Matrix-Analytic Methods in Stochastic Models

Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.

The only forum on the theoretical, algorithmic and methodological aspects of matrix-analytic and related methods in stochastic models, and their application across various fields This area of mathematics and its applications have grown and advanced tremendously over the past few years from the previous original and early developments in the area Presents the latest advances in this very important area of mathematics, as well as the latest advances in the applications of this area of mathematics across a broad spectrum of fields Includes supplementary material: sn.pub/extras

Auteur

Guy Latouche, Université Libre de Bruxelles, Belgium
Vaidyanathan Ramaswami , AT&T Labs Research, USA

Jay Sethuraman, Columbia University, USA

Karl Sigman, Columbia University, USA
Mark S. Squillante, IBM Thomas J. Watson Research Center, USA

David D. Yao, Columbia University, USA

Contenu

Factorization properties for a MAP-modulated fluid flow model under server vacation policies.- A compressed cyclic reduction for QBDs with low rank upper and lower transitions.- Bilateral matrix-exponential distribution.- AutoCAT: Automated Product-Form Solution of Stochastic Models.- Markovian trees subject to catastrophes: Would they survive forever?.- Majorization and Extremal PH-Distributions.- Acceptance-rejection methods for generating random variates from matrix exponential distributions and rational arrival processes.- Revisit to the tail asymptotics of the double QBD process: Refinement and complete solutions for the coordinate and diagonal directions.- Two-dimensional fluid queues with temporary assistance.- A Fluid Introduction To Brownian Motion & Stochastic Integration.- The impact of dampening demand variability in a production/inventory system with multiple retailers.