Level Crossing Methods in Stochastic Models
Authors: Brill, Percy H.
- Outlines the original developmental ideas that led to the discovery of the level crossing method in the 1970s and traces their evolution to the present
- Demonstrates the flexibility and adaptivity of the level crossing method by applying it to a variety of stochastic models, including: queues, inventories, dams, replacement models, renewal processes, counter models, multi-dimensional models, and models in the natural sciences
- Presents both introductory and advanced material that can be applied to practical problem solving and theory building
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- About this book
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems faster, more easily, and more intuitively.
The book includes introductory material for readers new to the area, as well as advanced material for experienced users of the method, highlighting its usefulness for analyzing a broad class of models and illustrating its flexibility and adaptivity. The concepts, techniques, examples, applications and theoretical results in this book may suggest potentially new theory and new applications. The result is an essential resource for researchers, students, and professionals in operations research, management science, engineering, applied probability, statistics, actuarial science, mathematics, and the natural sciences.
- About the authors
Percy Brill holds a BSc in mathematics and physics from Carleton University, Canada, an MA in mathematical statistics from Columbia University, USA, and a PhD in industrial engineering with a minor in mathematics from the University of Toronto, Canada. He has held an NSERC (Natural Sciences and Engineering Research Council of Canada) grant continuously for 26 years. He served as a consultant for an NSF (National Science Foundation, USA) grant for 4 years. In addition to his academic career, he worked in industry for 12 years as a research scientist, statistical programmer and data processing consultant. He is presently a Professor Emeritus in the Departments of Management Science and Mathematics & Statistics at the University of Windsor, Canada.
He has published over 99 articles in refereed journals, conference Proceedings, books and technical reports. In addition, he has presented over 110 talks and seminars at conferences, universities and professional society meetings. He served as president of the Southeastern-Michigan chapter of INFORMS from 1994 to 1996. He is a former associate editor of the journal INFOR. He received the CanQueue 2000 Award of Distinction in recognition of his work in Applied Probability especially in the area of Level Crossing Techniques, at the Canadian queueing conference held at the University of Western Ontario, Canada in September 2000. His research interests include: level crossing theory and methods, applied probability, stochastic processes, stochastic modeling, queueing theory, renewal theory, applied mathematics, and nonparametric statistical inference.
From the reviews:
This excellent book by the originator of level crossing methods for stochastic models is a highly welcome addition to the literature on queues and inventories. The level crossing method is very powerful and sometimes results in extremely quick and easy derivations when compared with other methods. This book is in a class by itself for its focus on level crossing and for its breadth of coverage, and abundance of new ideas. Some applications of the method even deserve to be inserted into standard texts on stochastic models. Researchers will find a wealth of ideas in this book just waiting for consideration. I suspect that the book will result in a number of dissertations which develop and apply some of the methods presented.
Dr. Myron Hlynka, Department of Mathematics & Statistics, University of Windsor
"As the title indicates, this monograph explores the LC method thoroughly for obtaining probability distributions of state variables in a variety of stochastic models. … The book is intended for research-and-applications-oriented workers in operations research, management science, engineering, probability and statistics, actuarial science, mathematics and the natural sciences. Intended for a large audience … . The book is a welcome addition to any library frequented by researchers interested in stochastic modelling." (Sreenivasan Ravi, Mathematical Reviews, Issue 2009 m)
“Level Crossing Methods in Stochastic Models is a book that describes how such methods can be used to analyse a variety of stochastic models including M/G/1 queues (and variants), M/M/c queues, G/M/c queues, multi-dimensional models, inventory models, and many others. … Overall, the book is well written … . I recommend the book for anyone doing research in queuing or stochastic models. The book is also helpful as a reference in that it summarizes results for a wide variety of systems.” (J. Shortle, Journal of the Operational Research Society, Vol. 61 (5), 2010)
“The book is aimed at the serious researcher in stochastic models, and is loaded with potential research topics. … If someone is working on a new stochastic model, my advice is to examine this book for a related model and try to adopt the methods of the book to the new model. … I highly recommend the book. … There is a large international community of researchers in queueing and stochastic models. It’s time to queue up to purchase this book.” (Myron Hlynka, Technometrics, Vol. 51 (3), August, 2009)
Table of contents (10 chapters)
Origin Of Level Crossing Method
Dams and Inventories
Sample Path And System Point
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- Bibliographic Information
- Book Title
- Level Crossing Methods in Stochastic Models
- Percy H. Brill
- Series Title
- International Series in Operations Research & Management Science
- Series Volume
- Springer US
- Copyright Holder
- Springer-Verlag US
- eBook ISBN
- Series ISSN
- Edition Number
- Number of Pages
- XXV, 480