Rational processes related to communicating markov processes

Peter Buchholz, M. Telek

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We define a class of stochastic processes, denoted as marked rational arrival processes (MRAPs), which is an extension of matrix exponential distributions and rational arrival processes. Continuous-time Markov processes with labeled transitions are a subclass of this more general model class. New equivalence relations between processes are defined, and it is shown that these equivalence relations are natural extensions of strong and weak lumpability and the corresponding bisimulation relations that have been defined for Markov processes. If a general rational process is equivalent to a Markov process, it can be used in numerical analysis techniques instead of the Markov process. This observation allows one to applyMRAPslike Markov processes and since the newequivalence relations are more general than lumpability and bisimulation, it is sometimes possible to find smaller representations of given processes. Finally, we show that the equivalence is preserved by the composition of MRAPs and can therefore be exploited in compositional modeling.

Original languageEnglish
Pages (from-to)40-59
Number of pages20
JournalJournal of Applied Probability
Volume49
Issue number1
DOIs
Publication statusPublished - Mar 2012

Fingerprint

Markov Process
Bisimulation
Equivalence relation
Continuous-time Markov Process
Matrix Exponential
Natural Extension
Exponential distribution
Markov process
Stochastic Processes
Numerical Analysis
Equivalence
Modeling
Class

Keywords

  • Equivalence
  • Lumpability
  • Markov process
  • Rational process

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Rational processes related to communicating markov processes. / Buchholz, Peter; Telek, M.

In: Journal of Applied Probability, Vol. 49, No. 1, 03.2012, p. 40-59.

Research output: Contribution to journalArticle

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