2ND-ORDER FLUID-FLOW MODELS - REFLECTED BROWNIAN-MOTION IN A RANDOM ENVIRONMENT

This paper considers a stochastic fluid model of a buffer content proc ess {X(t), t greater than or equal to 0} that depends on a finite-stat e, continuous-time Markov process {Z(t), t greater than or equal to 0} as follows: During the time-intervals when Z(t) is in state i, X(t) i s a Brownian motion with drift mu(i), variance parameter sigma(i)(2) a nd a reflecting boundary at zero. This paper studies the steady-state analysis of the bivariate process {(X(t), Z(t)), t greater than or equ al to 0} in terms of the eigenvalues and eigenvectors of a nonlinear m atrix system. Algorithms are developed to compute the steady-state dis tributions as well as moments. Numerical work is reported to show that the variance parameter has a dramatic effect on the buffer content pr ocess.