The following buffer management problem arises in network switches providing differentiated services: At the beginning of each time step, one packet can be sent, and afterwards an arbitrary number of new packets arrive. Packets that are not sent can be stored in a buffer. Each packet is attributed by a deadline, and a packet is automatically deleted from the buffer if it is still stored in the buffer by the end of its deadline. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy determines the packet to be sent in each time step. The goal of a buffer management strategy is to maximize the sum of the values of sent packets.

We introduce the concept of suppressed packets and present a deterministic strategy that is based on this concept. We show that this strategy achieves a competitive ratio of 2√2--1 ≈ 1.828, which is the best known competitive ratio in the deterministic case. Further, we present a memoryless version of this strategy that achieves a competitive ratio of ≈ 1.893. This is the first memoryless strategy that achieves a competitive ratio less than 2, and the competitive ratio of this strategy is even better than the ratios of all previously known deterministic strategies. This demonstrates the potential of the concept of suppressed packets. In addition, we present a simple strategy that achieves the optimal competitive ratio of min{(1 + α)/α, 2α/(α+1)} ≤ √2, if only two packet values 1 and α > 1 are possible.