the theoretical results can potentially result in significant performance gains in the operational management of many service systems. Furthermore, ideas from this project will be incorporated into a new stochastic modeling course for undergraduates that integrates theory, data modeling and optimization. The PI will also leverage summer research programs to facilitate research experiences for minority and female undergraduate students.

The theoretical objective of this research is to develop stochastic process and analytical approximations for the performance analysis and optimization of transitory stochastic models. The models considered include systems with many servers, queueing networks, and systems with heavy-tailed service times and non-stationary, correlated traffic. The systems are transitory in the sense that we are interested in predictions over a finite, but operationally significant time horizon, and the models require a purely transient analysis, which is non-trivial even in the simpler cases. The research has twin related foci: first, this effort will identify novel scaling regimes in which "universal" stochastic process approximations to the traffic and workload processes can be established, in the form of functional central limit theorems, strong approximations and conditioned limit theorems. Second, the research will also consider the identification of optimal controls for the underlying systems using these stochastic process approximations. The focus here will be on developing analytical approximations to the expected cost functions and identifying an accompanying notion of asymptotic optimality of controls.