Probability, Markov Chains, Queues, and Simulation (eBook)

The Mathematical Basis of Performance Modeling

William J. Stewart (Autor)

eBook Download: EPUB

2009
776 Seiten
Princeton University Press (Verlag)
978-1-4008-3281-1 (ISBN)

Infos

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 theoriesCarefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approachEach chapter concludes with an extensive set of exercises

Autor

William J. Stewart is professor of computer science at North Carolina State University. He is the author of An Introduction to the Numerical Solution of Markov Chains (Princeton).

Produkt-Details

• Erscheint lt. Verlag: 6.7.2009
• Zusatzinfo: 175 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: Accuracy and precision • Addition • algebraic equation • algorithm • Almost surely • Approximation • balance equation • Big O notation • Binomial Distribution • Block Matrix • coefficient • Coefficient matrix • combination • Computation • Conditional probability • Confidence interval • continuous-time Markov chain • convolution • Cumulative distribution function • Customer • Degrees of freedom (statistics) • Derivative • Diagram (category theory) • Distribution Function • Eigenvalues and Eigenvectors • Elementary event • Equation • Erlang distribution • estimation • expected value • exponential distribution • Fair coin • Gaussian elimination • geometric distribution • Hyperexponential distribution • Hypoexponential distribution • Independence (probability theory) • Independent and identically distributed random variables • Infinitesimal generator (stochastic processes) • Initial Condition • Integer • Iteration • Iterative Method • Joint probability distribution • Laplace transform • Law of total probability • Linear combination • Little's Law • Marginal distribution • Markov Chain • MATLAB • Moment (mathematics) • Monotonic Function • Mutual exclusivity • Natural number • Normal distribution • Numerical analysis • Parameter • Parameter (computer programming) • percentage • Permutation • Phase-type distribution • Poisson distribution • Poisson Point Process • polynomial • Probability • Probability density function • Probability Distribution • Probability Distribution Function • Probability mass function • Probability Theory • Proportionality (mathematics) • Quantity • Queueing Theory • Random Number • random number generation • Random Variable • real number • rectangle • Residual Time • Sample space • Sampling (Statistics) • scientific notation • Simulation • Simultaneous Equations • Special case • standard deviation • State diagram • stationary distribution • Statistic • Stochastic matrix • Stochastic process • Subset • Summation • Theorem • Transition rate matrix • Uniform distribution (discrete) • Unit interval • Utilization • Variance
• ISBN-10: 1-4008-3281-0 / 1400832810
• ISBN-13: 978-1-4008-3281-1 / 9781400832811