By William J. Stewart
ISBN-10: 0691140626
ISBN-13: 9780691140629
Probability, Markov Chains, Queues, and Simulation offers a latest and authoritative remedy of the mathematical approaches that underlie functionality modeling. The unique factors of mathematical derivations and diverse illustrative examples make this textbook simply available to graduate and complicated undergraduate scholars taking classes during which stochastic tactics play a primary position. The textbook is suitable to a large choice of fields, together with laptop technology, engineering, operations examine, statistics, and mathematics.
The textbook appears on the basics of likelihood thought, from the elemental options of set-based chance, via likelihood distributions, to bounds, restrict theorems, and the legislation of enormous numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational viewpoint. subject matters comprise the Chapman-Kolmogorov equations; irreducibility; the capability, primary, and reachability matrices; random stroll difficulties; reversibility; renewal techniques; and the numerical computation of desk bound and brief distributions. The M/M/1 queue and its extensions to extra basic birth-death methods are analyzed intimately, as are queues with phase-type arrival and repair strategies. The M/G/1 and G/M/1 queues are solved utilizing embedded Markov chains; the busy interval, residual provider time, and precedence scheduling are taken care of. Open and closed queueing networks are analyzed. the ultimate a part of the publication addresses the mathematical foundation of simulation.
each one bankruptcy of the textbook concludes with an intensive set of workouts. An instructor's answer handbook, during which all routines are thoroughly labored out, is usually to be had (to professors only).
- Numerous examples remove darkness from the mathematical theories
- Carefully specified factors of mathematical derivations warrantly a invaluable pedagogical method
- Each bankruptcy concludes with an in depth set of workouts
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Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling by William J. Stewart
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