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Introduction to the numerical solution of Markov Chains
- W. Stewart
- Computer Science, Mathematics
- 14 November 1994
This document discusses Markov Chains, Direct Methods, Iterative Methods, and Projection Methods for Stochastic Automata Networks, as well as some of the techniques used to design and implement these systems.
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
- W. Stewart
- 26 July 2009
The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers.
Efficient descriptor-vector multiplications in stochastic automata networks
The concept of a generalized tensor product is introduced and a number of lemmas concerning this product are proved to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions.
A Simultaneous Iteration Algorithm for Real Matrices
Simultaneous iteration methods are extensions of the power method whereby iteration is carried out with a number of trial vectors tha t converge onto the eigenvectors corresponding to the dominant…
The Kronecker product and stochastic automata networks
The numerical solution of stochastic automata networks
Iterative aggregation/disaggregation techniques for nearly uncoupled markov chains
It is shown that the method of Takahashi corresponds to a modified block Gauss-Seidel step and aggregation, whereas that of Vantilborgh corresponds to an modified block Jacobistep and aggregation.
A numerical study of large sparse matrix exponentials arising in Markov chains 1 1 This work has ben
TwoTowers: A Tool Integrating Functional and Performance Analysis of Concurrent Systems
TwoTowers is presented, a tool for analyzing functional and performance properties of concurrent systems expressed as terms in the stochastically timed reward process algebra EMPAr, which describes the application of TwoTowers to the Lehmann-Rabin randomized distributed algorithm for the dining philosopher problem.
The PEPS Software Tool
- A. Benoit, L. Brenner, Paulo Fernandes, B. Plateau, W. Stewart
- Computer ScienceComputer Performance Evaluation / TOOLS
- 2 September 2003
This paper presents the numerical techniques included in version 2003 of the Peps software, the basics of its interface and three practical examples.