Truncation of Passage-time Calculations in Semi-Markov Models

Abstract

Calculation of passage time distributions in large semi-Markov models can be accomplished by means of a previously-presented iterative algorithm, the core of which is repeated sparse matrix-vector multiplication. The algorithms performance is therefore highly dependent on the number of multiplications of matrix and vector elements that must be performed during each iteration. At the same time, the products of matrix and vector elements that are very small contribute little to the overall result of the multiplication. In this paper, we investigate the effect of ignoring these values on both the performance and accuracy of the iterative passage time algorithm. We show that in the models we analyse here this truncation significantly reduces the number of multiplications which must be performed, and hence significantly reduces the running time of the algorithm, with little effect on the accuracy of the final result.