Transient Analysis of Fluid Flow Models via Matrix Decomposition

□ We present a new approach to carry out transient analysis for Markov modulated fluid flows. The system of partial differential equations for the time-dependent distributions is transformed into a system of ordinary differential equations by Laplace transform. This system of ordinary differential equations is solved by means of decomposing its coefficient matrix into two parts, one with eigenvalues with negative real parts and the other with positive real parts. The results we obtained are equivalent, but in simpler form, to those of Ahn and Ramaswami, which are derived by probabilistic arguments.