A Computational Framework For Two-Dimensional Random Walks With Restarts

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in [D. A. Bini, S. Massei, and B. Meini, Math. Comp., 87 (2018), pp. 2811-2830] which allows us to deal with more general situations such as processes involving restart events. This is motivated by the need for modeling processes that can incur in unexpected failures like computer system reboots. We present a theoretical analysis of an enriched Banach algebra that, combined with appropriate algorithms, enables the numerical treatment of these problems. The results are applied to the solution of bidimensional quasi-birth-death processes with infinitely many phases which model random walks in the quarter plane, relying on the matrix analytic approach. The reliability of our approach is confirmed by extensive numerical experimentation on several case studies.


Published in:
Siam Journal On Scientific Computing, 42, 4, A2108-A2133
Year:
Jan 01 2020
Publisher:
Philadelphia, SIAM PUBLICATIONS
ISSN:
1064-8275
1095-7197
Keywords:
Laboratories:




 Record created 2020-09-26, last modified 2020-10-29


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