We consider the management of FIFO buffers for network 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, and the goal is to maximize the sum of the 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 √ 2 − ( 5 + 4 √ 2 − 3)/2 ≈ 1.282 if the buffer size tends to infinity and an optimal competitive ratio of ( √ 13 − 1)/2 ≈ 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 √ 3 ≈ 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/ √ 2 ≈ 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.
Englert and Westermann REF showed that PG is 1.732-competitive but no better than 1.707-competitive.
Lower and Upper Bounds on FIFO Buffer Management in QoS Switches
Algorithmica
Algorithmica
Mathematics Computer Science