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 $b_2$ from below. Stage 1 starts again when reaching threshold $b_1<b_2$ 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 $B>b_2$ . 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.