Annals of Operations Research

, Volume 202, Issue 1, pp 35–58 | Cite as

On minimal representations of Rational Arrival Processes

  • Peter Buchholz
  • Miklós TelekEmail author


Rational Arrival Processes (RAPs) form a general class of stochastic processes which include Markovian Arrival Processes (MAPs) as a subclass. In this paper we study RAPs and their representations of different sizes. We show some transformation methods between different representations and present conditions to evaluate the size of the minimal representation. By using some analogous results from linear systems theory, a minimization approach is defined which allows one to transform a RAP (from a redundant high dimension) into one of its minimal representations. An algorithm for computing a minimal representation is also given. Furthermore, we extend the approach to RAPs with batch arrivals (BRAPs) and to RAPs with arrivals of different customer types (MRAPs).


Rational arrival process Markov arrival process Minimal representation 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Informatik IVTU DortmundDortmundGermany
  2. 2.Department of TelecommunicationsTechnical University of BudapestBudapestHungary

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