Multi-stage stochastic fluid models for congestion control

We consider multi-stage stochastic fluid models (SFMs), driven by applications in telecommunications and manufacturing in which control of the behavior of the system during congestion may be required. In a two-stage SFM, the process starts from Stage 1 in level 0, and moves to Stage 2 when reaching threshold b2 from below. Stage 1 starts again when reaching threshold b1<b2 from above. While in a particular stage, the process evolves according to a traditional SFM with a unique set of phases, generator and fluid rates. We first consider a two-stage SFM with general, real fluid change rates. Next, we analyze a two-stage SFM with an upper boundary B>b2. Finally, we discuss a generalization to multi-stage SFMs. We use matrix-analytic methods and derive efficient methodology for the analysis of this class of models.