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→∞. Examples illustrating the theory are included.