Sojourn Time Distribution in Fluid Queues

We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.