Fluid queues to solve jump processes

We consider systems which exhibit a mixture of smooth behavior and occasional jumps, controlled by continuous-time Markovian processes on a finite state space, and we call these fluid queues with jumps, thereby emphasizing the fact that they constitute a generalization of fluid queues. We characterize their stationary distribution in an algorithmically tractable way by constructing an auxiliary fluid queue without jumps. We give a few examples to illustrate the procedure and we analyze in detail a buffer model where bursts of high priority traffic interrupt the transmission of low priority files.