"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
Professors: A supplementary Solutions Manual is available for
this book. It is restricted to teachers using the text in courses.
For information on how to obtain a copy, refer to: http:
//press.princeton.edu/class_use/solutions.html
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