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International Series in Operations Research & Management Science

Level Crossing Methods in Stochastic Models

Authors: Brill, Percy H.

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  • Brings the techniques of Level Crossing Methods completely up to date
  • New section on actuarial ruin models, and separate chapter on renewal theory
  • Author is the leading authority and inventor of Level Crossing Methods
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eBook $169.00
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  • ISBN 978-3-319-50332-5
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Hardcover $219.99
price for USA in USD
  • ISBN 978-3-319-50330-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $219.99
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  • ISBN 978-3-319-84375-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

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.

Reviews

“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 … . 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.” (János Sztrik, zbMATH 1380.60002, 2018)

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $169.00
price for USA in USD (gross)
  • ISBN 978-3-319-50332-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-3-319-50330-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $219.99
price for USA in USD
  • ISBN 978-3-319-84375-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Level Crossing Methods in Stochastic Models
Authors
Series Title
International Series in Operations Research & Management Science
Series Volume
250
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-50332-5
DOI
10.1007/978-3-319-50332-5
Hardcover ISBN
978-3-319-50330-1
Softcover ISBN
978-3-319-84375-9
Series ISSN
0884-8289
Edition Number
2
Number of Pages
XXVII, 559
Number of Illustrations
97 b/w illustrations, 27 illustrations in colour
Topics