Stationary behavior of TCP/AQM with many flows under aggressive packet marking

We consider a TCP/AQM system shared by many flows under general packet marking schemes. Traditional approaches in the literature require that the marking function p^N (x) be scaled linearly in the number of flows N, i.e., p^N (Nx)=p(x) for some function p, and they all invariably fail to predict the system performance if the marking function is scaled more aggressively, i.e. p^N(N^αx)=p(x) with α∈(0,1). In this paper, by noting that there are two different sources of randomness in packet arrivals to the queue, we develop a simple stationary model for a TCP/AQM system with N flows under the aggressive packet marking. Our main results show that, under any aggressive marking scale, the system always behaves nicely in the sense that the link utilization goes to I and the queueing delay decreases to zero as the system size N increases. We verify our results using ns-2 simulation under different AQM schemes, and show that the buffer size can be chosen much smaller than O(√N) as recently predicted by G. Appenzeller et al (ACM Sigcomm, 2004) without affecting all the key performance metrics.