A Feedback Fluid Queue with Two Congestion Control Thresholds

Feedback fluid queues play an important role in modelling 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 and can be used to maximize throughput performance. The lower threshold B2 is used to signal the end of congestion and can be used to minimize delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model an input source is active which 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 is hit from above. We present the exact analysis of the stationary distribution of the buffer occupancy and evaluate several other performance measures. We solve the model by setting up Kolmogorov equations, solving them using spectral expansion and finally finding sufficient constraints to solve for the unknowns in the solution. Important novelty of our model compared to earlier feedback models is that the traffic source may behave in two different ways between the two thresholds, depending on the past of the buffer process.