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Works (19)
Updated: April 4th, 2024 22:08
2014 book
A first course in probability
[Place of publication not identified]: [CreateSpace Independent Publishing Platform].
Source: NC State University Libraries
Added: August 6, 2018
2008 journal article
An algebraic condition for product form in stochastic automata networks without synchronizations
Performance Evaluation, 65(11-12), 854–868.
TL;DR:
A sufficient condition for the steady-state distribution to have product form is proved and this theorem generalizes former results on SANs as well as results on modulated Markovian queues, such as Boucherie's theory on competing Markov chain.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: NC State University Libraries
Added: August 6, 2018
2007 journal article
Phase-type distributions in stochastic automata networks
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 186(3), 1008–1028.
author keywords: stochastic automata networks; phase-type distributions
TL;DR:
It is shown how phase-type distributions may be incorporated into S ans thereby providing the wherewithal by which arbitrary distributions can be used which in turn leads to an improved ability for more accurately modeling numerous real phenomena.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2006 article
Memory-efficient Kronecker algorithms with applications to the modelling of parallel systems
Benoit, A., Plateau, B., & Stewart, W. J. (2006, August). FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE, Vol. 22, pp. 838–847.
author keywords: large and sparse Markov chains; stochastic automata networks; generalized tensor algebra; vector-descriptor multiplication; shuffle algorithm
open access via citeseerx.ist.psu.edu (repository)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2004 article
Kronecker product approximate preconditioner for SANs
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Vol. 11, pp. 723–752.
author keywords: stochastic automata networks; nearest Kronecker products; inultilinear alaebra; preconditioning
TL;DR:
The nearest Kr onecker product technique is extended to approximate the Q matrix for an SAN with a Kronecker product, A1 ⊗ A2 ⊷…⊗ AN, and taken as the authors' SAN NKP preconditioner.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
2004 journal article
On the benefits of using functional transitions and Kronecker algebra
PERFORMANCE EVALUATION, 58(4), 367–390.
author keywords: Markov chains; stochastic automata networks; generalized tensor algebra; vector-descriptor multiplication
TL;DR:
This paper proposes a suite of modelling strategems and numerical procedures that go a long way to alleviating the drawback of computation times in Kronecker or tensor product modeling techniques.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2004 article
Special issue devoted to papers presented at the Conference on the Numerical Solution of Markov Chains 2003 - Preface
Langville, A. N., & Stewart, W. J. (2004, July 15). LINEAR ALGEBRA AND ITS APPLICATIONS, Vol. 386, pp. 1–2.
Source: Web Of Science
Added: August 6, 2018
2004 journal article
Testing the nearest Kronecker product preconditioner on Markov chains and stochastic automata networks
INFORMS JOURNAL ON COMPUTING, 16(3), 300–315.
author keywords: probability; Markov processes; queues; Markovian; algorithms
TL;DR:
It is concluded that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a SAN.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
2004 journal article
The Kronecker product and stochastic automata networks
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 167(2), 429–447.
author keywords: stochastic automata networks; Kronecker products; Kronecker product properties; preconditioning
TL;DR:
The most useful properties of the Kronecker product are collected and cataloged and several new properties are discovered in the search for a stochastic automata network preconditioner.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
2003 chapter
The PEPS software tool
In W. H. S. P. Kemper (Ed.), Computer performance evaluation: Modelling techniques and tools: 13th international conference, TOOLS 2003, Urbana, IL, USA, September 2-5, 2003 (Vol. 2794, pp. 98–115).
Ed(s): W. P. Kemper
TL;DR:
This paper presents the numerical techniques included in version 2003 of the Peps software, the basics of its interface and three practical examples.
(via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018
2001 article
Fast simulation for road traffic network
RAIRO-RECHERCHE OPERATIONNELLE-OPERATIONS RESEARCH, Vol. 35, pp. 229–250.
author keywords: Markov chains; stochastic automata networks; simulation; stochastic modeling
TL;DR:
Une methode pour realiser des simulations rapides de grands systemes Markoviens, basee sur l'utilisation of trois concepts: l'uniformisation de chaine de Markov, une dynamique liee aux evenements et the modularite.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2000 article
Comparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chains
Dayar, T., & Stewart, W. J. (2000, May 21). SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol. 21, pp. 1691–1705.
author keywords: Markov chains; near-complete decomposability; partitioning; block SOR; iterative aggregation-disaggregation; Krylov subspace methods; preconditioning
TL;DR:
There is need for further research in this area, specifically to aid in the understanding of the effects of the degree of coupling of NCD Markov chains and their nonzero structure on the convergence characteristics and space requirements of iterative solvers.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
2000 chapter
Numerical analysis methods
In C. L. G. Haring & M. Reiser (Eds.), Performance evaluation: Origins and directions (Vol. 1769, pp. 355–376).
Ed(s): C. G. Haring & M. Reiser
TL;DR:
In the context of Performance Evaluation (PE), numerical analysis methods refer to those methods which work with a Markov chain representation of the system under evaluation and use techniques from the domain of numerical analysis to compute stationary and/or transient state probabilities or other measures of interest.
(via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018
1999 journal article
A numerical study of large sparse matrix exponentials arising in Markov chains
Computational Statistics & Data Analysis, 29(3), 345–368.
TL;DR:
A Krylov-based method is compared with some of the current approaches used for computing transient solutions of Markov chains on a power challenge array supercomputer on three different models.
(via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018
1998 book
Cornelius Lanczos: Collected published papers with commentaries
Raleigh, NC: College of Physical and Mathematical Sciences, North Carolina State University.
Source: NC State University Libraries
Added: August 6, 2018
1998 journal article
Efficient descriptor-vector multiplications in stochastic automata networks
JOURNAL OF THE ACM, 45(3), 381–414.
author keywords: generalized tensor algebra; Markov chains; stochastic automata networks; vector-descriptor multiplication
TL;DR:
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.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1998 journal article
Optimizing tensor product computations in stochastic automata networks
RAIRO. Recherche Operationnelle = Operations Research, 32(3), 325–351.
TL;DR:
This paper considers the possible benefits of grouping automata in a SAN with many small automata, to create an equivalent SAN having a smaller number of larger automata.
(via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018
1997 journal article
Quasi lumpability, lower-bounding coupling matrices, and nearly completely decomposable Markov chains
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 18(2), 482–498.
author keywords: Markov chains; quasi lumpability; decomposability; stationary probability; aggregation-disaggregation schemes
TL;DR:
It is shown that nearly completely decomposable (NCD) Markov chains are quasi-lumpable, and the technique may be used to compute lower and upper bounds on the stationary probability of each NCD block using a lower-bounding nonnegative coupling matrix.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1995 book
Computations with Markov chains: Proceedings of the 2nd International Workshop on the Numerical Solution of Markov Chains
Boston: Kluwer Academic Publishers.
Source: NC State University Libraries
Added: August 6, 2018
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