Efficient Solution for a Class of Markov Chain Models of Tandem Queueing Networks
We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077605Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1057
 E. Seneta, Non-Negative Matrices, John Wiley, New York, 1973.
 H. De Sterck, T.A. Manteuffel, S.F. McCormick, K. Miller, J. Pearson, J. Ruge, and G. Sanders, Smoothed aggregation multigrid for Markov chains, SIAM J. Sci. Comput., 2010, 32 (1): 40-61.
 G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM series on statistics and applied probability, 1999.
 S.D. Kamvar, T.H. Haveliwala, C.D. Manning, G.H. Golub, Extrapolation methods for accelerating PageRank computations, Proceedings of the Twelfth International World Wide Web Conference, 2003, pp. 261-270.
 B. Philippe, Y. Saad, W.J. Stewart, Numerical methods in Markov Chain modeling, Operations Research, 1992, 40 (6): 1156-1179.
 Z.-Z. Bai, G.H. Golub, L.-Z. Lu, J.F. Yin, Block triangular and skew- Hermitian splitting methods for positive-definite linear systems, SIAM J. Sci. Comput., 2005, 26 (3): 844-863.
 Z.-Z. Bai, G.H. Golub, M.K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 2003, 24 (3): 603-626.
 A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematics Science, Classics Allp. Math. 9, SIAM, Philadelphia, 1994.