Introduction to Stochastic Networks

Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable expressions for the equilibrium probability distribution of the numbers of units at the stations. Intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years, the text assumes a graduate course in stochastic processes without measure theory, emphasising multi-dimensional Markov processes. Alongside self-contained material on point processes involving real analysis, the book also contains complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queuing systems and space-time Poisson processes.

From the reviews: JOURNAL OF APPLIED MATHEMATICS AND STOCHASTIC ANALYSIS "…integral to today’s development of analytical methods for queuing networks…[collects] an interesting summary of what one might view as the heart of network theory." JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION "The book provides self-contained introductions to point processes and Palm probabilities, a point that I emphasize because these parts are extremely well-presented and might also be valuable for readers not particularly interested in stochastic networks…Serfozo has certainly written a book that is unique in its choice of topics and captures the most recent developments in research in stochastic networks. I recommend it to all mathematically interested readers in this area. I found the book extremely well written, with many insightful explanations that make it a pleasure to read. The notations used are very elegant and intuitive…thoroughly edited with very few typographical errors."