Solution method of some delay feedback schemes used in rate-based flow control analysis of high speed data channels

A solution method of a first order, delay differential system, modelling a class of rate-based, feedback control schemes, used in long haul high speed data transport is derived and discussed. In such networks the traffic pattern varies often unpredictably, while the large propagation delay is becoming a major factor. Our focus is on two basic virtual circuit networks of balanced form; the multi-hop virtual circuit network having M nodes in tandem and the single-hop virtual circuit network which aggregates many virtual circuits with various propagation delays and individual windows over the single hop. Using well known adaptive algorithms to dynamically adjust the window size, the above networks are presented as linear systems of some delay differential equations in which the rate of transmission and the queue occupancy are modelled as fluids. However, such schemes are locally unstable in a Lyapunov sense. We derived a numerical method for solving the resulting delay differential systems and we identify the appropriate scaling for the parameters so as to make the above schemes perform near their optimal theoretical values for a wide range of speeds. The analytical results so obtained are in a complete agreement with those already derived by simulation and reported in the literature. As it appears, oscillations are controlled to acceptably small magnitudes and therefore, such methods may be used as a powerful tool for optimum performance, by means of stabilizing the channel output and achieving fairness.