A note on the conservation law for continuous reflected processes and its application to queues with fluid inputs

In this note we provide a new derivation of a conservation law for stationary continuous reflected processes which arise in the context of fluid queueing models. This readily gives the so-called Little's law for fluid queues as a special case. We then apply the result to compute the Laplace transform of the stationary workload distribution for a queue with fluid ON–OFF inputs in terms of the Palm distribution associated with the beginning of ON periods.