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Second-order fluid flow models: Reflected Brownian motion in a random environment. (English) Zbl 0821.60087
Summary: This paper considers a stochastic fluid model of a buffer content process \(\{X(t), t \geq 0\}\) that depends on a finite-state, continuous-time Markov process \(\{Z(t), t \geq 0\}\) as follows: During the time-intervals when \(Z(t)\) is in state \(i\), \(X(t)\) is a Brownian motion with drift \(\mu_ i\), variance parameter \(\sigma^ 2_ i\) and a reflecting boundary at zero. This paper studies the steady-state analysis of the bivariate process \(\{(X(t), Z(t)), t \geq 0\}\) in terms of the eigenvalues and eigenvectors of a nonlinear matrix system. Algorithms are developed to compute the steady-state distributions as well as moments. Numerical work is reported to show that the variance parameter has a dramatic effect on the buffer content process.

60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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