Drop behavior of RED for bursty and smooth traffic

We prove analytically that, as claimed in Jacobson and Floyd's (1993) initial paper on RED, RED gateways "avoid the bias against bursty traffic", meaning that bursty traffic suffers more losses than smooth traffic with tail drop (TD) gateways, but both types of traffic suffer equally with RED gateways. We also show, again as claimed by Jacobson and Floyd, that RED gateways mark or drop packets from a connection at a rate proportional to that connection's arrival rate. Interestingly, both properties above only hold when the bursty traffic may be modeled by Poisson arrivals of bursts; we exhibit non-Poisson cases where these properties do not hold at all. We conclude the paper with a discussion on the implication of these results on traffic management in the Internet.