Big Queues

Ayalvadi Ganesh, Neil O’Connell, Damon Wischik (auth.)9783540209126, 3540209123

Big Queues aims to give a simple and elegant account of how large deviations theory can be applied to queueing problems. Large deviations theory is a collection of powerful results and general techniques for studying rare events, and has been applied to queueing problems in a variety of ways. The strengths of large deviations theory are these: it is powerful enough that one can answer many questions which are hard to answer otherwise, and it is general enough that one can draw broad conclusions without relying on special case calculations.

Table of contents :
Front Matter….Pages I-XI
1. The Single Server Queue….Pages 1-21
2. Large Deviations in Euclidean Spaces….Pages 23-45
3. More on the Single Server Queue….Pages 47-55
4. Introduction to Abstract Large Deviations….Pages 57-76
5. Continuous Queueing Maps….Pages 77-104
6. Large-Buffer Scalings….Pages 105-150
7. Many-Flows Scalings….Pages 151-181
8. Long Range Dependence….Pages 183-198
9. Moderate Deviations Scalings….Pages 199-209
10. Interpretations….Pages 211-238
Bibliography….Pages 239-248
Back Matter….Pages 249-254