Level Crossing Methods in Stochastic Models [electronic resource]/ by Percy H. Brill. - Boston: Springer: Springer, 2008. - XXVI, 482 p. digital. - International Series in Operations Research & Management Science, 123 0884-8289; . - International series in operations research & management science; 123 .

Preface -- Origin of level crossing method -- Sample path and system point -- M/G/1 queues and variants -- M/M/C queues -- G/M/c queues -- Dams and inventories -- Multi-dimensional models -- Embedded level crossing methods -- Level crossing estimation -- Additional applications -- References -- Partial bibliography -- Index .

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. ;

9780387094212

10.1007/978-0-387-09421-2 doi

Mathematics.

Computer system performance

Distribution (Probability theory)

Industrial engineering--Mathematics.

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Mathematical Modeling and Industrial Mathematics

Probability Theory and Stochastic Processes

Operations Research/Decision Theory

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System Performance and Evaluation