A Levy input fluid queue with input and workload regulation

We consider a controlled queuing model with L,vy input. The controls take place at random times. They involve the current workload and the input processes and may also depend on whether the workload process has reached certain critical values since the last control epoch. We propose a solution strategy for deriving the steady-state distribution of this model which is based on recent advances in the fluctuation theory of spectrally one-sided L,vy process. We provide illustrative examples involving a clearing model, an inventory model, and a model for the TCP protocol.