A Markovian canonical form of second-order matrix-exponential processes |
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Authors: | L Bodrog A Heindl G Horváth M Telek |
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Institution: | 1. Department of Telecommunications, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary;2. Institute of Computer Science, University of Erlangen-Nuremberg, D-91058 Erlangen, Germany |
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Abstract: | 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. |
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Keywords: | Markovian arrival process Matrix-exponential process Canonical representation Moment/correlation matching |
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