Showing posts with label markov chains. Show all posts
Showing posts with label markov chains. Show all posts

6/04/2012

Applied Probability and Stochastic Processes Review

Applied Probability and Stochastic Processes
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I randomly ran across this book in my math library trying to find an extra book to help with the difficult Stochastics Process class I was taking. Little did I know I would find a book I value as much as Douglas Kelly's Introduction to Probability. This book has applied problems and examples! It is not the dry, endless pages of confusing equations we have come to expect from Stochastics Processes books. There is something better out there! This book saved me as an undergraduate, and am now looking forward to it living up to my God like expecations as a post grad. If you are a professor, please use this book for you students. It ties together and lets you appreciate many fields such as linear analysis and even graph theory from computer science. This book will not disappoint.

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This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues.Included in the second edition are appendices at the end of several chapters giving suggestions for the use of Excel in solving the problems of the chapter. Also new in this edition are an introductory chapter on statistics and a chapter on Poisson processes that includes some techniques used in risk assessment. The old chapter on queues has been expanded and broken into two new chapters: one for simple queuing processes and one for queuing networks. Support is provided through the web site http://apsp.tamu.edu where students will have the answers to odd numbered problems and instructors will have access to full solutions and Excel files for homework.

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11/30/2011

Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications Review

Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications
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The authors give a nice overview of computer performance evaluation using queueing theory and continuous and discrete-time Markov chains. After a short review of the relevant probability and statistics, the authors discuss Markov chains in the second chapter, pointing out that Markov processes can be used to model queueing systems even when these systems have behavior governed by non-exponential distributions. They characterize these as Markovizing methods. Their treatment of both discrete and continuous time Markov models is short but adequate, covering all the necessary concepts such as ergodicity and irreducibility. They then give a thorough discussion of the modeling process as actually done in practice. Their discussion of model sizing sets up their methodologies for dealing with large models later in the book. Performance measures for system requirements are discussed in terms of Markov reward models. Their treatment here is very detailed and they also give a large collection of helpful references on the subject.Petri nets are also discussed in the context of model generation. The authors state, correctly I think, that more time should be spent of developing models rather than the underlying mathematics. In their treatment of networks with non-exponential service time and interarrival time distributions, the authors employ the diffusion approximation via the solution of the Fokker-Planck equation. The don't discuss this in detail but give references for those who can read German. This would have been a place for a detailed analysis and derivation, given the surprising introduction of the Fokker-Planck equation in queueing theory. They also use, interestingly, maximum entropy methods to get approximate solutions of open and closed queueing networks. A very short chapter on optimization is given in the next chapter, which could stand to be more lengthy given the importance of this in implementing networks commercially. The next chapter covers some of the performance tools that are available for studying networks. The Performance Evaluation and Prediction System (PEPSY), stochastic Petri net package (SPNP), the CSPL language, the Model Description Language (MOSEL), the symbolic hierarchical automated reliability performance evaluator (SHARPE) are discussed with examples of each. Readers not having these tools will of course will not benefit too much from reading this chapter, except for maybe to get an idea of what is available. The OPNET and Ns-simulator packages,which are very nice modeling tools are not treated at all for some reason.
The last chapter covers applications, with case studies of queueing networks, Markov chains, stochastic Petri nets, and hierarchical models. Although of somewhat limited value in practice, the examples given do give the reader an idea of how the material in the book can be applied. And here again, the authors stress the use of modeling packages such as SHARPE and PEPSY, to verify the calculations in the case studies. They consider a closed non-product form queueing model of a medium-sized LAN in some detail with Ethernet links and a FDDI ring, solving it using Marie's method. Also interesting is their model of the UNIX operating system, which is also represented by a closed non-product queueing network. They compare the computation time needed to solve the model using CTMC, shadow, and DES techniques. Although the discussion is rather hurried, their model of an ATM network is also interesting, in that they use Markov reward models, obtaining both the state and transient solutions.
The book is one that will be of great assistance to those doing network modeling, performance analysis, and other time-scheduling modeling activiites. It is somewhat expensive, but worth the price I think considering the care which the authors take in their exposition.

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Critically acclaimed text for computer performance analysis--now in its second editionThe Second Edition of this now-classic text provides a current and thorough treatment of queueing systems, queueing networks, continuous and discrete-time Markov chains, and simulation. Thoroughly updated with new content, as well as new problems and worked examples, the text offers readers both the theory and practical guidance needed to conduct performance and reliability evaluations of computer, communication, and manufacturing systems.Starting with basic probability theory, the text sets the foundation for the more complicated topics of queueing networks and Markov chains, using applications and examples to illustrate key points. Designed to engage the reader and build practical performance analysis skills, the text features a wealth of problems that mirror actual industry challenges.New features of the Second Edition include:* Chapter examining simulation methods and applications* Performance analysis applications for wireless, Internet, J2EE, and Kanban systems* Latest material on non-Markovian and fluid stochastic Petri nets, as well as solution techniques for Markov regenerative processes* Updated discussions of new and popular performance analysis tools, including ns-2 and OPNET* New and current real-world examples, including DiffServ routers in the Internet and cellular mobile networksWith the rapidly growing complexity of computer and communication systems, the need for this text, which expertly mixes theory and practice, is tremendous. Graduate and advanced undergraduate students in computer science will find the extensive use of examples and problems to be vital in mastering both the basics and the fine points of the field, while industry professionals will find the text essential for developing systems that comply with industry standards and regulations.
Additionally, a solution manual and an FTP site with links to author-provided data for the book are available for deeper study.

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10/25/2011

Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling Review

Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
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This is the most succinct, clear mathematics book I have ever own. Unlike many mathematics books whose mathematical derivations usually have several missing yet important steps make people scratching their heads, this books is not one of them. All the derivations are very detailed along with great explanations and numerical examples. It is a rare gem in mathematical literature and I salute Prof. Stewart for his great achievement.

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Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics.

The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation.

Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only).

Numerous examples illuminate the mathematical theories
Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach
Each chapter concludes with an extensive set of exercises

Professors: A supplementary Solutions Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html


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