Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation

Abstract

The steady-state distribution of the two-sided reflected Markov Modulated Brownian motion is derived through an alternative fluid approximation approach. In this paper, we have shown that the distribution can be obtained by taking limit on the steady-state distribution of a weakly convergent Markov modulated fluid model. In addition, we present how the duality theorem developed by Ahn and Ramaswami is applied to get the limit result. For computation, we introduce a quadratically convergent algorithm and its related theories which rely on the fluid approximation approach. Through numerical examples, we finally illustrate behaviors of the steady-state distribution and also some performances of the algorithm.