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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.

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

Source: NC State University Libraries

Added: August 6, 2018

2008 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.

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

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

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.

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.

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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