A simple fluid model for servicing priority traffic

We consider a simple priority queueing system with two different types of t raffic, high and low priority. Each type of traffic generates arrivals to i ts own buffer that are modeled by continuous fluid flows. The input flow in to the high priority buffer is Markov modulated, while the input rate into the low priority buffer is constant. The fluid is transmitted from the buff ers with the high priority buffer having priority over the low priority buf fer. The problem fur the joint distribution of the buffer contents is deriv ed and solved explicitly. Approximations are constructed for the tail behav ior of the buffer content.