Extension of some MAP results to transient MAPs and Markovian binary trees

Sophie Hautphenne, Miklós Telek

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4 Citations (Scopus)


In this work we extend previous results on moment-based characterization and minimal representation of stationary Markovian arrival processes (MAPs) and rational arrival processes (RAPs) to transient Markovian arrival processes (TMAPs) and Markovian binary trees (MBTs). We show that the number of moments that characterize a TMAP of size n with full rank marginal is n2 + 2n - 1, and an MBT of size n with full rank marginal is n3 + 2n - 1. We provide a non-Markovian representation for both processes based on these moments. Finally, we discuss the minimal representation of TMAPs and MBTs. In both cases, the minimal representation, which is not necessarily Markovian, can be found using different adaptations of the STAIRCASE algorithm presented in an earlier work by Buchholz and Telek (2011) [9]. Crown

Original languageEnglish
Pages (from-to)607-622
Number of pages16
JournalPerformance Evaluation
Issue number9
Publication statusPublished - Jan 1 2013



  • Markovian binary tree
  • Minimal representation
  • Moments of inter-arrival time distribution
  • Parameter fitting
  • Transient Markovian arrival process

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications

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