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Markovian Arrival Processes

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Input Modeling with Phase-Type Distributions and Markov Models

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Abstract

PHDs can be extended to describe correlated inter-event times. The resulting models are denoted as Markovian Arrival Processes (MAPs) and have been introduced in the pioneering work of Neuts [124]. MAPs are a very flexible and general class of stochastic processes. In this chapter we first introduce the general model and its analysis, then the specific case of MAPs with only two states is considered because it allows one to derive some analytical results and canonical representations. The last section extends the model class to stochastic processes generating different event types.

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Authors and Affiliations

  1. Department of Computer Science, Technical University of Dortmund, Dortmund, Germany

    Peter Buchholz, Jan Kriege & Iryna Felko

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  1. Peter Buchholz
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  2. Jan Kriege
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  3. Iryna Felko
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© 2014 Peter Buchholz, Jan Kriege, Iryna Felko

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Buchholz, P., Kriege, J., Felko, I. (2014). Markovian Arrival Processes. In: Input Modeling with Phase-Type Distributions and Markov Models. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06674-5_4

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