### Abstract

The analysis of practical queueing problems benefits if realistic distributions can be used as parameters. Phase type (PH) distributions can approximate many distributions arising in practice, but their practical applicability has always been limited when they are described by a non-Markovian vector-matrix pair. In this case it is hard to check whether the non-Markovian vector-matrix pair defines a non-negative matrix-exponential function or not. In this paper we propose a numerical procedure for checking if the matrix-exponential function defined by a non-Markovian vector-matrix pair can be represented by a Markovian vector-matrix pair with potentially larger size. If so, then the matrix-exponential function is non-negative. The proposed procedure is based on O'Cinneide's characterization result, which says that a non-Markovian vector-matrix pair with strictly positive density on 0.

Original language | English |
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Pages (from-to) | 40-51 |

Number of pages | 12 |

Journal | Performance Evaluation |

Volume | 81 |

DOIs | |

Publication status | Published - Nov 2014 |

### Keywords

- Phase-type distribution
- Randomization
- Uniformization
- Vector-matrix representation

### ASJC Scopus subject areas

- Software
- Modelling and Simulation
- Hardware and Architecture
- Computer Networks and Communications