Level Crossing Methods in Stochastic Models

  • Percy H. Brill

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

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Percy H. Brill
    Pages 1-17
  3. Percy H. Brill
    Pages 19-47
  4. Percy H. Brill
    Pages 49-185
  5. Percy H. Brill
    Pages 187-284
  6. Percy H. Brill
    Pages 285-335
  7. Percy H. Brill
    Pages 337-387
  8. Percy H. Brill
    Pages 389-409
  9. Percy H. Brill
    Pages 411-427
  10. Percy H. Brill
    Pages 429-450
  11. Percy H. Brill
    Pages 451-484
  12. Percy H. Brill
    Pages 485-527
  13. Back Matter
    Pages 529-559

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.


Level Crossing Methods Stochastic Models Applied Probability Inventory Control Renewal Theory Probability Distribution Queueing Theory Actuarial ruin models Operations Research

Authors and affiliations

  • Percy H. Brill
    • 1
  1. 1.Departments of Management Science and Mathematics and StatisticsUniversity of WindsorWindsorCanada

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