A two-fluid storage model with Lévy inputs and alternating outputs

In this paper we consider a storage model with two types of inputs and outputs that are subject to seasonal switching. Inputs are assumed to occur in a fluid fashion whereas outputs occur at a unit rate so long as the corresponding storage is non-empty. The distribution properties of the storage levels {Z ₁(t),Z ₂(t)} are derived at finite time as well as in stationary regime. We first investigate this process embedded at the successive switching points. This process is Markovian with independent components. In continuous time the components {Z ₁(t),Z ₂(t)} are also independent for each finite t, but are dependent in stationary regime.