An Optimal Algorithm for 2-Bounded Delay Buffer Management with Lookahead

Abstract

The bounded delay buffer management problem, which was proposed by Kesselman et al. (STOC 2001 and SIAM Journal on Computing 33(3), 2004), is an online problem focusing on buffer management of a switch supporting Quality of Service (QoS). The problem definition is as follows: Packets arrive to a buffer over time and each packet is specified by the release time, deadline and value. An algorithm can transmit at most one packet from the buffer at each integer time and can gain its value as the profit if transmitting a packet by its deadline after its release time. The objective of this problem is to maximize the gained profit. We say that an instance of the problem is s-bounded if for any packet, an algorithm has at most s chances to transmit it. For any $s \ge 2$, Hajek (CISS 2001) showed that the competitive ratio of any deterministic algorithm is at least $(1 + \sqrt{5})/2 \ge 1.618$. Very recently, Veselý et al. (SODA 2019) designed an online algorithm matching the lower bound.

Böhm et al. (ISAAC 2016 and Theoretical Computer Science, 2019) introduced the lookahead ability to an online algorithm, that is the algorithm can gain information about future arriving packets, and showed that for $s=2$, there is an algorithm which achieves the competitive ratio of $(-1 + \sqrt{13})/2 \le 1.303$. Also, they showed that the competitive ratio of any deterministic algorithm is at least $(1 + \sqrt{17})/4 \ge 1.280$. In this paper, for the 2-bounded model with lookahead, we design an algorithm with a matching competitive ratio of $(1 + \sqrt{17})/4$.