Probability, Markov Chains, Queues, and Simulation
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Accuracy and precision
Addition
Algorithm
Almost surely
Approximation
Author_William J. Stewart
Category=PBT
Category=PBWH
Coefficient
Combination
Computation
Conditional probability
Continuous-time Markov chain
Convolution
Cumulative distribution function
Customer
Distribution function
Eigenvalues and eigenvectors
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Erlang distribution
Estimation
Expected value
Exponential distribution
Fair coin
Gaussian elimination
Geometric distribution
Hyperexponential distribution
Independence (probability theory)
Independent and identically distributed random variables
Infinitesimal generator (stochastic processes)
Integer
Iteration
Iterative method
Law of total probability
Little's law
Marginal distribution
Markov chain
MATLAB
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
Proportionality (mathematics)
Quantity
Queueing theory
Random number
Random number generation
Random variable
Real number
Sample space
Simulation
Simultaneous equations
Standard deviation
State diagram
Stationary distribution
Statistic
Stochastic matrix
Subset
Summation
Theorem
Transition rate matrix
Variance
Product details
- ISBN 9780691140629
- Weight: 1474g
- Dimensions: 178 x 254mm
- Publication Date: 26 Jul 2009
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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
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).
