Algorithms for Coxianization of Phase-Type Generators

Authors:
Qi-Ming He;Hanqin Zhang;Jungong Xue
Affiliations:
Department of Industrial Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4, Canada;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080 Beijing, People's Republic of China/ and NUS Business School, Singapore 119245;School of Mathematical Science, Fudan University, 200433 Shanghai, People's Republic of China
Venue:
INFORMS Journal on Computing
Year:
2011

Citing 3
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Topics in matrix analysis

Topics in matrix analysis
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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 Pe = e. Conditions on T are identified for S to be an ordered Coxian generator and for P to be nonnegative, which consequently implies that SPH-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.