We consider a cyclic stochastic fluid model {(X(t), J(t)) : t ≥ 0} driven by a continuous-time Markov chain {J(t) : t ≥ 0} with a time-varying generator T(t) and cycle of length 1 such that T(t) = T(t + 1) for all t ≥ 0.

We derive theoretical expressions and methodology for the computation of the asymptotic periodic distribution of the model. This work is an extension of the results in Margolius and O’Reilly [1], where the model was introduced.