Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Numerical Methods In Markov Chains And Bulk Queues PDF full book. Access full book title Numerical Methods In Markov Chains And Bulk Queues.
| Author | : T. P. Bagchi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 100 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642807127 |
| Author | : Tapan Prasad Bagchi |
| Publisher | : |
| Total Pages | : 89 |
| Release | : 1972 |
| Genre | : Markov processes |
| ISBN | : |
| Author | : Dario A. Bini |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 340 |
| Release | : 2005-02-03 |
| Genre | : Computers |
| ISBN | : 0198527683 |
Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible toengineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature.The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description andanalysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the bookends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.
| Author | : William J. Stewart |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 605 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461522412 |
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
| Author | : William J. Stewart |
| Publisher | : CRC Press |
| Total Pages | : 738 |
| Release | : 1991-05-23 |
| Genre | : Mathematics |
| ISBN | : 9780824784058 |
Papers presented at a workshop held January 1990 (location unspecified) cover just about all aspects of solving Markov models numerically. There are papers on matrix generation techniques and generalized stochastic Petri nets; the computation of stationary distributions, including aggregation/disagg
| Author | : T. P. Bagchi |
| Publisher | : |
| Total Pages | : 89 |
| Release | : 1972 |
| Genre | : Markov-kæder |
| ISBN | : |
| Author | : David Michael Lucantoni |
| Publisher | : |
| Total Pages | : 103 |
| Release | : 1978 |
| Genre | : Markov processes |
| ISBN | : |
An algorithm is discussed for computing the stationary probability vector of an infinite-state Markov chain whose transition probability matrix has a block-partitioned structure. Such matrices arise in a wide variety of queueing models as well as generalized random walk problems. Traditionally, the analytic approach to this type of problem has been through complex variable methods. An alternate and unified treatment of this problem is presented and an algorithm is obtained which utilizes only real arithmetic computations. In addition, most of the intermediate steps of the algorithm have useful probabilistic interpretations.
| Author | : Harold Kushner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 436 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1468404415 |
This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. The random process models of the controlled or uncontrolled stochastic systems are either diffusions or jump diffusions. Stochastic control is a very active area of research and new prob lem formulations and sometimes surprising applications appear regularly. We have chosen forms of the models which cover the great bulk of the for mulations of the continuous time stochastic control problems which have appeared to date. The standard formats are covered, but much emphasis is given to the newer and less well known formulations. The controlled process might be either stopped or absorbed on leaving a constraint set or upon first hitting a target set, or it might be reflected or "projected" from the boundary of a constraining set. In some of the more recent applications of the reflecting boundary problem, for example the so-called heavy traffic approximation problems, the directions of reflection are actually discontin uous. In general, the control might be representable as a bounded function or it might be of the so-called impulsive or singular control types. Both the "drift" and the "variance" might be controlled. The cost functions might be any of the standard types: Discounted, stopped on first exit from a set, finite time, optimal stopping, average cost per unit time over the infinite time interval, and so forth.
| Author | : G. George Yin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 442 |
| Release | : 2012-11-14 |
| Genre | : Mathematics |
| ISBN | : 1461443466 |
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 | : William J. Stewart |
| Publisher | : Princeton University Press |
| Total Pages | : 561 |
| Release | : 2021-01-12 |
| Genre | : Mathematics |
| ISBN | : 0691223386 |
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains.
