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On minimal representations of Rational Arrival Processes

Annals of Operations Research volume 202, pages 35–58 (2013)Cite this article

Abstract

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).

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Authors and Affiliations

  1. Informatik IV, TU Dortmund, 44221, Dortmund, Germany

    Peter Buchholz

  2. Department of Telecommunications, Technical University of Budapest, 1521, Budapest, Hungary

    Miklós Telek

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  1. Peter Buchholz
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  2. Miklós Telek
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Correspondence to Miklós Telek.

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Buchholz, P., Telek, M. On minimal representations of Rational Arrival Processes. Ann Oper Res 202, 35–58 (2013). https://doi.org/10.1007/s10479-011-1001-5

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  • DOI: https://doi.org/10.1007/s10479-011-1001-5

Keywords

  • Rational arrival process
  • Markov arrival process
  • Minimal representation