An optimal online algorithm for packet scheduling with agreeable deadlines

An important issue in IP-based QoS networks is the effective management of packets at the router level. Specifically, if the arriving packets cannot all be stored in a buffer, or if the packets have deadlines by which they must be delivered, the router needs to identify the packets that should be dropped. In recent work, Kesselman et al. [6] propose a model, called <i>buffer management with bounded delay</i>, which can be thought of as an online scheduling problem on a single machine: packets arrive at a network switch and are stored in a buffer of size <i>B.</i> Each packet has a positive weight and a deadline, with the weight representing the value of transmitting the packet by its deadline. At each integer time step, exactly one packet can be transmitted, and the objective is to maximize the total weight of the transmitted packets. If <i>B</i> = ∞, this is the online version of the scheduling problem 1| <i>p<inf>j</inf></i> = 1, <i>r<inf>j</inf></i>, <i>d<inf>j</inf></i> |Σ <i>w<inf>j</inf> U<inf>j</inf></i>. (We assume that <i>r<inf>j</inf></i> and <i>d<inf>j</inf></i> are integers.)