Level crossing methods in stochastic models (Q5892402)

The present book is a complete update of the first edition published in 2008 [Zbl 1157.60003]. Level crossing methods are a set of sample path-based mathematical tools used in applied probability to create reliable probability distributions. It consists of 11 Chapters, 145 items in the References and an additional Partial bibliography. The topic of the chapters are the following: Chapter 1: Origin of level crossing method, Chapter 2: Sample path and system point, Chapter 3: \(\mathrm{M}/\mathrm{G}/1\) queues and variants, Chapter 4: \(\mathrm{M}/\mathrm{M}/c\) queues, Chapter 5: \(\mathrm{G}/\mathrm{M}/1\) and \(\mathrm{G}/\mathrm{M}/c\) queues, Chapter 6: Dams and inventories, Chapter 7: Multi-dimensional models, Chapter 8: Embedded level crossing method, Chapter 9: Level crossing estimation, Chapter 10: Renewal theory using level crossing, Chapter 11: Additional applications of level crossing. ``The second edition includes a new chapter with a novel derivation of the Beneš series for \(\mathrm{M}/\mathrm{G}/1\) queues. It gives new results on the service time for three \(\mathrm{M}/\mathrm{G}/1\) queueing models with bounded workload. It investigates new applications of queues where zero-wait customers get exceptional service, including several examples on \(\mathrm{M}/\mathrm{G}/1\) queues, and a new section on \(\mathrm{G}/\mathrm{M}/1\) queues. Furthermore, there are two other important new sections on the level-crossing derivation of the finite time-\(t\) probability distributions of excess, age, and total life, in renewal theory; and on a level-crossing analysis of a risk model in insurance.'' ``The original Chapter 10 has been split into two chapters: the new Chapter 10 is on renewal theory, and the first section of the new Chapter 11 is on a risk model. More explicit use is made of the renewal reward theorem throughout, and many technical and editorial changes have been made to facilitate readability.'' Overall, this edition is a valuable tool for all researchers working on stochastic application problems, for example, inventory control, queueing theory, reliability theory, actuarial ruin theory, renewal theory, and related Markov processes.