On minimal representations of Rational Arrival Processes

Peter Buchholz and Miklós Telek ()

Annals of Operations Research, 2013, vol. 202, issue 1, 35-58

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). Copyright Springer Science+Business Media, LLC 2013

Keywords: Rational arrival process; Markov arrival process; Minimal representation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10479-011-1001-5

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