William James Stewart

Works (19)

Updated: February 10th, 2025 16:10

2014 book

A first course in probability

[Place of publication not identified]: [CreateSpace Independent Publishing Platform].

By: W. Stewart

Source: NC State University Libraries
Added: August 6, 2018

2008 article

An algebraic condition for product form in stochastic automata networks without synchronizations

Fourneau, J. M., Plateau, B., & Stewart, W. J. (2008, May 16). Performance Evaluation.

By: J. Fourneau*, B. Plateau* & W. Stewart n

topics (OpenAlex): Advanced Queuing Theory Analysis; Petri Nets in System Modeling; Distributed systems and fault tolerance
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)
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Source: NC State University Libraries
Added: August 6, 2018

2007 article

Phase-type distributions in stochastic automata networks

Sbeity, I., Brenner, L., Plateau, B., & Stewart, W. J. (2007, March 21). European Journal of Operational Research.

By: I. Sbeity, L. Brenner, B. Plateau & W. Stewart n

author keywords: stochastic automata networks; phase-type distributions
topics (OpenAlex): Petri Nets in System Modeling; Formal Methods in Verification; Advanced Queuing Theory Analysis
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)
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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, March 30). Future Generation Computer Systems.

By: A. Benoit, B. Plateau & W. Stewart n

author keywords: large and sparse Markov chains; stochastic automata networks; generalized tensor algebra; vector-descriptor multiplication; shuffle algorithm
topics (OpenAlex): Petri Nets in System Modeling; Formal Methods in Verification; Advanced Queuing Theory Analysis
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Source: Web Of Science
Added: August 6, 2018

2004 article

A Kronecker product approximate preconditioner for SANs

Langville, A. N., & Stewart, W. J. (2004, May 20). Numerical Linear Algebra with Applications.

By: A. Langville n & W. Stewart n

author keywords: stochastic automata networks; nearest Kronecker products; inultilinear alaebra; preconditioning
topics (OpenAlex): Matrix Theory and Algorithms; Tensor decomposition and applications; Advanced NMR Techniques and Applications
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 article

On the benefits of using functional transitions and Kronecker algebra

Benoit, A., Fernandes, P., Plateau, B., & Stewart, W. J. (2004, July 21). Performance Evaluation.

By: A. Benoit *, P. Fernandes *, B. Plateau* & W. Stewart n

author keywords: Markov chains; stochastic automata networks; generalized tensor algebra; vector-descriptor multiplication
topics (OpenAlex): Parallel Computing and Optimization Techniques; Embedded Systems Design Techniques; Real-Time Systems Scheduling
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)
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Source: Web Of Science
Added: August 6, 2018

2004 article

Preface

Langville, A. N., & Stewart, W. J. (2004, April 22). Linear Algebra and Its Applications.

By: A. Langville n & W. Stewart n

topics (OpenAlex):
Source: Web Of Science
Added: August 6, 2018

2004 article

Testing the Nearest Kronecker Product Preconditioner on Markov Chains and Stochastic Automata Networks

Langville, A. N., & Stewart, W. J. (2004, August 1). INFORMS Journal on Computing.

By: A. Langville n & W. Stewart n

author keywords: probability; Markov processes; queues; Markovian; algorithms
topics (OpenAlex): Metal-Organic Frameworks: Synthesis and Applications; Matrix Theory and Algorithms; Advanced Battery Materials and Technologies
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 article

The Kronecker product and stochastic automata networks

Langville, A. N., & Stewart, W. J. (2004, February 10). Journal of Computational and Applied Mathematics.

By: A. Langville n & W. Stewart*

author keywords: stochastic automata networks; Kronecker products; Kronecker product properties; preconditioning
topics (OpenAlex): Petri Nets in System Modeling; Formal Methods in Verification; semigroups and automata theory
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 article

The Peps Software Tool

Benoit, A., Brenner, L., Fernandes, P., Plateau, B., & Stewart, W. J. (2003, January 1). Lecture Notes in Computer Science.

By: A. Benoit *, L. Brenner *, P. Fernandes *, B. Plateau* & W. Stewart n

Ed(s): P. Kemper, W. H. Sanders (Eds.),

topics (OpenAlex): Petri Nets in System Modeling; Formal Methods in Verification; Real-Time Systems Scheduling
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

Jungblut-Hessel, R., Plateau, B., Stewart, W. J., & Ycart, B. (2001, April 1). RAIRO - Operations Research.

By: R. Jungblut-Hessel*, B. Plateau*, W. Stewart n & B. Ycart

author keywords: Markov chains; stochastic automata networks; simulation; stochastic modeling
topics (OpenAlex): Traffic control and management; Simulation Techniques and Applications; Transportation Planning and Optimization
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)
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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, January 1). SIAM Journal on Scientific Computing.

By: T. Dayar & W. Stewart*

author keywords: Markov chains; near-complete decomposability; partitioning; block SOR; iterative aggregation-disaggregation; Krylov subspace methods; preconditioning
topics (OpenAlex): Matrix Theory and Algorithms; Markov Chains and Monte Carlo Methods; Sparse and Compressive Sensing Techniques
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 article

Numerical Analysis Methods

Stewart, W. J. (2000, January 1). Lecture Notes in Computer Science.

By: W. Stewart n

Ed(s): G. Haring, C. Lindemann, & M. Reiser (Eds.),

topics (OpenAlex): Petri Nets in System Modeling; Real-Time Systems Scheduling; Formal Methods in Verification
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 article

A numerical study of large sparse matrix exponentials arising in Markov chains

Sidje, R. B., & Stewart, W. J. (1999, January 1). Computational Statistics & Data Analysis.

By: R. Sidje * & W. Stewart n

topics (OpenAlex): Matrix Theory and Algorithms; Numerical methods for differential equations; Parallel Computing and Optimization Techniques
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.

By: W. Davis, M. Chu , J. McConnell, P. Dolan, L. Norris, E. Ortiz, R. Plemmon, D. Ridgeway ...

Source: NC State University Libraries
Added: August 6, 2018

1998 article

Efficient descriptor-vector multiplications in stochastic automata networks

Fernandes, P., Plateau, B., & Stewart, W. J. (1998, May 1). Journal of the ACM.

By: P. Fernandes *, B. Plateau* & W. Stewart n

author keywords: generalized tensor algebra; Markov chains; stochastic automata networks; vector-descriptor multiplication
topics (OpenAlex): Advanced Queuing Theory Analysis; Petri Nets in System Modeling; Distributed systems and fault tolerance
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)
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Source: Web Of Science
Added: August 6, 2018

1998 article

Optimizing tensor product computations in stochastic automata networks

Fernandes, P., Plateau, B., & Stewart, W. J. (1998, January 1). RAIRO - Operations Research.

By: P. Fernandes *, B. Plateau* & W. Stewart n

topics (OpenAlex): Formal Methods in Verification; Petri Nets in System Modeling; Distributed systems and fault tolerance
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 article

Quasi Lumpability, Lower-Bounding Coupling Matrices, and Nearly Completely Decomposable Markov Chains

Dayar, T., & Stewart, W. J. (1997, April 1). SIAM Journal on Matrix Analysis and Applications.

By: T. Dayar & W. Stewart*

author keywords: Markov chains; quasi lumpability; decomposability; stationary probability; aggregation-disaggregation schemes
topics (OpenAlex): Matrix Theory and Algorithms; Graph theory and applications; graph theory and CDMA systems
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)
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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.

By: W. Stewart

Source: NC State University Libraries
Added: August 6, 2018

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