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

Introduction to Probability Models, Ninth Edition Review

Introduction to Probability Models, Ninth Edition
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The first four chapters alone (intro, random variables, conditonal probability, markov chains) are worth the price of the book. The author packs each chapter with very interesting examples and problems. The one I found most interesting was his probabilistic analysis of the 2-SAT and SAT problems of computer science. Here he gives an informal math argument as to why 2-SAT is polynomial time decidable and why SAT should be intractable.
On the other hand, I think someone relatively new to probability theory may find his neat problems and examples a bit too much with a first reading. The book is in its seventh edition, and I think Ross has taken advantage of this by providing newer insights and more interesting problems, but in doing so it may overwhelm the novice.
If you are learning probability for the first or second time, I recommend you supplement this book with Roussas "A Course in Mathematical Statistics". Despite its title, the first 9 chapters give a calculus-based intro to probability. And the rest of the book is *excellent* for a calculus-based intro to statistics.

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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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Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling Review

Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling
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This book is suitable for my graduate studies on computer performance. The author directs us from combinatorics, distribution theory, queue theory to queueing networks in a systematic way. I have read the book at ease for its stepwise elaboration of concepts. However, I have also read with hardship as it requires the readers to possess a good command of mathematics, both pure and applied, in order to go through the book.
For a mathematics graduate studying computer networks, I recommend this book. A novice or a mediocrity should pay more patience to read if not yet at a loss.
This book has aroused my interest and eagerness to know more about computer performance from the viewpoint of queueing and networking. In a word, I enjoy reading this book.

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This textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modelling. The author's aim is to derive the theory in a way that combines its formal, intuitive, and applied aspects so that students may apply this indispensable tool in a variety of different settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including the concept of limit, but otherwise this book provides a self-contained approach suitable for graduate or advanced undergraduate students. The first half of the book covers the basic concepts of probability including expectation, random variables, and fundamental theorems. In the second half of the book the reader is introduced to stochastic processes. Subjects covered include renewal processes, queueing theory, Markov processes, and reversibility as it applies to networks of queues. Examples and applications are drawn from problems in computer performance modelling.

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Modeling, Analysis, Design, and Control of Stochastic Systems (Springer Texts in Statistics) Review

Modeling, Analysis, Design, and Control of Stochastic Systems (Springer Texts in Statistics)
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This is probably ideal as a reference source for a graduate student or professor who knows stochastics very well already.
However, if you are a novice trying to learn about stochastics and want good explanations and examples with an appropriate buildup, I would not recommend the book.
As an example, the review discussion of probability in the first four chapters didn't even come close to comparing with the probability book I used in another class. If you are near a bookstore, you can easily verify this. I imagine that this comparison (or lack thereof) would hold for many other probability textbooks. Also, if presentation makes a difference to you, this is quite minimalist.
Another area that I found lacking is that the answers in the back just provide a numerical answer without any explanation to how solutions were arrived at. While this is often the case for other books, the author did not provide a sufficient base for a novice to work the problems. As a result, most of the end of chapter problems were of little use in helping me better learn the materials. A good workbook or better explanations would be very helpful.
While there are certainly couple areas that I found worthwhile and this does appear to be one of the only books on this niche area (the lack of competition may explain a lot of why the shortcomings exist and why this doesn't have the feel of real textbook), this first edition book needs some serious work to make it truly effective and user friendly.

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An introductory level text on stochastic modelling, suited for undergraduates or graduates in actuarial science, business management, computer science, engineering, operations research, public policy, statistics, and mathematics. It employs a large number of examples to show how to build stochastic models of physical systems, analyse these models to predict their performance, and use the analysis to design and control them. The book provides a self-contained review of the relevant topics in probability theory: In discrete and continuous time Markov models it covers the transient and long term behaviour, cost models, and first passage times; under generalised Markov models, it covers renewal processes, cumulative processes and semi-Markov processes. All the material is illustrated with many examples, and the book emphasises numerical answers to the problems. A software package called MAXIM, which runs on MATLAB, is available for downloading.

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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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