Algorithmic Solution to Second - order Fluid

| We develop a numerically stable algorithm for the solution of a general Fluid-Flow model in steady-state. The uid dynamics is modulated by a Semi-Markov process, with Phase-type distributions for the sojourn times. We use an algo-rithmic solution to examine the impact of variance in the case of homogeneous On-OO sources, and diierences between the innnite and nite buuer case. The need for the complete distribution of the buuer is demonstrated through analysis of two existing approximations, which perform unsatisfactorily. Our numerical results demonstrate the ro-bustness of the numerical algorithm; we compute both the CDF and the moments of the process, over a wide range of timescales and system parameters.