The stochastic fluid–fluid model: a stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself

We introduce the Stochastic Fluid-Fluid Model, which o ffers powerful modelling ability for a wide range of real-life systems of signifi cance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace-Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace-Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the fi rst direct analysis of a stochastic fluid model that is Markovian on a continuous state space.