We consider a saturated tree network with flow control. The network consists of two layers
of polling stations, and all polling stations use the random polling service discipline. We
obtain the equilibrium distribution of the network using a Markov chain approach. This equilibrium distribution can be used to efficiently compute the division of throughput over packets from different sources. Our study shows that this throughput division is determined by an interaction between the flow control limits, buffer sizes, and the service discipline parameters. A numerical study provides more insight in this interaction. The study is motivated by networks on chips where multiple masters share a single slave, operating under flow control
