Abstract
MAMsolver is a software tool for the solution of M/G/1-type, GI/M/1-type, and QBD processes. The collection of solution algorithms implemented by MAMsolver are known as matrix-analytic methods and are used to compute stationary measures of interest such as the probability vector, the queue length distribution, the waiting time, the system queue length, and any higher moments of the queue length. The tool also provides probabilistic measures that describe the stability of the queueing system such as the caudal characteristic.
This work was partially supported by National Science Foundation under grants EIA-9974992, EIA-77030, CCR-0098278, and ACI-0090221.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D.A. Bini and B. Meini. Using displacement structure for solving non-skip-free M/G/1 type Markov chains. In A. Alfa and S. Chakravarthy Eds. Advances in Matrix Analytic Methods for Stochastic Models, pages 17–37, Notable Publications Inc, NJ, 1998.
G. Ciardo, A. Riska, and E. Smirni. An aggregation-based solution method for M/G/1-type processes. In B. Plateau, W. J. Stewart, and M. Silva, editors, Numerical Solution of Markov Chains, pages 21–40. Prensas Universitarias de Zaragoza, Zaragoza, Spain, Sept. 1999.
G. Ciardo and E. Smirni. ETAQA: an efficient technique for the analysis of QBD-processes by aggregation. Performance Evaluation, Vol.(36–37), pages 71–93, 1999.
B.R. Haverkort, A.P.A. Van Moorsel and A. Dijkstra. MGMtool: A Performance Analysis Tool Based on Matrix Geometric Methods. In R. Pooley, and J. Hillston, editors Modelling Techniques and Tools, pages 312–316, Edinburgh University Press, 1993.
G. Latouche and V. Ramaswami. Introduction to Matrix Geometric Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability, SIAM Press, Philadelphia, PA, 1999.
B. Meini. An improved FFT-based version of Ramaswami’s formula. Comm. Statist. Stochastic Models, Vol. 13 pages 223–238, 1997.
M. F. Neuts. Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore, MD, 1981.
M. F. Neuts. Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York, NY, 1989.
V. Ramaswami. A stable recursion for the steady state vector in Markov chains of M/G/1 type. Commun. Statist.-Stochastic Models, Vol. 4 pages 183–263, 1988.
V. Ramaswami and G. Latouche. A general class of Markov processes with explicit matrix-geometric solutions. OR Spektrum, 8:209–218, Aug. 1986.
A. Riska, and E. Smirni. An exact aggregation approach for M/G/1-type Markov chains. to appear at ACM SIGMETRICS’02 Conference, Marina Del Rey, CA, June 2002.
Mark.S. Squillante. MAGIC: A computer performance modeling tool based on matrix-geometric techniques. In Proc. Fifth International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Riska, A., Smirni, E. (2002). MAMSolver: A Matrix Analytic Methods Tool. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds) Computer Performance Evaluation: Modelling Techniques and Tools. TOOLS 2002. Lecture Notes in Computer Science, vol 2324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46029-2_14
Download citation
DOI: https://doi.org/10.1007/3-540-46029-2_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43539-6
Online ISBN: 978-3-540-46029-9
eBook Packages: Springer Book Archive