A Markovian canonical form of second-order matrix-exponential processes

L. Bodrog, A. Heindl, G. Horváth, M. Telek

Research output: Contribution to journalArticle

37 Citations (Scopus)


Besides the fact that - by definition - matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the precise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that - in two dimensions - the respective sets, MAP(2) and MEP(2), are indeed identical with respect to the stationary behavior. Furthermore, this equivalence extends to acyclic MAPs, i.e., AMAP(2), so that AMAP (2) ≡ MAP (2) ≡ MEP (2). For higher orders, these equivalences do not hold. The second-order equivalence is established via a novel canonical form for the (correlated) processes. An explicit moment/correlation-matching procedure to construct the canonical form from the first three moments of the interarrival time distribution and the lag-1 correlation coefficient shows how these compact processes may conveniently serve as input models for arrival/service processes in applications.

Original languageEnglish
Pages (from-to)459-477
Number of pages19
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - Oct 16 2008


  • Canonical representation
  • Markovian arrival process
  • Matrix-exponential process
  • Moment/correlation matching

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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