Introduction.- 1 A classical model for storage system activity -- 2 A fractal model for storage system activity -- 3 Disk scheduling, airplane boarding and Lorentzian geometry -- 4 Mirrored configurations -- 5 On queues and numbers -- 6 Appendix A: Some basic definitions and facts -- 7 Appendix B: Proofs of theorems -- References.

This monograph describes problems in the field of performance analysis, primarily the study of storage systems and the diverse mathematical techniques that are required for solving such problems. Topics covered include best practices for scheduling I/O requests to a disk drive, how this problem is related to airplane boarding, and how both problems can be modeled using space-time geometry. The author also explains how Riemann's proof of the analytic continuation and functional equation of the Riemann zeta function can be used to analyze express-line queues in a minimarket. Overall, the book reveals the surprising applicability of abstract mathematical ideas that are not usually associated with applied topics. Advanced undergraduate students or graduate students with an interest in the applications of mathematics will find this book a useful resource. It will also be of interest to professional mathematicians who want exposure to the surprising ways that theoretical mathematics may be applied to engineering problems. To encourage further study, each chapter ends with notes pointing to various related topics that the reader may want to pursue.