A Near-Optimal Memoryless Online Algorithm for FIFO Buffering Two Packet Classes

We consider scheduling packets with values in a capacity-bounded buffer in an online setting. In this model, there is a buffer with limited capacity B. At any time, the buffer cannot accommodatemore than B packets. Packets arrive over time. Each packet has a nonnegative value. Packets leave the buffer only because they are either sent or dropped. Those packets that have left the bufferwill not be reconsidered for delivery anymore. In each time step, at most one packet in the buffer can be sent. The order in which the packets are sent should comply with the order of their arrival time. The objective is to maximize the total value of the packets sent in an online manner. In this paper, we study a variant of this FIFO buffering model in which a packet’s value is either 1 or α > 1. We present a deterministic memoryless 1.304-competitive algorithm. This algorithmhas the same competitive ratio as the one presented in Lotker and Patt-Shamir [Z. Lotker, B. Patt-Shamir, Nearly optimal FIFO buffer management for DiffServ, in: Proceedings of the 21st Annual ACM Symposium on Principles of Distributed Computing, PODC, 2002, pp. 134–142; Z. Lotker, B. Patt-Shamir, Nearly optimal FIFO buffer management for DiffServ, Computer Networks 17 (1) (2003) 77–89]. However, our algorithm is simpler and does not employ anymarking bits. The idea used in our algorithm is novel and different from all previous approaches that have been applied for the general model and its variants. We do not proactively preempt one packet when a new packet arrives. Instead, we may preempt more than one 1-value packet at the time when the buffer contains sufficiently many α-value packets. © 2011 Elsevier B.V. All rights reserved.