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Markovian Arrival Processes in Multi-dimensions

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Quantitative Evaluation of Systems (QEST 2020)

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Phase Type Distributions (PHDs) and Markovian Arrival Processes (MAPs) are established models in computational probability to describe random processes in stochastic models. In this paper we extend MAPs to Multi-Dimensional MAPs (MDMAPs) which are a model for random vectors that may be correlated in different dimensions. The computation of different quantities like joint moments or conditional densities is introduced and a first approach to compute parameters with respect to measured data is presented.

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  1. 1.

    In an n-dimensional space elements are always numbered from 0 through \(n-1\) because this numbering is more appropriate for mapping multi-dimensional spaces into a single space.

  2. 2.

    We use the names \(\textit{\textbf{D}}\) and \(\textit{\textbf{C}}\) rather than \(\textit{\textbf{D}}_0\) and \(\textit{\textbf{D}}_1\) for the matrices of a MAP because the numbers in the postfix are later used to denote matrices of different MAPs or PHDs.


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Correspondence to Peter Buchholz .

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Blume, A., Buchholz, P., Scherbaum, C. (2020). Markovian Arrival Processes in Multi-dimensions. In: Gribaudo, M., Jansen, D.N., Remke, A. (eds) Quantitative Evaluation of Systems. QEST 2020. Lecture Notes in Computer Science(), vol 12289. Springer, Cham.

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  • Print ISBN: 978-3-030-59853-2

  • Online ISBN: 978-3-030-59854-9

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