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

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Springer Science & Business Media, Jan 8, 2002 - Mathematics - 602 pages
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.
 

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Contents

Experiencing Statistical Regularity Iw_Dl
1
StochasticProcess Limits
23
2
48
Preservation of Pointwise Convergence
51
An Application to Simulation
73
The Framework for StochasticProcess Limits
75
A Panorama of StochasticProcess Limits 95
94
HeavyTraffic Limits for Queues
97
Fluid Queues with OnOff Sources
243
Errors Discovered in the Book
281
SingleServer Queues
287
Multiserver Queues 341
340
More on the Mathematical Framework
367
The Space D
391
Useful Functions
427
Queueing Networks
457

The Space D
113
HeavyTraffic Limits for Fluid Queues
137
Useful Functions
163
Unmatched Jumps in the Limit Process
193
Queueing Networks
195
More StochasticPro cess Limits
225
Nonlinear Centering and Derivatives
235
The Spaces E and F 515
514
References
541
Appendix A Regular Variation
569
Notation Index
577
Subject Index
585
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