A Better Memoryless Online Algorithm for FIFO Buffering Packets with Two Values

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 accommodate more than $B$ packets. Packets arrive over time. Each packet is associated with a non-negative value. Packets leave the buffer only because they are either sent or dropped. Those packets that have left the buffer will not be reconsidered for delivery any more. 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 $\alpha > 1$. We present a deterministic memoryless 1.304-competitive algorithm. This algorithm has the same competitive ratio as the one presented in (Lotker and Patt-Shamir. PODC 2002, Computer Networks 2003). However, our algorithm is simpler and does not employ any marking bits. The idea used in our algorithm is novel and different from all previous approaches 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 when the buffer contains sufficiently many $\alpha$-value packets.