Scheduling Multiclass Packet Streams to Minimize Weighted Loss

We consider the problem of scheduling an arriving sequence of packets at a single server. Associated with each packet is a deadline by which the packet must be scheduled. Each packet belongs to one of a predetermined set of classes, and each class has an associated weight value. The goal is to minimize the total weighted value of the packets that miss their deadlines. We first prove that there is no policy that minimizes this weighted loss for all finite arrival sequences of packets. We then present a class of greedy scheduling policies, called the current-minloss throughput-optimal (CMTO) policies. We characterize all CMTO policies, and provide examples of easily implementable CMTO policies. We compare CMTO policies with a multiclass extension of the earliest-deadline-first (EDF) policy, called EDF+, establishing that a subclass of CMTO policies achieves no more weighted loss than EDF+ for any traffic sequence, and at the same time achieves a substantial weighted-loss advantage over EDF+ for some traffic sequences – this advantage is shown to be arbitrarily close to the maximum possible achievable advantage. We also provide empirical results to quantify the weighted-loss advantage of CMTO policies over EDF+ and the static-priority (SP) policy, showing an advantage exceeding an order of magnitude when serving heavy-tailed aggregations of MPEG traces.