Regenerative processes are a popular subject in pure and applied probability, as well as in engineering (particularly simulation). This book provides important insight into new methods for investigating regenerative processes. Quantitative estimates play the key role in the book, and all developed methods support possibilities for obtaining such estimates, including probability metrics, test functions, crossing, and coupling. These methods are applied to a variety of problems, such as Markov chains, simulation, queueing systems, storage, and reliability. The book illustrates a unique application of the theory of probability metrics for examining regenerative processes, and it elaborates on the criteria required for uniform-in-time stability of wide sense regenerative processes. New accurate bounds of distribution functions of first occurrence times for regenerative models are also presented.
"This is a well-written book on a very specialized topic…useful for students and researchers in this area."
- Publication of the International Statistical Institute
"This book, written by a famous expert in renewal and queueing theories, can serve as an excellent handbook on regenerative processes, and also can be helpful for graduate courses."
- Mathematical Reviews (American Mathematical Society), Issue 96d
Crossing and Coupling
Ergodicity and Comparison
First Occurrence Times