Continuos-time Markov-modulated Chains In Operations Research PDF Download
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Author: Alexander M Andronov
Publisher: World Scientific
ISBN: 9811286175
Category : Mathematics
Languages : en
Pages : 227
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Book Description
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
Author: Alexander M Andronov
Publisher: World Scientific
ISBN: 9811286175
Category : Mathematics
Languages : en
Pages : 227
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Book Description
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
Author: Alexander Andronov
Publisher: World Scientific Publishing Company
ISBN: 9789811286155
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
Author: George Yin
Publisher: Springer Science & Business Media
ISBN: 9780387219486
Category : Business & Economics
Languages : en
Pages : 372
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Book Description
Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.
Author: G. George Yin
Publisher: Springer Science & Business Media
ISBN: 1461443466
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
Author: Xianping Guo
Publisher: Springer Science & Business Media
ISBN: 3642025471
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.
Author: William J. Anderson
Publisher: Springer Science & Business Media
ISBN: 1461230381
Category : Mathematics
Languages : en
Pages : 367
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Book Description
Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.
Author: Tomás Prieto-Rumeau
Publisher: World Scientific
ISBN: 1848168489
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This book is also concerned with Markov games, where two decision-makers (or players) try to optimize their own objective function. Both decision-making processes appear in a large number of applications in economics, operations research, engineering, and computer science, among other areas.An extensive, self-contained, up-to-date analysis of basic optimality criteria (such as discounted and average reward), and advanced optimality criteria (e.g., bias, overtaking, sensitive discount, and Blackwell optimality) is presented. A particular emphasis is made on the application of the results herein: algorithmic and computational issues are discussed, and applications to population models and epidemic processes are shown.This book is addressed to students and researchers in the fields of stochastic control and stochastic games. Moreover, it could be of interest also to undergraduate and beginning graduate students because the reader is not supposed to have a high mathematical background: a working knowledge of calculus, linear algebra, probability, and continuous-time Markov chains should suffice to understand the contents of the book.
Author: Arie Hordijk
Publisher:
ISBN:
Category : Discrete-time systems
Languages : en
Pages : 32
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Book Description
The regenerative method for analyzing simulations of positive recurrent, continuous time Markov chains yields confidence intervals for parameters associated with the stationary distribution of the Markov chain. In this paper two methods are developed which permit the simulator to simulate discrete time Markov chains and still produce confidence intervals for the original continuous time Markov chain. These methods are computationally more efficient in that exponential holding times need not be generated. Furthermore, one of the methods is also statistically more efficient in that it leads to a smaller 'variance' constant in the resulting confidence interval.
Author: George G Yin
Publisher:
ISBN: 9781461206286
Category :
Languages : en
Pages : 372
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Book Description
Author: G. George Yin
Publisher:
ISBN: 9783540982449
Category :
Languages : en
Pages : 349
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Book Description
