Transient analysis of Markov-fluid-driven queues

In this paper we study two transient characteristics of a Markov-fluid-driven queue, viz., the busy period and the covariance function of the workload process. Both metrics are captured in terms of their Laplace transforms. Relying on sample-path large deviations we also identify the logarithmic asymptotics of the probability that the busy period lasts longer than t, as t \to\infty. Examples are included that illustrate the theory.