This book provides a systematic treatment of continuous-time Markov chains and their applications, particularly focusing on systems arising in queueing theory, control, optimization, and manufacturing. The author, Qing Zhang, utilizes a singular perturbation approach to explore these complex systems, consolidating scattered ideas from the literature into a cohesive framework. The work details asymptotic expansions of probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality, with a specific emphasis on Markov chains exhibiting weak and strong interactions and their structural properties. Much of the content is derived from the author's recent research, with some results appearing for the first time.

This book is positioned as an important reference for researchers in applied mathematics, probability, stochastic processes, operations research, control theory, and optimization. Its systematic treatment of singularly perturbed systems and consolidation of disparate literature suggest it aims to be a comprehensive resource for advanced study and research. The inclusion of recent, and in some cases unpublished, research indicates its value for those at the forefront of these fields. The technical depth implied by the topics covered points to a readership of specialists and academics.