Algorithms for Coxianization of Phase-Type Generators
Qi-Ming He, Hanqin Zhang, Jungong Xue
INFORMS Journal on Computing · 2011 · Volume 23 · Issue 1
Abstract
This paper develops algorithms for finding Coxian generators to phase-type (PH)-majorize a PH -generator T with only real eigenvalues. In the first part of this paper, we investigate matrices S and P satisfying TP = PS and P e = e . Conditions on T are identified for S to be an ordered Coxian generator and for P to be nonnegative, which consequently implies that S PH -majorizes T . It is shown that every PH -generator with only real eigenvalues is PH -majorized by some Coxian generator. In the second part of this paper, the results on S and P and the conditions on T are used to develop efficient algorithms for Coxianization of PH -generators. Numerical examples are presented for a comparison between the developed algorithms.
Keywords
matrix-analytic methods, Coxian distribution, phase-type distribution, probability distribution
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