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Stochastic Process Limits 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 emphasizes the continuous-mapping approach to obtain new stochastic-process limits from previously established stochastic-process limits. The continuous-mapping approach is applied to obtain heavy-traffic-stochastic-process limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavy-traffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. The book will be of interest to researchers and graduate students working in the areas of probability, stochastic processes, and operations research. In addition this book won the 2003 Lanchester Prize for the best contribution to Operation Research and Management in English, see: http://www.informs.org/Prizes/LanchesterPrize.html
Content Level »Research
Keywords »Approximation - Queueing - Queueing Theory - STATISTICA - Stochastic Processes - Stochastic-Process Limits - fluid queue - linear optimization - operations research - random walk - stochastic process
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