Second-order fluid flow models: Reflected Brownian motion in a random environment

This paper considers a stochastic fluid model of a buffer content process that depends on a finite-state, continuous-time Markov process as follows: During the time-intervals when is in state i, is a Brownian motion with drift , variance parameter and a reflecting boundary at zero. This paper studies the steady-state analysis of the bivariate process in terms of the eigenvalues and eigenvectors of a nonlinear matrix system. Algorithms are developed to compute the steady-state distribution as well as moments. Numerical work is reported to show that the variance parameter has a dramatic effect on the buffer content process.