Analyzing Markov Chains Using Kronecker Products
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| Author | : Tugrul Dayar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 91 |
| Release | : 2012-07-25 |
| Genre | : Mathematics |
| ISBN | : 1461441900 |
Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.
| Author | : Tuğrul Dayar |
| Publisher | : Springer |
| Total Pages | : 284 |
| Release | : 2018-09-21 |
| Genre | : Mathematics |
| ISBN | : 3319971298 |
This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods. Having grown out of research from the past twenty years, this book expands upon the author’s previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.
| Author | : Mohamed Ibnkahla |
| Publisher | : CRC Press |
| Total Pages | : 428 |
| Release | : 2018-10-08 |
| Genre | : Technology & Engineering |
| ISBN | : 135183570X |
Adaptive techniques play a key role in modern wireless communication systems. The concept of adaptation is emphasized in the Adaptation in Wireless Communications Series through a unified framework across all layers of the wireless protocol stack ranging from the physical layer to the application layer, and from cellular systems to next-generation wireless networks. Adaptation and Cross Layer Design in Wireless Networks is devoted to adaptation in the data link layer, network layer, and application layer. The book presents state-of-the-art adaptation techniques and methodologies, including cross-layer adaptation, joint signal processing, coding and networking, selfishness in mobile ad hoc networks, cooperative and opportunistic protocols, adaptation techniques for multimedia support, self –organizing routing, and tunable security services. It presents several new theoretical paradigms and analytical findings which are supported with various simulation and experimental results. Adaptation in wireless communications is needed in order to achieve high capacity and ubiquitous communications. The current trend in wireless communication systems is to make adaptation dependent upon the state of the relevant parameters in all layers of the system. Focusing on simplified cross layer design approaches, this volume describes advanced techniques such as adaptive resource management, adaptive modulation and coding, 4G communications, QoS, diversity combining, and energy and mobility aware MAC protocols. The first volume in the series, Adaptive Signal Processing in Wireless Communications (cat no.46012) covers adaptive signal processing at the physical layer.
| 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 | : Carl D. Meyer |
| Publisher | : SIAM |
| Total Pages | : 903 |
| Release | : 2000-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898719518 |
Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer's book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.
| Author | : J. MacGregor Smith |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 397 |
| Release | : 2013-05-17 |
| Genre | : Business & Economics |
| ISBN | : 1461467772 |
This handbook surveys important stochastic problems and models in manufacturing system operations and their stochastic analysis. Using analytical models to design and control manufacturing systems and their operations entail critical stochastic performance analysis as well as integrated optimization models of these systems. Topics deal with the areas of facilities planning, transportation, and material handling systems, logistics and supply chain management, and integrated productivity and quality models covering: • Stochastic modeling and analysis of manufacturing systems • Design, analysis, and optimization of manufacturing systems • Facilities planning, transportation, and material handling systems analysis • Production planning, scheduling systems, management, and control • Analytical approaches to logistics and supply chain management • Integrated productivity and quality models, and their analysis • Literature surveys of issues relevant in manufacturing systems • Case studies of manufacturing system operations and analysis Today’s manufacturing system operations are becoming increasingly complex. Advanced knowledge of best practices for treating these problems is not always well known. The purpose of the book is to create a foundation for the development of stochastic models and their analysis in manufacturing system operations. Given the handbook nature of the volume, introducing basic principles, concepts, and algorithms for treating these problems and their solutions is the main intent of this handbook. Readers unfamiliar with these research areas will be able to find a research foundation for studying these problems and systems.
| Author | : Ed Brinksma |
| Publisher | : Springer |
| Total Pages | : 438 |
| Release | : 2003-06-29 |
| Genre | : Computers |
| ISBN | : 3540446672 |
Traditionally, models and methods for the analysis of the functional correctness of reactive systems, and those for the analysis of their performance (and - pendability) aspects, have been studied by di?erent research communities. This has resulted in the development of successful, but distinct and largely unrelated modeling and analysis techniques for both domains. In many modern systems, however, the di?erence between their functional features and their performance properties has become blurred, as relevant functionalities become inextricably linked to performance aspects, e.g. isochronous data transfer for live video tra- mission. During the last decade, this trend has motivated an increased interest in c- bining insights and results from the ?eld of formal methods – traditionally - cused on functionality – with techniques for performance modeling and analysis. Prominent examples of this cross-fertilization are extensions of process algebra and Petri nets that allow for the automatic generation of performance models, the use of formal proof techniques to assess the correctness of randomized - gorithms, and extensions of model checking techniques to analyze performance requirements automatically. We believe that these developments markthe - ginning of a new paradigm for the modeling and analysis of systems in which qualitative and quantitative aspects are studied from an integrated perspective. We are convinced that the further worktowards the realization of this goal will be a growing source of inspiration and progress for both communities.
| Author | : Svenja Lagershausen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 189 |
| Release | : 2012-10-24 |
| Genre | : Business & Economics |
| ISBN | : 364232214X |
This book deals with the performance analysis of closed queueing networks with general processing times and finite buffer spaces. It offers a detailed introduction to the problem and a comprehensive literature review. Two approaches to the performance of closed queueing networks are presented. One is an approximate decomposition approach, while the second is the first exact approach for finite-capacity networks with general processing times. In this Markov chain approach, queueing networks are analyzed by modeling the entire system as one Markov chain. As this approach is exact, it is well-suited both as a reference quantity for approximate procedures and as extension to other queueing networks. Moreover, for the first time, the exact distribution of the time between processing starts is provided.
| Author | : Luca de Alfaro |
| Publisher | : Springer |
| Total Pages | : 228 |
| Release | : 2003-06-30 |
| Genre | : Mathematics |
| ISBN | : 3540448047 |
This book constitutes the refereed proceedings of the Joint Workshop on Process Algebra and Performance Modeling and Probabilistic Methods in Verification, PAPM-PROBMIV 2001, held in Aachen, Germany in September 2001. The 12 revised full papers presented together with one invited paper were carefully reviewed and selected from 23 submissions. Among the topics addressed are model representation, model checking, probabilistic systems analysis, refinement, Markov chains, random variables, stochastic timed systems, Max-Plus algebra, process algebra, system modeling, and the Mobius modeling framework.
| Author | : William Turin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 451 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1441990704 |
This book is an expanded third edition of the book Performance Analysis of Digital Transmission Systems, originally published in 1990. Second edition of the book titled Digital Transmission Systems: Performance Analysis and Modeling was published in 1998. The book is intended for those who design communication systems and networks. A computer network designer is interested in selecting communication channels, error protection schemes, and link control protocols. To do this efficiently, one needs a mathematical model that accurately predicts system behavior. Two basic problems arise in mathematical modeling: the problem of identifying a system and the problem of applying a model to the system analysis. System identification consists of selecting a class of mathematical objects to describe fundamental properties of the system behavior. We use a specific class of hidden Markov models (HMMs) to model communication systems. This model was introduced by C. E. Shannon more than 50 years ago as a Noisy Discrete Channel with a finite number of states. The model is described by a finite number of matrices whose elements are estimated on the basis of experimental data. We develop several methods of model identification and show their relationship to other methods of data analysis, such as spectral methods, autoregressive moving average CARMA) approximations, and rational transfer function approximations.
