Uniformization: Basics, extensions and applications

N.M. van Dijk (Corresponding Author), S.P.J. van Brummelen, R.J. Boucherie

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)
1 Downloads (Pure)


Uniformization, also referred to as randomization, is a well-known performance evaluation technique to model and analyse continuous-time Markov chains via an easier to performance measures via iteration of the one-step transition matrix of the discrete-time Markov chain. The number of iterations has a Poisson distribution with rate dominating the maximum exit rate from the states of the continuous-time Markov chain. This paper contains an expository presentation of uniformization techniques to increase awareness and to provide a formal and intuitive justification of several exact and approximate extensions, including:
•exact uniformization for reward models,
•exact uniformization for time-inhomogeneous rates,
•a numerical comparison with simple time-discretization,
•approximate uniformization for unbounded transition rates, and
•exact uniformization for continuous state variables for non-exponential networks.
Furthermore, several of these results are numerically illustrated for a processor sharing web server tandem model of practical interest.
Original languageEnglish
Pages (from-to)8-32
Number of pages25
JournalPerformance evaluation
Early online date16 Oct 2017
Publication statusPublished - 1 Feb 2018


  • Uniformization
  • Randomization
  • Time discretization
  • Time inhomogeneous
  • Cumulative reward model
  • Web server tandem model


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