RAP-modulated Fluid Processes: First Passages and the Stationary Distribution
Probability
2021-01-12 v1
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.
Cite
@article{arxiv.2101.03242,
title = {RAP-modulated Fluid Processes: First Passages and the Stationary Distribution},
author = {Nigel G. Bean and Giang T. Nguyen and Bo F. Nielsen and Oscar Peralta},
journal= {arXiv preprint arXiv:2101.03242},
year = {2021}
}