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Level Crossing Methods in Stochastic Models

  • Book
  • © 2017

Overview

Authors:
  1. Percy H. Brill

    1. Departments of Management Science and Mathematics and Statistics, University of Windsor, Windsor, Canada

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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
  • Includes supplementary material: sn.pub/extras

Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 250)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxvii
    Download chapter PDF

  2. Origin of Level Crossing Method

    • Percy H. Brill
    Pages 1-17

  3. Sample Path and System Point

    • Percy H. Brill
    Pages 19-47

  4. M/G/1 Queues and Variants

    • Percy H. Brill
    Pages 49-185

  5. M/M/c Queue

    • Percy H. Brill
    Pages 187-284

  6. G/M/1 and G/M/c Queues

    • Percy H. Brill
    Pages 285-335

  7. Dams and Inventories

    • Percy H. Brill
    Pages 337-387

  8. Multi-dimensional Models

    • Percy H. Brill
    Pages 389-409

  9. Embedded Level Crossing Method

    • Percy H. Brill
    Pages 411-427

  10. Level Crossing Estimation

    • Percy H. Brill
    Pages 429-450

  11. Renewal Theory Using LC

    • Percy H. Brill
    Pages 451-484

  12. ADDITIONAL APPLICATIONS of LC

    • Percy H. Brill
    Pages 485-527

  13. Back Matter

    Pages 529-559
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Keywords

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 getexceptional 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.

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)

Authors and Affiliations

  • Departments of Management Science and Mathematics and Statistics, University of Windsor, Windsor, Canada

    Percy H. Brill

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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