Phase-type distributions and representations: Some results and open problems for system theory

@article{Commault2003PhasetypeDA,
  title={Phase-type distributions and representations: Some results and open problems for system theory},
  author={Christian Commault and St{\'e}phane Mocanu},
  journal={International Journal of Control},
  year={2003},
  volume={76},
  pages={566 - 580}
}
In this paper we consider phase-type distributions. These distributions correspond to the random hitting time of an absorbing Markov chain. They are used for modelling various random times, in particular, those which appear in manufacturing systems as processing times, times to failure, repair times, etc. The Markovian nature of these distributions allows the use of very efficient matrix based computer methods for performance evaluation. In this paper we give a system theory oriented… 
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