Dealing with Zero Density Using Piecewise Phase-Type Approximation

  • L’uboš Korenčiak
  • Jan Krčál
  • Vojtěch Řehák
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8721)


Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing this class of distributions, we suggest an alternative representation by CTMC extended with discrete-time transitions. Using discrete-time transitions we split the density function into multiple intervals. Within each interval, we then approximate the density with standard phase-type fitting. We provide an experimental evidence that our method requires only a moderate number of states to approximate such distributions with regions of zero density. Furthermore, the usage of CTMC with discrete-time transitions is supported by a number of techniques for their analysis. Thus, our results promise an efficient approach to the transient analysis of a class of non-Markovian models.


Transient Analysis Continuous Time Markov Chain Interval Distribution Erlang Distribution Positive Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • L’uboš Korenčiak
    • 1
  • Jan Krčál
    • 2
  • Vojtěch Řehák
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Computer ScienceSaarland UniversitySaarbrückenGermany

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