Introduction to Stochastic Level Crossing Techniques PDF Download
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Author: Percy H. Brill
Publisher:
ISBN: 9780367343941
Category : Distribution (Probability theory)
Languages : en
Pages : 0
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Book Description
"Introduction to Stochastic Level Crossing Techniques describes stochastic models using the System Point Level Crossing method. This involves deriving probability density functions (pdfs) or cumulative probability distribution functions (cdfs) of key random variables, applying simple level-crossing limit theorems. The pdfs and/or cdfs are used to specify operational characteristics about the stochastic model of interest. This book is meant for students of mathematics, management science, engineering, natural sciences, and researchers who use applied probability. It will also be useful to technical workers in a range of professions"--
Author: Percy H. Brill
Publisher: CRC Press
ISBN: 1000907368
Category : Business & Economics
Languages : en
Pages : 278
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Book Description
Introduction to Stochastic Level Crossing Techniques describes stochastic models and their analysis using the System Point Level Crossing method (abbreviated SPLC or LC). This involves deriving probability density functions (pdfs) or cumulative probability distribution functions (cdfs) of key random variables, applying simple level-crossing limit theorems developed by the author. The pdfs and/or cdfs are used to specify operational characteristics about the stochastic model of interest. The chapters describe distinct stochastic models and associated key random variables in the models. For each model, a figure of a typical sample path (realization, i.e., tracing over time) of the key random variable is displayed. For each model, an analytic (Volterra) integral equation for the stationary pdf of the key random variable is created−by inspection of the sample path, using the simple LC limit theorems. This LC method bypasses a great deal of algebra, usually required by other methods of analysis. The integral equations will be solved directly, or computationally. This book is meant for students of mathematics, management science, engineering, natural sciences, and researchers who use applied probability. It will also be useful to technical workers in a range of professions. Key Features: A description of one representative stochastic model (e.g., a single-server M/G/1 queue; a multiple server M/M/c queue; an inventory system; etc.) Construction of a typical sample path of the key random variable of interest (e.g., the virtual waiting time or workload in queues; the net on-hand inventory in inventory systems; etc.) Statements of the simple LC theorems, which connect the sample-path upcrossing and downcrossing rates across state-space levels, to simple mathematical functions of the stationary pdf of the key random variable, at those state-space levels Creation of (usually Volterra) integral equations for the stationary pdf of the key random variable, by inspection of the sample path Direct analytic solution of the integral equations, where feasible; or, computational solutions of the integral equations Use of the derived stationary pdfs for obtaining operational characteristics of the model
Author: Percy H. Brill
Publisher: CRC Press
ISBN: 1000907376
Category : Business & Economics
Languages : en
Pages : 394
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Book Description
Introduction to Stochastic Level Crossing Techniques describes stochastic models and their analysis using the System Point Level Crossing method (abbreviated SPLC or LC). This involves deriving probability density functions (pdfs) or cumulative probability distribution functions (cdfs) of key random variables, applying simple level-crossing limit theorems developed by the author. The pdfs and/or cdfs are used to specify operational characteristics about the stochastic model of interest. The chapters describe distinct stochastic models and associated key random variables in the models. For each model, a figure of a typical sample path (realization, i.e., tracing over time) of the key random variable is displayed. For each model, an analytic (Volterra) integral equation for the stationary pdf of the key random variable is created−by inspection of the sample path, using the simple LC limit theorems. This LC method bypasses a great deal of algebra, usually required by other methods of analysis. The integral equations will be solved directly, or computationally. This book is meant for students of mathematics, management science, engineering, natural sciences, and researchers who use applied probability. It will also be useful to technical workers in a range of professions. Key Features: A description of one representative stochastic model (e.g., a single-server M/G/1 queue; a multiple server M/M/c queue; an inventory system; etc.) Construction of a typical sample path of the key random variable of interest (e.g., the virtual waiting time or workload in queues; the net on-hand inventory in inventory systems; etc.) Statements of the simple LC theorems, which connect the sample-path upcrossing and downcrossing rates across state-space levels, to simple mathematical functions of the stationary pdf of the key random variable, at those state-space levels Creation of (usually Volterra) integral equations for the stationary pdf of the key random variable, by inspection of the sample path Direct analytic solution of the integral equations, where feasible; or, computational solutions of the integral equations Use of the derived stationary pdfs for obtaining operational characteristics of the model
Author: Percy H. Brill
Publisher: Springer
ISBN: 3319503324
Category : Business & Economics
Languages : en
Pages : 574
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Book Description
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.
Author: Saul I. Gass
Publisher: Springer Science & Business Media
ISBN: 1461304598
Category : Business & Economics
Languages : en
Pages : 774
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Book Description
Operations Research: 1934-1941," 35, 1, 143-152; "British The goal of the Encyclopedia of Operations Research and Operational Research in World War II," 35, 3, 453-470; Management Science is to provide to decision makers and "U. S. Operations Research in World War II," 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: "The Origin of Operational Research," ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II.
Author: S. Chakravarthy
Publisher: CRC Press
ISBN: 1482292173
Category : Mathematics
Languages : en
Pages : 398
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Book Description
Based on the proceedings of the first International Conference on Matrix-Analytic Methods (MAM) in Stochastic Models, held in Flint, Michigan, this book presents a general working knowledge of MAM through tutorial articles and application papers. It furnishes information on MAM studies carried out in the former Soviet Union.
Author: Qi-Ming He
Publisher: Springer Science & Business Media
ISBN: 1461473306
Category : Computers
Languages : en
Pages : 363
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Book Description
Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
Author: Mircea Grigoriu
Publisher: Springer Science & Business Media
ISBN: 0817682287
Category : Mathematics
Languages : en
Pages : 784
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Book Description
Algebraic, differential, and integral equations are used in the applied sciences, en gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time. Generally, the coefficients of and/or the input to these equations are not precisely known be cause of insufficient information, limited understanding of some underlying phe nomena, and inherent randonmess. For example, the orientation of the atomic lattice in the grains of a polycrystal varies randomly from grain to grain, the spa tial distribution of a phase of a composite material is not known precisely for a particular specimen, bone properties needed to develop reliable artificial joints vary significantly with individual and age, forces acting on a plane from takeoff to landing depend in a complex manner on the environmental conditions and flight pattern, and stock prices and their evolution in time depend on a large number of factors that cannot be described by deterministic models. Problems that can be defined by algebraic, differential, and integral equations with random coefficients and/or input are referred to as stochastic problems. The main objective of this book is the solution of stochastic problems, that is, the determination of the probability law, moments, and/or other probabilistic properties of the state of a physical, economic, or social system. It is assumed that the operators and inputs defining a stochastic problem are specified.
Author: Arvid Naess
Publisher: Cambridge University Press
ISBN: 0521881552
Category : Mathematics
Languages : en
Pages : 425
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Book Description
For students and professionals, this covers theory and methods for stochastic modelling and analysis of marine structures under environmental loads.
Author: P.D. Spanos
Publisher: CRC Press
ISBN: 9789058090393
Category : Computers
Languages : en
Pages : 628
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Book Description
Proceedings of the June, 1998 conference. Seventy contributions discuss Monte Carlo and signal processing methods, random vibrations, safety and reliability, control/optimization and modeling of nonlinearity, earthquake engineering, random processes and fields, damage/fatigue materials, applied prob
Author: Kjell A. Doksum
Publisher: World Scientific
ISBN: 9812795251
Category : Technology & Engineering
Languages : en
Pages : 569
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Book Description
This book contains extended versions of 34 carefully selected and reviewed papers presented at the Third International Conference on Mathematical Methods in Reliability, held in Trondheim, Norway in 2002. It provides a broad overview of current research activities in reliability theory and its applications. There are chapters on reliability modelling, network and system reliability, reliability optimization, survival analysis, degradation and maintenance modelling, and software reliability. The authors are all leading experts in the field. A particular feature of the book is a historical review by Professor Richard E Barlow, well known for his pioneering research on reliability. The list of authors also includes the plenary session speakers Odd O Aalen, Philip J Boland, Sallie A Keller-McNulty, and Nozer Singpurwalla. Contents: Reliability Theory in the Past and Present Centuries; General Aspects of Reliability Modelling; Reliability of Networks and Systems; Stochastic Modelling and Optimization in Reliability; Modelling in Survival and Reliability Analysis; Statistical Methods for Degradation Data; Statistical Methods for Maintained Systems; Statistical Inference in Survival Analysis; Software Reliability Methods. Readership: Graduate students, academics and professionals in probability & statistics, reliability analysis, survival analysis, industrial engineering, software engineering, operations research and applied mathematics research.
