Publications

William J. Stewart

Billy's Home Page


BOOKS

Probability, Markov Chains, Queues, and Simulation.
Princeton University Press, 780 pages, 2009.

An Introduction to the Numerical Solution of Markov Chains.
Princeton University Press, 550 pages, 1994.

Numerical Solution of Markov Chains.
Edited Proceedings of The Third International Conference on the Numerical Solution of Markov Chains. Prensas Universitarias de Zaragoza, Spain, 344 pages, 1999.

Computations with Markov Chains.
Edited Proceedings of The Second International Conference on the Numerical Solution of Markov Chains. Kluwer Academic Publisher, 616 pages, 1995.

Numerical Solution of Markov Chains.
Edited Proceedings of The First International Conference on the Numerical Solution of Markov Chains. Marcel Dekker, Inc., New York, 1991, 704 pages.

CHAPTERS

Numerical Methods for Computing Stationary Distributions of Finite Irreducible Markov Chains. Chapter 3 of Advances in Computational Probability. Edited by Winfried Grassmann; Kluwer Academic Publishers, 1999.
Postscript copy available

Stochastic Automata Networks. (with Brigitte Plateau). Chapter 4 of Advances in Computational Probability. Edited by Winfried Grassmann; Kluwer Academic Publishers, 1999.
Postscript copy available

Numerical Analysis Methods. Performance Evaluation: Origins and Directions, Springer Verlag, Eds. G. Haring, C. Lindemann, M. Reiser, pp. 355--376, 1999.
Postscript copy available

Numerical Solution of Markov Chain Equations. Encyclopedia of Operations Research and Management Science Kluwer Academic Publishers, Ed. C.M. Harris, 1999
Postscript copy available

Numerical Techniques. Chapter 5 of Analysis of Queueing Networks, AFCET Publishers, 1979.

SELECTED PAPERS

Recent Articles

Memory-efficient Kronecker algorithms with applications to modelling parallel systems. To appear in Future Generation Computer Systems: Special Issue on System Performance Analysis and Evaluation. (with A. Benoit and B. Plateau)
PDF copy available.

Discrete-time Stochatic Automata Networks, in French. To appear in Technique et Science Informatiques. (with A. Benoit and B. Plateau)
PDF copy available.

The PEPS Software Tool. In P. Kemper, W.H. Sanders (eds), 13th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, TOOLS 2003, LNCS 2794 pages 98-115, Urbana, Illinois, USA, September 2003. (with A. Benoit, L. Brenner, P. Fernandes, B. Plateau.)
PDF copy available.

The Kronecker Product and Stochastic Automata Networks. Journal of Computational and Applied Mathematics, Vol. 167, No. 2, pp. 429-447, 2004. (with A. Langville).
PDF copy available.

On the benefits of Using Functional transitions and Kronecker Algebra. Performance Evaluation. Vol 58, pp. 367--390, 2004. (with A. Benoit, P. Fernandes and B. Plateau).
Postscript copy available.

Testing the nearest Kronecker product preconditioner on MCs and SANs. INFORMS Journal on Computing, Vol. 16, No. 3, pp. 300--315, 2004. (with A. Langville).
Postscript copy available.

Autonomous Solution Methods for Large-Scale Markov Chains. Submitted for Publication: (with W. Barge).
Postscript copy available.

A Kronecker Product Approximate Preconditioner for SANs. Journal of Numerical Linear Algebra, Vol. 11, No. 8, pp. 723--752, 2004. (with A. Langville).
Postscript copy available.

Comparison of Partitioning Techniques for Two-level Iterative Solvers on Large, Sparse Markov Chains. SIAM Journal on Scientific Computing. Volume 21, Number 5, pp. 1691-1705, 2000. (with T. Dayar).
Postscript copy available.

A Survey of Methods for Computing Large Sparse Matrix Exponentials Arising in Markov Chains. (with R.B. Sidje). Computational Statistics and Data Analysis, Vol. 29, pp. 345-368, 1999.
Postscript copy available.

Efficient Descriptor-Vector Multiplication in Stochastic Automata Networks. (with P. Fernandes and B. Plateau). Journal of the ACM, Vol. 45, No.3, May 1998.
Postscript copy available.

Optimizing Tensor Product Computations in Stochastic Automata Networks. (with Paulo Fernandes and Brigitte Plateau). Operations research, Vol. 32, pp. 325-351, 1998.
Postscript copy available.

Quasi-Lumpability, Lower Bounding Coupling Matrices and Nearly Completely Decomposable Markov Chains. SIAM Journal on Matrix Analysis and Applications, Volume 18, Number 2, 1997. (with T. Dayar).
Postscript copy available.

Numerical Issues for Stochastic Automata Networks. Proceedings of the Fourth Process Algebras and Performance Modelling Workshop, pp. 215--234, Torino, CLUT Editions, ISBN 88-7992-120-7, 1996. (with Paulo Fernandes and Brigitte Plateau).
Postscript copy available.

On the Effects of Using the Grassmann-Taskar-Heyman Method in Iterative Aggregation Disaggregation. SIAM Journal on Scientific Computing, Vol. 17, No.1, pp. 287 - 303, 1996. (with T. Dayar).
Postscript copy available.

The Numerical Solution of Stochastic Automata Networks. European Journal of Operations Research. Volume 86, Number 3, pp. 503 -- 525, 1995. (with K. Atif and B. Plateau).
Postscript copy available.

From Queueing Networks to Markov Chains: The XMarca Interface. Performance Evaluation, Vol. 24, pp. 23 -- 45, 1995. (with R. Klevans).
Postscript copy available.

On the Use of Periodicity Properties for the Efficient Numerical Solution of Certain Markov Chains. Journal of Numerical Linear Algebra with Applications, Vol. 1, Issue 3, pp. 265-286, May-June 1994. (with F. Bonhoure and Y. Dallery).
Postscript copy available.

Algorithms for Periodic Markov Chains. IMA Volume 48, Linear Algebra, Markov Chains and Queueing Models, Springer-Verlag, 1992, (with F. Bonhoure and Y. Dallery).
Postscript copy available.

A Two Stage Iteration for Solving Nearly Uncoupled Markov Chains. IMA Volumes in Mathematics and its Applications, Vol. 60, Recent Advances in Iterative Methods, pp. 201-216, July 1993. (with D.F. McAllister and G.W. Stewart).
Postscript copy available.

On the Use of Numerical Methods for ATM Models. Modelling and Performance Evaluation of ATM Technology. North-Holland Publishers, pp. 375-396, 1993.
Postscript copy available.

A General Framework for Iterative Aggregation/Disaggregation Methods. Proceedings of the Fourth Copper Mountain Conference on Iterative Methods, 1992. (with H.D. Kafeety and C.D. Meyer).
Postscript copy available.

Numerical Experiments with Iteration and Aggregation for Markov Chains. ORSA Journal on Computing, Vol 4, No. 3, pp. 336-350, 1992. (with Wei Wu).
Postscript copy available.

Numerical Methods in Markov Chain Modelling. Operations Research, Vol. 40, No. 6, pp. 1156-1179, 1992, (with B. Philippe and Y. Saad).
Postscript copy available.

Block Cyclic SOR for Markov Chains with p-Cyclic Infinitesimal Generator. Linear Algebra and its Applications, Vol. 154, pp. 145-223, 1991, (with K. Kontovassilis and R. Plemmons).
Postscript copy available.

Some Pre-1990 Articles

Recursive Procedures for the Numerical Solution of Markov Chains. Queueing Networks with Blocking, Edited by H.G. Perros and T. Altiok, North Holland Publishers, 1989, pp. 229-248.

Analysis of a Hybrid Multiple Access Protocol with Free Access of New Arrivals During Conflict Resolution. IEEE Transactions on Communications, Vol. 36, No. 7, 1988, pp. 806-815. (with P. Nain and N.D. Georganas).

Queueing Models, Block Hessenberg Matrices and the Method of Neuts. Annals of OR, Vol. 8, 1987, pp. 265-284, (with W.L. Cao).

A Queueing System where Customers Require a Random Number of Servers Simultaneously. European Journal of Operations Research, Vol. 23, 1986, pp. 331-342, (with G.Y. Fletcher and H.G. Perros).

A Note on the Inverse of Hessenberg-like Matrices. Linear Algebra and Its Applications, Vol. 76, 1986, pp. 233-240, (with W.L. Cao).

A Queueing Network Model of a Circuit Switching Access Scheme in the Integrated Services Environment. IEEE Transactions on Communications, Vol. COM-34, No. 1 (1986) pp. 25-30, (with G.Y. Fletcher and H.G. Perros).

Matrix Methods in Large Dependability Models. IBM Technical Report, T.J. Watson Research Center, Yorktown Heights, N.Y., 1985, (with A. Goyal).

An Approximate Numerical Solution for Multiclass Preemptive Priority Queues with General Service Time Distributions. ACM SIGMETRICS Performance Evaluation Review, Vol. 13, No. 4, 1985, pp 155-165, (with P. Snyder).

Iterative Aggregation/Disaggregation Techniques for Nearly Uncoupled Markov Chains. Journal of the ACM, Vol. 32, No. 3, 1985, pp. 702-719, (with W.L. Cao).

Explicit and Iterative Numerical Approaches to Solving Queueing Models. Operations Research" (ORSA), Vol. 33, No. 1, January 1985, pp. 183-202, (with P. Snyder).

Some Results on Equivalent Properties of Closed Load-Independent Exponential Queueing Networks. IEEE Transactions on Software Engineering, Vol. SE-10, No. 4, 1984, pp. 414-422, (with W. Stohs).

On a Rayleigh-Ritz Refinement Technique for Nearly Uncoupled Stochastic Matrices. Journal of Linear Algebra and Its Applications, Vol. 60, pp. 1-25, August 1984, (with D.F. McAllister and G.W. Stewart).

Iterative Methods for Computing Stationary Distributions of Nearly Completely Decomposable Markov Chains. SIAM Journal of Algebraic and Discrete Methods, Vol. 5, No. 2, pp. 164-186, June 1984.

Extensions and Computational Aspects of an Iterative Method. ACM SIGMETRICS Performance Evaluation Review, Vol. 11, No. 4, 1982, pp. 186-194, (with R. Marie and P. Snyder).

Workload Characterization and Performance Evaluation in a Research Environment. ACM SIGMETRICS Performance Evaluation Review, Vol. 11, No. 4, 1984, pp. 39-50, (with L. Hodges).

On Computing the Stationary Probability Vector of a Network of Two Coxian Servers. Applied Probability - Computer Science: The Interface, Vol. I, Birkhauser Publishers, 1982, pp. 275-296.

An Iterative Method for the Exact Solution of General Queueing Networks. ACM SIGMETRICS Performance Evaluation Review, Vol. 10, No. 3, 1981, pp. 97-104, (with S. Dodd and D.F. McAllister).

Algorithm 570: LOPSI. ACM Transactions on Mathematical Software (TOMS), Vol. 7, No. 2, June 1981, pp. 230-232, (with A. Jennings.)

A Simultaneous Iteration Algorithm for Real Matrices ACM Transactions on Mathematical Software (TOMS) Vol. 7, No. 2, June 1981, pp. 184-198, (with A. Jennings).

A Numerical Solution of the Lambda(n) /C_k/r/N Queue. European Journal of Operations Research, Vol. 5, 1980, pp. 56-68, (with R. Marie).

On the Existence of Composite Flow Equivalent Markovian Servers ACM SIGMETRICS Performance Evaluation Review, Vol. 9, No. 2, 1980, pp. 105-116.

A Direct Numerical Solution for Queueing Networks. Proceedings of the Fourth International Symposium on Modelling and Performance Evaluation of Computer Systems, February 1979, Vienna, Austria.

A Comparison of Numerical Techniques in Markov Modelling. Communications of the ACM, Vol 21, No. 2, February 1978, pp. 144-152.

A Hybrid Iterative-Numerical Technique for the Solution of a General Queueing Network. Proceedings of the Third International Symposium on Modelling and Performance Evaluation of Computer Systems, October 1977, Bonn, West Germany, pp. 173-188, (with R. Marie).

A New Approach to the Numerical Analysis of Markovian Model. Computer Performance, Chandy and Reiser, eds. North Holland Publishers, New York, 1977.

Practical Considerations in the Numerical Analysis of Markovian Models. Modelling and Performance Evaluation of Computer Systems, Beilner and Gelenbe, eds., North Holland Publishers, New York, 1976, pp. 363-376.

Markov Modelling Using Simultaneous Iteration. Dundee Biennial Conference on Numerical Analysis, July 1-4, 1975, Dundee, Scotland.

Simultaneous Iteration for Partial Eigensolution of Real Matrices. Journal of the Inst. Maths. Applics., Vol. 15, 1975, pp. 351-361, (with A. Jennings.).

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