Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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THE DIMENSION REDUCTION ALGORITHM FOR THE POSITIVE REALIZATION OF DISCRETE PHASE-TYPE DISTRIBUTIONS

  • Kim, Kyung-Sup (DEPARTMENT OF COMPUTER ENGINEERING, CHUNGNAM NATIONAL UNIVERSITY)
  • Received : 2011.12.06
  • Accepted : 2012.01.25
  • Published : 2012.03.25
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Abstract

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

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