Performance analysis of TCP/AQM with generalized AIMD under intermediate buffer sizes

摘要

For TCP/AQM systems, the issue of buffer sizing has recently received much attention. The classical rule-of-thumb suggests O(N) buffer size to ensure full link utilization when N TCP flows share a bottleneck link of capacity O(N), while recent empirical study shows the buffer of size O(N~(1/2)) is enough to yield high utilization (say, 95%) for large N. However, these results are all limited to the drop-tail scheme and there has been no systematic modeling framework for any buffer sizing between O(N~(1/2)) and O(N). In this paper, we study the limiting behavior of a TCP/AQM system for an intermediate buffer sizing of O(N~γ) (0.5 ≤ γ < 1). We develop a stochastic model in a discrete-time setting to characterize the system dynamics and then show that we can have 100% link utilization and zero packet loss probability for a large number of flows when the buffer size is chosen anywhere between O(N~(1/2)) and O(N). Our model is general enough to cover any queue-based AQM scheme with ECN marking (including the drop-tail) and various generalized AIMD (additive-increase-multiplicative-decrease) algorithms for each TCP flow. We also provide arguments showing that the discrete-time based modeling can effectively capture all the essential system dynamics under our choice of scaling (0.5 ≤ γ < 1) for buffer size as well as AQM parameters.