Artículos relacionados a Level Crossing Methods in Stochastic Models
Sinopsis
This is a complete update of the first edition of Level Crossing Methods in Stochastic Models, which was published in 2008. Level crossing methods are a set of sample-path based mathematical tools used in applied probability to establish reliable probability distributions. Since the basis for solving any applied probability problem requires a reliable probability distribution, Level Crossing Methods in Stochastic Models, Second Edition is a useful tool for all researchers working on stochastic application problems, including inventory control, queueing theory, reliability theory, actuarial ruin theory, renewal theory, pharmacokinetics, and related Markov processes.
The second edition includes a new section with a novel derivation of the Beneš series for M/G/1 queues. It provides new results on the service time for three M/G/I queueing models with bounded workload. It analyzes new applications of queues where zero-wait customers get exceptional service, including several examples on M/G/1 queues, and a new section on G/M/1 queues. Additionally, 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.
Percy H. Brill, Ph.D., is a Professor emeritus at the University of Windsor, Canada. Dr. Brill is the creator of the level crossing method for analyzing stochastic models. He has published extensively in stochastic processes, queueing theory and related models, especially using level crossing methods.
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Review
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)
About the Author
Percy H. Brill is a Professor emeritus at the University of Windsor, Canada. He received a B.Sc. in Mathematics and Physics from Carleton University, Canada, an M.A. in Mathematical Statistics from Columbia University, U.S.A., and a Ph.D. in Industrial Engineering from the University of Toronto, Canada. He is the creator of the level crossing method used in stochastic models. He has published extensively in stochastic processes, and queueing, especially using level crossing methods.
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