These same examples are used as illustrations later.
Introduction to matrix analytic methods in stochastic modeling in SearchWorks catalog
The second part of the book deals with phase-type distributions and related-point processes, which provide a versatile set of tractable models for applied probability. Part three reviews birth-and-death processes, and points out that the arguments for these processes carry over to more general processes in a parallel manner and are based on Markov renewal theory. Part four covers material where algorithmic and probabilistic reasoning are most intimately connected.
In three steps, the authors take you from one of the simplest iterative procedures to the fastest, relating the successive approximations to the dynamic behavior of the stochastic process itself. The final part goes beyond simple QBDs with a sequence of short chapters where the authors discuss various extensions to the analyzed processes. Their intention is to show that the fundamental ideas extend beyond simple homogeneous QBD.
Matrix analytic methods constitute a success story, illustrating the enrichment of a science, applied probability, by a technology, that of digital computers. Marcel Neuts has played a seminal role in these exciting developments, promoting numerical investigation as an essential part of the solution of probability models. He wrote in ,. When done properly, it conforms to the highest standard of scientific research.
This had been long accepted among numerous scientific communities but was not at the time the prevalent view among applied probabilists. The excitement one feels when dealing with that subject stems from the synergy resulting from keeping algorithmic considerations in the forefront when solving stochastic problems.
The connection was already noted in by Kemeny and Snell who wrote,.
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Latouche and V. Return to All Sections. Front Matter. PH Distributions. Markovian Point Processes. Birth-and-Death Processes.
Processes under a Taboo. Homogeneous QBDs. Stability Condition.
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