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.

A classical queueing model consists of three parts - arrival process, service process, and queue discipline. However, a vacation queueing model has an additional part - the vacation process which is governed by a vacation policy - and a vacation policy can be characterized by three aspects: 1) vacation start-up rule; 2) vacation termination rule, and 3) vacation duration distribution. Hence, vacation queueing models are an extension of classical queueing theory.

Vacation Queueing Models: Theory and Applications discusses systematically and in detail the many variations of vacation policy. These discussions include: General Service Single Server Vacation Models (Exhaustive and Non-Exhaustive Service Type), General Input Single Server Vacation Models, Markovian Multi-Server Vacation Models, General Input Multi-Server Vacation Models, Optimization in Vacation Models, and Applications of Vacation Models.

By allowing servers to take vacations makes the queueing models more realistic and flexible in studying real-world waiting line systems. Integrated in the book's discussion are a variety of typical vacation model applications. These applications include call centers with multi-task employees, customized manufacturing, telecommunication networks, maintenance activities, etc. Finally, contents are present in a "theorem and proof" format and it is invaluable reading for operations researchers, applied mathematicians, statisticians; industrial, computer, electrical and electronics, and communication engineers; computer, management scientists; and graduate students in the above disciplines.

This book discusses systematically the many variations of vacation policy. The book discusses a variety of typical vacation model applications. The presentation style is unique compared with the books published in the same field a "theorem and proof" format is used. Also, this is the first time G1/M/1 multi-server vacation models, both continuous and discrete, and the optimization and control issues have been presented in book form.