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Algorithmic solution to second-order fluid flow

We develop a numerically stable algorithm for the solution of a general fluid-flow model in steady-state. The fluid dynamics is modulated by a semi-Markov process, with phase-type distributions for the sojourn times. We use an algorithmic solution to examine the impact of variance in the case of homogeneous on-off sources, and differences between the infinite and finite buffer case. The need for the complete distribution of the buffer is demonstrated through analysis of two existing approximations, which perform unsatisfactorily. Our numerical results demonstrate the robustness of the numerical algorithm; we compute both the cumulative distribution functions (CDF) and the moments of the process, over a wide range of time-scales and system parameters.