Second-Order Fluid Flow Models: Reflected Brownian Motion in a Random Environment

Rajeeva L. Karandikar and Vidyadhar G. Kulkarni
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Rajeeva L. Karandikar: Indian Statistical Institute, New Delhi, India
Vidyadhar G. Kulkarni: University of North Carolina, Chapel Hill, North Carolina

Operations Research, 1995, vol. 43, issue 1, 77-88

Abstract: This paper considers a stochastic fluid model of a buffer content process { X ( t ), t ≥ 0} that depends on a finite-state, continuous-time Markov process { Z ( t ), t ≥ 0} as follows: During the time-intervals when Z ( t ) is in state i , X ( t ) is a Brownian motion with drift μ i , variance parameter σ i 2 and a reflecting boundary at zero. This paper studies the steady-state analysis of the bivariate process {( X ( t ), Z ( t )), t ≥ 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.

Keywords: communication: fluid models using diffusion; probability; diffusion: reflected Brownian motion; random environment (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (11)

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