By William J. Stewart
Probability, Markov Chains, Queues, and Simulation presents a contemporary and authoritative therapy of the mathematical procedures that underlie functionality modeling. The specified reasons of mathematical derivations and various illustrative examples make this textbook with ease obtainable to graduate and complicated undergraduate scholars taking classes within which stochastic tactics play a primary position. The textbook is appropriate to a large choice of fields, together with machine technology, engineering, operations study, records, and mathematics.
The textbook seems on the basics of chance idea, from the fundamental strategies 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 perspective. subject matters comprise the Chapman-Kolmogorov equations; irreducibility; the capability, basic, and reachability matrices; random stroll difficulties; reversibility; renewal strategies; and the numerical computation of desk bound and brief distributions. The M/M/1 queue and its extensions to extra common birth-death strategies are analyzed intimately, as are queues with phase-type arrival and repair approaches. 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 handled. Open and closed queueing networks are analyzed. the ultimate a part of the ebook addresses the mathematical foundation of simulation.
each one bankruptcy of the textbook concludes with an intensive set of routines. An instructor's answer guide, within which all routines are thoroughly labored out, is additionally to be had (to professors only).
- Numerous examples remove darkness from the mathematical theories
- Carefully designated reasons of mathematical derivations warrantly a precious pedagogical process
- Each bankruptcy concludes with an in depth set of workouts
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Additional info for Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling by William J. Stewart