A Doubly-Stochastic Model for a TCP/AQM System under Aggressive Packet Marking

We consider a TCP/AQM system with large link capacity shared by many flows. Traditional approaches via fluid-based modeling require that the buffer size be chosen in proportion to the number of flows (N) for system stability. However, they are all unable to predict the true system performance if the buffer size at the bottleneck link and the corresponding AQM scheme are scaled as O(N^alpha) with alpha<0.5. In this paper, we develop a doubly-stochastic model for a TCP/AQM system with many flows by taking into account the packet-level dynamics over finer time scales. Our model differs from any other fluid-based models in that it can explicitly capture two different sources of randomness in packet arrivals to the bottleneck link, while the existing approaches do not capture both of them simultaneously. Under our stochastic framework, we show that the the TCP/AQM system actually yields high link utilization and low packet loss probability even with much smaller buffer size than what has been suggested. We also provide simulation results using ns-2 under different AQM schemes and show that they are in good agreement with all the theoretical results derived in this paper.