  In this paper we analyze the transient behavior of the workload process in a
L\'evy input queue. We are interested in the value of the workload process at a
random epoch; this epoch is distributed as the sum of independent exponential
random variables. We consider both cases of spectrally one-sided L\'evy input
processes, for which we succeed in deriving explicit results. As an application
we approximate the mean and the Laplace transform of the workload process after
a deterministic time.
