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Mathematics | Level Crossing Methods in Stochastic Models

Level Crossing Methods in Stochastic Models

Brill, Percy H.

2008, XXV, 480 p.

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  • Outlines the original developmental ideas that led to the discovery of the level crossing method in the 1970s and traces their evolution to the present
  • Demonstrates the flexibility and adaptivity of the level crossing method by applying it to a variety of stochastic models, including: queues, inventories, dams, replacement models, renewal processes, counter models, multi-dimensional models, and models in the natural sciences
  • Presents both introductory and advanced material that can be applied to practical problem solving and theory building

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.

 

 

Content Level » Research

Keywords » M/G/1 queue - Operations Research - Probability distribution - Stochastic model - Stochastic models - dams - embedded process - estimation - inventories - level crossing - linear optimization - queues - sample path - statistics - system point

Related subjects » Communication Networks - Mathematics - Operations Research & Decision Theory - Probability Theory and Stochastic Processes - Production & Logistics - Production & Process Engineering

Table of contents 

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 Method.- Level Crossing Estimation.- Additional Applications.

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