A simple fluid model for servicing priority traffic

We consider a simple priority queueing system with two different types of traffic, high and low priority. Each type of traffic generates arrivals to its own buffer that are modeled by continuous fluid flows. The input flow into the high priority buffer is Markov modulated, while the input rate into the low priority buffer is constant. The fluid is transmitted from the buffers with the high priority buffer having priority over the low priority buffer. The problem for the joint distribution of the buffer contents is derived and solved explicitly. Approximations are constructed for the tail behavior of the buffer content.