Analysis of Dynamic Congestion Control Protocols: A Fokker-Planck Approximation

We present an approximate analysis of a queue with dynamically changing input rates that are based on implicit or explicit feedback. This is motivated by recent proposals for adaptive congestion control algorithms [RaJa 88, Jac 88], where the sender\u27s window size at the transport level is adjusted based on perceived congestion level of a bottleneck node. We develop an analysis methodology for a simplified system; yet it is powerful enough to answer the important questions regarding stability, convergence (or oscillations), fairness and the significant effect that delayed feedback plays on performance. Specifically, we find that, in the absence of feedback delay, the linear increase/exponential decrease algorithm of Jacobson and Ramakrishnan-Jain [Jac 88, RaJa 88] is provably stable and fair. Delayed feedback on the other hand, introduces oscillations for every individual user as well as unfairness across those competing for the same resource. While the simulation study of Zhang [Zha 89] and the fluid-approximation study of Bolot and Shanker [BoSh 90] have observed the oscillations in cumulative queue length and measurements by Jacobson [Jac 88] have revealed some of the unfairness properties, the reasons for these have not been identified. We identify quantitatively the cause of these effects, via-a-vis the systems parameters and properties of the algorithm used. The model presented is fairly general and can be applied to evaluate the performance of a wide range of feedback control schemes. It is an extension of the classical Fokker-Planck equation. Therefore, it addresses traffic viability (to some extent) that fluid approximation techniques do not address