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In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.

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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

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

In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as an expository example, the individual steps of scientific computing are presented: the derivation of the mathematical model; the discretization of the model equations; the development of algorithms; parallelization; and visualization of the computed data. In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids - the Navier-Stokes equations - the authors look at the simulation of free surface flows; energy and chemical transport; and turbulence. Readers are enabled to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 92 black-and-white and 18 color illustrations. After reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and apply their new knowledge to other scientific fields.

The development of computer simulation models is an important growth area in both pure and applied ecology. The opportunity that mathematical models provide to integrate the components of an ecosystem, results in the ability to make quantitative predictions about the future behavior of that system, or of elements within it. This means that they are powerful tools with wide applications and enormous potential for increasing our understanding of natural systems and our ability to use them in a sustainable way. This book is, almost uniquely, a complete account of one such model, the Hurley Pasture Model, a dynamic, deterministic, mechanistic simulation model for grassland, which has been developed by the author over some 20 years, in collaboration with scientists at several centers. Firstly, the rationale and theoretical elements of this type of model are described. An overview of the Hurley grassland simulator and the derivation and construction of its plant, animal, soil and litter, water, and environment and management components is then given. Next, the model is evaluated by a series of long and short-term dynamic simulations and steady state responses, which demonstrate how predictions can be made about the effects of, for example, climate change or particular regimes of fertilizer application, grazing or cutting. This book will be of great value to grassland agronomists and modellers, crop physiologists and plant ecologists, and to students of ecology as a case study of a plant ecosystem model. It will also be of interest to other ecologists and environmentalists and those in the field of computer modelling and its applications.

About the book: Mathematical modeling and computer simulation make it possible to understand and control the dynamic processes taking place in complex systems. Simulation provides insights into the often surprising diversity of possible behaviors, and allows identifying possibilities for intervention and options for alternative development. About one hundred simulation models from all areas of life are fully documented in the three volumes of the 'System Zoo'. They can be quickly implemented and easily operated using freely available system dynamics software. Volume 3 of the System Zoo contains simulation models of economic and social systems and global development, among them: production, stocks and orders, marketing and consumption, competition, life planning, employment, ecotax, escalation, dependence, aggression, population and community development, debt crisis, globalization, the world models of the Club of Rome (by Forrester and the Meadows group) and examples of nonnumerical knowledge processing applied to impact assessment and decision processes. The System Zoo collection of simulation models is particularly well-suited for teaching, training, and research projects at all levels from high school to university, and for individual study. Volume 1 of the System Zoo contains simulation models of elementary systems, and of systems from the fields of physics and engineering. Volume 2 of the System Zoo presents simulation models related to climate, vegetation, ecosystems and resources. About the author: Hartmut Bossel is Professor Emeritus of environmental systems analysis. He taught for many years at the University of California in Santa Barbara and the University of Kassel, Germany, where he was director of the Center for Environmental Systems Research until his retirement. He holds an engineering degree from the Technical University of Darmstadt, and a Ph.D. degree from the University of California at Berkeley. With a background in engineering, systems science,

The Phase-Locked Loop (PLL), and many of the devices used for frequency and phase tracking, carrier and symbol synchronization, demodulation, and frequency synthesis, are fundamental building blocks in today's complex communications systems. It is therefore essential for both students and practicing communications engineers interested in the design and implementation of modern communication systems to understand and have insight into the behavior of these important and ubiquitous devices. Since the PLL behaves as a nonlinear device (at least during acquisition), computer simulation can be used to great advantage in gaining insight into the behavior of the PLL and the devices derived from the PLL. The purpose of this Synthesis Lecture is to provide basic theoretical analyses of the PLL and devices derived from the PLL and simulation models suitable for supplementing undergraduate and graduate courses in communications. The Synthesis Lecture is also suitable for self study by practicing engineers. A significant component of this book is a set of basic MATLAB-based simulations that illustrate the operating characteristics of PLL-based devices and enable the reader to investigate the impact of varying system parameters. Rather than providing a comprehensive treatment of the underlying theory of phase-locked loops, theoretical analyses are provided in sufficient detail in order to explain how simulations are developed. The references point to sources currently available that treat this subject in considerable technical depth and are suitable for additional study. Table of Contents: Introduction / Basic PLL Theory / Structures Developed From The Basic PLL / Simulation Models / MATLAB Simulations / Noise Performance Analysis

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Digital Modulations using Matlab is a learner-friendly, practical and example driven book, that gives you a solid background in building simulation models for digital modulation systems in Matlab. This book, an essential guide for understanding the implementation aspects of a digital modulation system, shows how to simulate and model a digital modulation system from scratch. The implemented simulation models shown in this book, mostly will not use any of the inbuilt communication toolbox functions and hence provide an opportunity for an engineer to understand the basic implementation aspects of modeling various building blocks of a digital modulation system. It presents the following key topics with required theoretical background along with the implementation details in the form of Matlab scripts.* Basics of signal processing essential for implementing digital modulation techniques - generation of test signals, interpreting FFT results, power and energy of a signal, methods to compute convolution, analytic signal and applications.* Waveform and complex equivalent baseband simulation models.* Digital modulation techniques covered: BPSK and its variants, QPSK and its variants, M-ary PSK, M-ary QAM, M-ary PAM, CPM, MSK, GMSK,M-ary FSK. * Monte Carlo simulation for ascertaining performance of digital modulation techniques in AWGN and fading channels - Eb/N0 Vs BER curves.* Design and implementation of linear equalizers - zero forcing and MMSE equalizers, using them in a communication link.* Simulation and performance of modulation systems with receiver impairments.

This textbook provides a comprehensive and instructive coverage of vehicular traffic flow dynamics and modeling. It makes this fascinating interdisciplinary topic, which to date was only documented in parts by specialized monographs, accessible to a broad readership. Numerous figures and problems with solutions help the reader to quickly understand and practice the presented concepts. This book is targeted at students of physics and traffic engineering and, more generally, also at students and professionals in computer science, mathematics, and interdisciplinary topics. It also offers material for project work in programming and simulation at college and university level.The main part, after presenting different categories of traffic data, is devoted to a mathematical description of the dynamics of traffic flow, covering macroscopic models which describe traffic in terms of density, as well as microscopic many-particle models in which each particle corresponds to a vehicle and its driver. Focus chapters on traffic instabilities and model calibration/validation present these topics in a novel and systematic way.  Finally, the theoretical framework is shown at work in selected applications such as traffic-state and travel-time estimation, intelligent transportation systems, traffic operations management, and a detailed physics-based model for fuel consumption and emissions.

An expert guide to understanding and making optimum use of BSIM Used by more chip designers worldwide than any other comparable model, the Berkeley Short-Channel IGFET Model (BSIM) has, over the past few years, established itself as the de facto standard MOSFET SPICE model for circuit simulation and CMOS technology development. Yet, until now, there have been no independent expert guides or tutorials to supplement the various BSIM manuals currently available. Written by a noted expert in the field, this book fills that gap in the literature by providing a comprehensive guide to understanding and making optimal use of BSIM3 and BSIM4. Drawing upon his extensive experience designing with BSIM, William Liu provides a brief history of the model, discusses the various advantages of BSIM over other models, and explores the reasons why BSIM3 has been adopted by the majority of circuit manufacturers. He then provides engineers with the detailed practical information and guidance they need to master all of BSIM's features. He: Summarizes key BSIM3 components Represents the BSIM3 model with equivalent circuits for various operating conditions Provides a comprehensive glossary of modeling terminology Lists alphabetically BSIM3 parameters along with their meanings and relevant equations Explores BSIM3's flaws and provides improvement suggestions Describes all of BSIM4's improvements and new features Provides useful SPICE files, which are available online at the Wiley ftp site

This book takes recent theoretical advances in Finance and Economics and shows how they can be implemented in the real world. It presents tactics for using mathematical and simulation models to solve complex tasks of forecasting income, valuing businesses, predicting retail sales, and evaluating markets and tax and regulatory problems. Business Economics and Finance with Matlab, GIS, and Simulation Models provides a unique overview of sophisticated business and financial applications. It describes models that have been developed for analysis of retail sales, tax policy, location, economic impact, public policy issues, and other challenges faced by executives, investors, and economists on a daily basis. It also offers groundbreaking insight into the many calculation and modeling tools that can be remotely hosted and run over the Internet, resulting in substantial user benefits and cost savings. This book is the first to fully explore the capabilities of MATLAB in the field of business economics, and explain how the benefits of sophisticated mathematical models can be provided to users via the Internet, using a thin-client environment. Many techniques directly incorporate geographic information and GIS in a way that was impossible until quite recently. Some techniques, such as fuzzy logic, retail sales, economic and fiscal impact models, and other Matlab and Simulink models, are described for the first time in print in this book. The sections on business income and value break new ground by directly incorporating uncertainty, real option value, and prediction of variables using Ito and jump processes. Using dozens of examples, hundreds of references, and rigorous explanations of both theory and practice, it will become a prized reference for analysts demanding the best techniques.

This book takes recent theoretical advances in Finance and Economics and shows how they can be implemented in the real world. It presents tactics for using mathematical and simulation models to solve complex tasks of forecasting income, valuing businesses, predicting retail sales, and evaluating markets and tax and regulatory problems. Business Economics and Finance with Matlab, GIS, and Simulation Models provides a unique overview of sophisticated business and financial applications. It describes models that have been developed for analysis of retail sales, tax policy, location, economic impact, public policy issues, and other challenges faced by executives, investors, and economists on a daily basis. It also offers groundbreaking insight into the many calculation and modeling tools that can be remotely hosted and run over the Internet, resulting in substantial user benefits and cost savings. This book is the first to fully explore the capabilities of MATLAB in the field of business economics, and explain how the benefits of sophisticated mathematical models can be provided to users via the Internet, using a thin-client environment. Many techniques directly incorporate geographic information and GIS in a way that was impossible until quite recently. Some techniques, such as fuzzy logic, retail sales, economic and fiscal impact models, and other Matlab and Simulink models, are described for the first time in print in this book. The sections on business income and value break new ground by directly incorporating uncertainty, real option value, and prediction of variables using Ito and jump processes. Using dozens of examples, hundreds of references, and rigorous explanations of both theory and practice, it will become a prized reference for analysts demanding the best techniques.

The development of computer simulation models is an important growth area in both pure and applied ecology. The opportunity that mathematical models provide to integrate the components of an ecosystem, results in the ability to make quantitative predictions about the future behavior of that system, or of elements within it. This means that they are powerful tools with wide applications and enormous potential for increasing our understanding of natural systems and our ability to use them in a sustainable way. This book is, almost uniquely, a complete account of one such model, the Hurley Pasture Model, a dynamic, deterministic, mechanistic simulation model for grassland, which has been developed by the author over some 20 years, in collaboration with scientists at several centers. Firstly, the rationale and theoretical elements of this type of model are described. An overview of the Hurley grassland simulator and the derivation and construction of its plant, animal, soil and litter, water, and environment and management components is then given. Next, the model is evaluated by a series of long and short-term dynamic simulations and steady state responses, which demonstrate how predictions can be made about the effects of, for example, climate change or particular regimes of fertilizer application, grazing or cutting. This book will be of great value to grassland agronomists and modellers, crop physiologists and plant ecologists, and to students of ecology as a case study of a plant ecosystem model. It will also be of interest to other ecologists and environmentalists and those in the field of computer modelling and its applications.

The design of communication systems has grown too complicated for the traditional design tools--mathematical analysis and laboratory breadboards. Enter the computer simulation, a powerful and versatile tool that is becoming essential for anyone who designs signal transmission or storage systems. This volume explains in detail how to use simulation programs as a software breadboard to analyze and evaluate the performance of data communications links. It describes the engineering principles of signal transmission and its simulation, explores programming issues, and provides a comprehensive reference for models of signal processes. The book clearly demonstrates how simulation techniques can be used to: * Create valid models of signal processes * Provide exibility through the use of modules * Simulate various elements of communications systems, from filters and modulators to test instruments * Explore alternative models for a given system * Circumvent the mathematical intractability of modern transmission links * Plan and construct a computer model in a matter of hours or days, versus the weeks or months needed for laboratory breadboards * Make parameter changes in minutes once a link has been modeled * Provide engineers and students with complete training on the elements of simulation A must have for designers, practicing engineers, and graduate students, this volume presents real-world techniques that can be used with the authors' ST?DT program (a companion work also published by Wiley), or independently with other commercially available simulators.

Digital Modulations using Matlab is a learner-friendly, practical and example driven book, that gives you a solid background in building simulation models for digital modulation systems in Matlab. This book, an essential guide for understanding the implementation aspects of a digital modulation system, shows how to simulate and model a digital modulation system from scratch. The implemented simulation models shown in this book, mostly will not use any of the inbuilt communication toolbox functions and hence provide an opportunity for an engineer to understand the basic implementation aspects of modeling various building blocks of a digital modulation system. It presents the following key topics with required theoretical background along with the implementation details in the form of Matlab scripts.* Basics of signal processing essential for implementing digital modulation techniques - generation of test signals, interpreting FFT results, power and energy of a signal, methods to compute convolution, analytic signal and applications.* Waveform and complex equivalent baseband simulation models.* Digital modulation techniques covered: BPSK and its variants, QPSK and its variants, M-ary PSK, M-ary QAM, M-ary PAM, CPM, MSK, GMSK,M-ary FSK. * Monte Carlo simulation for ascertaining performance of digital modulation techniques in AWGN and fading channels - Eb/N0 Vs BER curves.* Design and implementation of linear equalizers - zero forcing and MMSE equalizers, using them in a communication link.* Simulation and performance of modulation systems with receiver impairments.

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In the 1950s, John Reber convinced many Californians that the best way to solve the state's water shortage problem was to dam up the San Francisco Bay. Against massive political pressure, Reber's opponents persuaded lawmakers that doing so would lead to disaster. They did this not by empirical measurement alone, but also through the construction of a model. Simulation and Similarity explains why this was a good strategy while simultaneously providing an account of modeling and idealization in modern scientific practice. Michael Weisberg focuses on concrete, mathematical, and computational models in his consideration of the nature of models, the practice of modeling, and nature of the relationship between models and real-world phenomena. In addition to a careful analysis of physical, computational, and mathematical models, Simulation and Similarity offers a novel account of the model/world relationship. Breaking with the dominant tradition, which favors the analysis of this relation through logical notions such as isomorphism, Weisberg instead presents a similarity-based account called weighted feature matching. This account is developed with an eye to understanding how modeling is actually practiced. Consequently, it takes into account the ways in which scientists' theoretical goals shape both the applications and the analyses of their models.