First passage times in fluid models with an application to two priority fluid systems

In this paper we analyze the first passage time in a fluid flow model where the input and output rates are controlled by a finite state Continuous Time Markov Chain (CTMC). We derive explicit expressions for the Laplace Transform of the joint distribution of the first time the buffer becomes empty and the state of the CTMC at that time. We discuss both infinite and finite buffer cases. We illustrate the results with the case of a fluid model with an on-off source. We apply these results to a fluid model where the input consists of two types of fluid and a single server removes the fluid. The server gives complete priority to the fluid of type 1 over that of type 2. In this case the down time of the server for priority 2 fluid is the same as the busy period of the fluid of priority 1. We derive the steady state marginal distributions of the buffer-content process for fluids of type 1 and 2. We present numerical results and their interpretations.