Solving multi-regime feedback fluid queues

In this paper, we study Markov fluid queues with multiple thresholds, or the so-called multi-regime feedback fluid queues. The boundary conditions are derived in terms of joint densities and for a relatively wide range of state types including repulsive and zero drift states. The ordered Schur factorization is used as a numerical engine to find the steady-state distribution of the system. The proposed method is numerically stable and accurate solution for problems with two regimes and 210 states is possible using this approach. We present numerical examples to justify the stability and validate the effectiveness of the proposed approach.