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We construct a stochastic fluid process with an underlying piecewisedeterministic Markov process (PDMP) akin to the one used in the construction ofthe rational arrival process (RAP), which we call the RAP-modulated fluidprocess. As opposed to the classic stochastic fluid process driven by a Markovjump process, the underlying PDMP of a RAP-modulated fluid process has acontinuous state space and is driven by matrix parameters which may not berelated to an intensity matrix. Through novel techniques we show how well-knownformulae associated to the classic stochastic fluid process, such as firstpassage probabilities and the stationary distribution of its queue, translateto its RAP-modulated counterpart.

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