RAP-modulated Fluid Processes: First Passages and the Stationary Distribution

Nigel G. Bean; Giang T. Nguyen; Bo F. Nielsen; Oscar Peralta

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arXiv · 2101.03242

RAP-modulated Fluid Processes: First Passages and the Stationary Distribution

Nigel G. Bean·Giang T. Nguyen·Bo F. Nielsen·Oscar Peralta

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Abstract

We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (RAP), which we call the RAP-modulated fluid process. As opposed to the classic stochastic fluid process driven by a Markov jump process, the underlying PDMP of a RAP-modulated fluid process has a continuous state space and is driven by matrix parameters which may not be related to an intensity matrix. Through novel techniques we show how well-known formulae associated to the classic stochastic fluid process, such as first passage probabilities and the stationary distribution of its queue, translate to its RAP-modulated counterpart.

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BibTeX RIS

Nigel G. Bean, Giang T. Nguyen, Bo F. Nielsen, Oscar Peralta. 2021-01-08. RAP-modulated Fluid Processes: First Passages and the Stationary Distribution. https://arxiv.org/abs/2101.03242

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