In a stochastic network, such as those in computer/telecommunications and manufacturing, discrete units move among a network of stations where they are processed or served. Randomness may occur in the servicing and routing of units, and there may be queueing for services. This book describes several basic stochastic network processes, beginning with Jackson networks and ending with spatial queueing systems in which units, such as cellular phones, move in a space or region where they are served. The focus is on network processes that have tractable (closed-form) expressions for the equilibrium probability distribution of the numbers of units at the stations. These distributions yield network performance parameters such as expectations of throughputs, delays, costs, and travel times. The book is 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. Assuming a graduate course in stochastic processes without measure theory, the emphasis is on multi-dimensional Markov processes. There is also some self-contained material on point processes involving real analysis. The book also contains rather complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queueing systems and space-time Poisson processes. This material is used in describing reversible networks, waiting times at stations, travel times and space-time flows in networks. Richard Serfozo received the Ph.D. degree in Industrial Engineering and Management Sciences at Northwestern University in 1969 and is currently Professor of Industrial and Systems Engineering at Georgia Institute of Technology. Prior to that he held positions in the Boeing Company, Syracuse University, and Bell Laboratories. He has held

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models.

The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes."

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system's data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models. The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.

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.