Abstract
Markovian arrival processes (MAPs) can be represented in many different ways such as the Markovian representation, Laplace transform, Jordan representation, and minimal realization problem (MRP) representation, to name a few. The MRP representation is given in two real-valued matrices (K’, R’) and can be used to determine the Markovian representation (D<SUB>0</SUB>, D₁) by similarity transformation. The MRP representation has been claimed to be unique but redundant. In this paper, we show that the MRP representation is not unique and then provide a non-redundant MRP representation of MAP(2)s. We also present closed-form formulas for the transformation from the MRP representation to the Markovian representation (D<SUB>0</SUB>, D₁) for MAP(2)s.
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