Efficient algorithms for transient analysis of stochastic fluid flow models

We derive several algorithms for the busy period distribution of the canonical Markovian fluid flow model. One of them is similar to the Latouche-Ramaswami algorithm for quasi-birth-death models and is shown to be quadratically convergent. These algorithms significantly increase the efficiency of the matrix-geometric procedures developed earlier by the authors for the transient and steady-state analyses of fluid flow models.