Annals of Operations Research

, Volume 239, Issue 2, pp 643–665 | Cite as

Heuristic representation optimization for efficient generation of PH-distributed random variates

  • Gábor Horváth
  • Philipp ReineckeEmail author
  • Miklós Telek
  • Katinka Wolter


Phase-type (PH) distributions are being used to model a wide range of phenomena in performance and dependability evaluation. The resulting models may be employed in analytical as well as in simulation-driven approaches. Simulations require the efficient generation of random variates from PH distributions. PH distributions have different representations and different associated computational costs for pseudo random-variate generation (PRVG). In this paper we study the problem of efficient representation and efficient generation of PH distributed variates. We introduce various PH representations of different sizes and optimize them according to different cost functions associated with PRVG.


PH distribution Pseudo random variate generation Monocyclic representation 



This work was partially supported by DFG grants Wo 898/3-1 and Wo 898/5-1, by the European Union TAMOP-4.2.2C-11/1/KONV-2012-0001, the OTKA K101150 and the Research and Technology Innovation Fund EITKIC_12-1-2012-0001 projects, and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. We would also like to thank the anonymous reviewers for their extremely helpful suggestions on improving the paper.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Gábor Horváth
    • 1
    • 2
  • Philipp Reinecke
    • 3
    Email author
  • Miklós Telek
    • 1
    • 4
  • Katinka Wolter
    • 5
  1. 1.Department of TelecommunicationsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.MTA-BME Information systems research groupBudapestHungary
  3. 3.HP LabsBristolEngland
  4. 4.Inter-University Center for Telecommunications and InformaticsDebrecenHungary
  5. 5.Institut für InformatikFreie Universität BerlinBerlinGermany

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