We consider the online problem of active queue management. In our model, the input is a sequence of packets with values υ ∈ [1, α] that arrive to a queue that can hold up to B packets. Specifically, we consider a FIFO non-preemptive queue, where any packet that is accepted into the queue must be sent, and packets are sent by the order of arrival. The benefit of a scheduling policy, on a given input, is the sum of values of the scheduled packets. Our aim is to find an online policy that maximizes its benefit compared to the optimal offline solution. Previous work proved that no constant competitive ratio exists for this problem, showing a lower bound of ln(α) + 1 for any online policy. An upper bound of e[ln(α)] was proved for a few online policies. In this paper we suggest and analyze a RED-like online policy with a competitive ratio that matches the lower bound up to an additive constant proving an upper bound of ln(α)+2+O(ln2(α)/B). For large values of α, we prove that no policy whose decisions are based only on the number of packets in the queue and the value of the arriving packet, has a competitive ratio lower than ln(α) + 2 - ∈, for any constant ∈ > 0.