Explicit Inverse Characterizations of Acyclic MAPs of Second Order

  • Armin Heindl
  • Gábor Horváth
  • Karsten Gross
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4054)


This paper shows how to construct a Markovian arrival process of second order from information on the marginal distribution and on its autocorrelation function. More precisely, closed-form explicit expressions for the MAP(2) rate matrices are given in terms of the first three marginal moments and one parameter that characterizes the behavior of the autocorrelation function. Besides the permissible moment ranges, which were known before, also the necessary and sufficient bounds for the correlation parameter are computed and shown to depend on a free parameter related to equivalent acyclic PH(2) representations of the marginal distribution. We identify the choices for the free parameter that maximize the correlation range for both negative and positive correlation parameters.


Acyclic Markovian arrival processes of second order inverse characterization moment and correlation bounds 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Armin Heindl
    • 1
  • Gábor Horváth
    • 2
  • Karsten Gross
    • 1
  1. 1.Computer Networks and Communication SystemsUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Dept. of TelecommunicationsTechnical University of BudapestBudapestHungary

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