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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

Probabilities --- Markov processes. --- Queuing theory. --- Computer simulation.

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Electronic digital computers --- System analysis. --- Queuing theory --- Ordinateurs --- Analyse de systèmes --- Files d'attente, Théorie des --- Evaluation --- Evaluation

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Queueing Theory deals with systems where there is contention for resources, but the demands are only known probabilistically. This book can be considered as either a monograph or a textbook on the subject, and thus is aimed at two audiences. It can be useful for those who already know queueing theory, but would like to know more about the linear algebraic approach. It can also be used as a textbook in a first course on queueing theory for students who feel more comfortable with matrices and algebraic arguments than with probability theory. The equations are well-suited to easy computation. The text has much discussion on how various properties can be computed using any language that has built-in matrix operations (e.g., MATLAB, Mathematica, Maple). To help with physical insight, there are over 80 figures, numerous examples, and many exercises distributed throughout the book. There are over 50 books on queueing theory that are available today and most practitioners have several of them on their shelves. Because of its unusual approach, this book would be an excellent addition. It would also make a good supplement where another book was selected as the primary text for a course in system performance modelling. This second edition has been greatly expanded and updated thoughout, including a new chapter on semi-Markov processes and new material on representations of distributions. In particular, there is much discussion of power-tailed distributions and their effects on queues. Lester Lipsky is a professor in the Department of Computer Science and Engineering at the University of Connecticut.

Algebras, Linear. --- Queuing theory. --- Queuing theory --- Algebras, Linear --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Erlang traffic formula --- Queueing theory --- Theory of queues --- Waiting-line theory --- Linear algebra --- Mathematics. --- Operations research. --- Decision making. --- Algorithms. --- Computers. --- Management science. --- Probabilities. --- Economic theory. --- Operations Research, Management Science. --- Operation Research/Decision Theory. --- Information Systems and Communication Service. --- Probability Theory and Stochastic Processes. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Algorithm Analysis and Problem Complexity. --- Production scheduling --- Stochastic processes --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

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Advances in Queueing Theory and Network Applications presents several useful mathematical analyses in queueing theory and mathematical models of key technologies in wired and wireless communication networks such as channel access controls, Internet applications, topology construction, energy saving schemes, and transmission scheduling. In sixteen high-quality chapters, this work provides novel ideas, new analytical models, and simulation and experimental results by experts in the field of queueing theory and network applications. The text serves as a state-of-the-art reference for a wide range of researchers and engineers engaged in the fields of queueing theory and network applications, and can also serve as supplemental material for advanced courses in operations research, queueing theory, performance analysis, traffic theory, as well as theoretical design and management of communication networks.

Mathematics. --- Number theory. --- Queuing theory. --- Telecommunication systems -- Mathematical models. --- Queuing theory --- Telecommunication systems --- Civil & Environmental Engineering --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Electrical Engineering --- Operations Research --- Mathematical models --- Computer networks. --- Erlang traffic formula --- Queueing theory --- Theory of queues --- Waiting-line theory --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Homology theory. --- Moduli theory. --- Engineering. --- Information theory. --- Mathematical models. --- Operations research. --- Management science. --- Probabilities. --- Complexity, Computational. --- Electrical engineering. --- Communications Engineering, Networks. --- Mathematical Modeling and Industrial Mathematics. --- Complexity. --- Operations Research, Management Science. --- Probability Theory and Stochastic Processes. --- Information and Communication, Circuits. --- 517 <061.3> --- 517 <061.3> Analysis--?<061.3> --- Analysis--?<061.3> --- Ordered algebraic structures --- Mathematical analysis --- Production scheduling --- Stochastic processes --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Distributed processing --- Geometry, Algebraic. --- Differentiable dynamical systems --- Differential operators --- Number theory --- Congresses. --- Telecommunication. --- Distribution (Probability theory. --- Global analysis (Mathematics) --- Analyse globale (mathématiques) --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Construction --- Industrial arts --- Technology --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Computational complexity. --- Communication theory --- Cybernetics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Complexity, Computational --- Machine theory --- Models, Mathematical --- Simulation methods --- Electric engineering --- Engineering --- Analyse globale (mathématiques) --- Theorie des nombres --- Theorie multiplicative --- Algebres et anneaux associatifs --- Geometrie algebrique --- Ideaux et modules