Stochastic Modeling and Optimization

Stochastic Modeling and Optimization Synopsis

The objective of this volume is to highlight through a collection of chap- ters some of the recent research works in applied prob ability, specifically stochastic modeling and optimization. The volume is organized loosely into four parts. The first part is a col- lection of several basic methodologies: singularly perturbed Markov chains (Chapter 1), and related applications in stochastic optimal control (Chapter 2); stochastic approximation, emphasizing convergence properties (Chapter 3); a performance-potential based approach to Markov decision program- ming (Chapter 4); and interior-point techniques (homogeneous self-dual embedding and central path following) applied to stochastic programming (Chapter 5). The three chapters in the second part are concerned with queueing the- ory. Chapters 6 and 7 both study processing networks - a general dass of queueing networks - focusing, respectively, on limit theorems in the form of strong approximation, and the issue of stability via connections to re- lated fluid models. The subject of Chapter 8 is performance asymptotics via large deviations theory, when the input process to a queueing system exhibits long-range dependence, modeled as fractional Brownian motion.