Continuous-time Markov Chains and Applications: A Singular Perturbation Approach

This is author-approved bcc which should be copy-edited: This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in Markov chains and singular perturbations which are scattered throughout the literature. It presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. The emphasis is on Markov chains with weak and strong interactions and structural properties. To bridge the gap between theory and applications, a large portion of the book is devoted to various applications in controlled dynamic systems, production planning, and numerical methods for control and optimization. It aims at the reduction of dimensionality for problems under Markovian disturbances and provides tools for dealing with large -scale and complex real-world problems. Much of the content is an outgrowth of the authors' recent research. Some of the results have not appeared elsewhere. The book will be an important reference for researchers in applied mathematics, probabilty and stochatic processes, operations research, control theory, and optimization.