Past Awards
- “Big Queues,” Springer-Verlag, Lecture Notes in Mathematics, Vol. 1838, 2004
As communication networks have grown in complexity, approximate models have become essential, and approximations based on large deviations theory are among the most popular. This book provides an elegant introduction to the associated literature, placing particular emphasis on the importance of time scales. For example, the chapter on "Moderate Deviations in Queueing Theory" identifies a continuum of scales between large deviations theory and the central limit theorem. Those two extreme scaling regimes have each generated large literatures, and have given different, useful insights into many queueing problems. The chapter shows how moderate deviations theory combines the simplicity of large deviations techniques with the parsimony of heavy traffic approximations. In the book’s final chapter, the authors underline the importance of scaling by analyzing particular traffic models of interest.
The authors are three exceptionally able applied mathematicians who have made significant contributions to this area. Their contributions, brought together in this book, provide new ways to address difficult issues surrounding time-scale and dependence, and are among the most important advances in queueing theory of the last decade.
Big Queues provides a remarkably accessible introduction to a highly technical area. It will undoubtedly have significant impact in queueing theory and practice.
Sean Meyn, Chair
J. Michael Harrison
Peter Taylor