Comparison-based FIFO buffer management in QoS switches

The following online problem arises in network devices, e.g., switches, with quality of service (QoS) guarantees. In each time step, an arbitrary number of packets arrive at a single FIFO buffer and only one packet can be transmitted. Packets may be kept in the buffer of limited size and, due to the FIFO property, the sequence of transmitted packets has to be a subsequence of the arriving packets. The differentiated service concept is implemented by attributing each packet with a non-negative value corresponding to its service level. A buffer management algorithm can reject arriving packets and preempt buffered packets. The goal is to maximize the total value of transmitted packets. We study comparison-based buffer management algorithms, i.e., algorithms that make their decisions based solely on the relative order between packet values with no regard to the actual values. This kind of algorithms proves to be robust in the realm of QoS switches. Kesselman et al. (SIAM J. Comput., 2004) present a comparison-based algorithm that is 2-competitive. For a long time, it has been an open problem whether a comparison-based algorithm exists with a competitive ratio below 2. We present a lower bound of 1 + 1/√2 ≈ 1.707 on the competitive ratio of any deterministic comparison-based algorithm and give an algorithm that matches this lower bound in the case of monotonic sequences, i.e., packets arrive in a non-decreasing order according to their values