Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues

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 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. This book was the recipient of the 2003 INFORMS Frederick W. Lanchester Prize, awarded annually by the Institute for Operations Research and the Management Sciences (INFORMS) for the best contribution to operations research and the management sciences published in English.