Experiencing Statistical Regularity Random Walks in Applications The Framework for Stochastic-Process Limits A Panorama of Stochastic-Process Limits Heavy-Traffic Limits for Fluid Queues Unmatched Jumps in the Limit Process More Stochastic-Process Limits Fluid Queues with On-Off Sources Single-Server Queues Multi-Server Queues More on the Mathematical Framework The Space D Useful Functions Queueing Networks The Spaces E and F Appendices
Experiencing Statistical Regularity * Random Walks in Applications * The Framework for Stochastic-Process Limits * A Panorama of Stochastic-Process Limits * Heavy-Traffic Limits for Fluid Queues * Unmatched Jumps in the Limit Process * More Stochastic-Process Limits * Fluid Queues with On-Off Sources * Single-Server Queues * Multi-Server Queues * More on the Mathematical Framework * The Space D * Useful Functions * Queueing Networks * The Spaces E and F * Appendices
From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
This book is about stochastic-process limits -- limits in which a sequence of stochastic processes converges to another stochastic process. These are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book will be of interest to researchers and graduate students working in the areas of probability, stochastic processes, and operations research.