Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Cet article n’est pas disponible.Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach

Topics include matrix-geometric invariant vectors, buffer models, queues in a random environment and more.

Based on a series of lectures the author gave at The Johns Hopkins University, this graduate-level treatment contains a variety of results on queues and stochastic models with the unifying feature of ready algorithmic implementation. The material comes under the broader heading of computational probability, defined as the study of stochastic models with concern for algorithmic feasibility over a wide, realistic range of parameter values.

Chapter I contains a systematic discussion of the general properties of a class of Markov chains and processes that in the positive recurrent case have a matrix-geometric invariant probability vector. Chapter 2 is a self-contained treatment of the properties of phase type distributions, while Chapter 3 deals with the case of block-tridiagonal transition probability matrices. Chapter 4 treats the GI/PH/1 queue and several of its variants and generalizations, including a lengthy discussion of semi-Markovian arrival processes and their applications. Chapters 5 and 6 deal with an eclectic variety of models suggested by diverse applications. To keep the volume reasonably concise, the author has limited discussion to one class of structured Markov chains, and to a broad selection of its applications. This will be a valuable text for anyone involved in probability, numerical computation or computer modelling.