Malhotra, R., Mandjes, M.R.H., Scheinhardt, W.R.W. et al. Math Meth Oper Res (2009) 70: 149. doi:10.1007/s00186-008-0235-8
Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B1 is used to signal the beginning of congestion while the lower threshold B2 signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B1 has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B2 (smaller than B1) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.