1st Edition

Fundamentals of Stochastic Models

By Zhe George Zhang Copyright 2023
    814 Pages 116 B/W Illustrations
    by CRC Press

    Stochastic modeling is a set of quantitative techniques for analyzing practical systems with random factors. This area is highly technical and mainly developed by mathematicians. Most existing books are for those with extensive mathematical training; this book minimizes that need and makes the topics easily understandable.

    Fundamentals of Stochastic Models offers many practical examples and applications and bridges the gap between elementary stochastics process theory and advanced process theory. It addresses both performance evaluation and optimization of stochastic systems and covers different modern analysis techniques such as matrix analytical methods and diffusion and fluid limit methods. It goes on to explore the linkage between stochastic models, machine learning, and artificial intelligence, and discusses how to make use of intuitive approaches instead of traditional theoretical approaches.

    The goal is to minimize the mathematical background of readers that is required to understand the topics covered in this book. Thus, the book is appropriate for professionals and students in industrial engineering, business and economics, computer science, and applied mathematics.

    1. Introduction. Part I. Fundamentals of Stochastic Models. 2. Discrete-time Markov Chains. 3. Continuous-Time Markov Chains. 4. Structured Markov Chains. 5. Renewal Processes and Embedded Markov Chains. 6. Random Walks and Brownian Motions. 7. Reflected Brownian Motion Approximations to Simple Stochastic Systems. 8. Large Queueing Systems. 9. Static Optimization in Stochastic Models. 10. Dynamic Optimization in Stochastic Models. 11. Learning in Stochastic Models. Part II. Appendices: Elements of Probability and Stochastics. A. Basics of Probability Theory. B. Conditional Expectation and Martingales. C. Some Useful Bounds, Inequalities, and Limit Laws. D. Non-linear Programming in Stochastics. E. Change of Probability Measure for a Normal Random Variable. F. Convergence of Random Variables. G. Major Theorems for Stochastic Process Limits. H. A Brief Review on Stochastic Calculus. I. Comparison of Stochastic Processes - Stochastic Orders. J. Matrix Algebra and Markov Chains.


    Professor Zhe George Zhang is a professor of Management Science in the Department of Decision Sciences, at the College of Business and Economics, Western Washington University. He has published more than 110 papers in prestigious journals such as Management Science, Operations Research, Manufacturing & Service Operations Management, Production and Operations Management, IIE Transactions, IEEE Transactions, Queueing Systems, Journal of Applied Probability. Co-authored with N. Tian, he published the research monograph entitled Vacation Queueing Models – Theory and Applications in 2006 by Springer, which is the first book on this topic and has been widely cited since its publication. Professor Zhang is one of the Editors-in-Chief for Journal of the Operational Research Society, the first Operational Research journal in the world, and one of the founding Editors-in-Chief for new journal Queueing Models and Service Management and is on the editorial board of several international journals.