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Markovian Arrival Processes in Multi-dimensions

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Quantitative Evaluation of Systems (QEST 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12289))

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Abstract

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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Notes

  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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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. https://doi.org/10.1007/978-3-030-59854-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-59854-9_14

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