Lower and upper bounds on FIFO buffer management in QoS switches

We consider FIFO buffer management for switches providing differentiated services. In each time step, an arbitrary number of packets arrive, and only one packet can be sent. The buffer can store a limited number of packets, and, due to the FIFO property, the sequence of sent packets has to be a subsequence of the arriving packets. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy can drop packets. The goal is to maximize the sum of values of sent packets. For only two different packet values, we introduce the account strategy and prove that this strategy achieves an optimal competitive ratio of ≈1.282, if the buffer size tends to infinity, and an optimal competitive ratio of $(\sqrt{13}-1)/2 \approx 1.303$ , for arbitrary buffer sizes. For general packet values, the simple preemptive greedy strategy (PG) is studied. We show that PG achieves a competitive ratio of $\sqrt{3} \approx 1.732$ which is the best known upper bound on the competitive ratio of this problem. In addition, we give a lower bound of $1 + 1 / \sqrt{2} \approx 1.707$ on the competitive ratio of PG which improves the previously known lower bound. As a consequence, the competitive ratio of PG cannot be further improved significantly