Optimal scheduling for jobs with progressive deadlines

This paper considers the problem of server-side scheduling for jobs composed of multiple pieces with consecutive (progressive) deadlines. One example is server-side scheduling for video service, where clients request flows of content from a server with limited capacity, and any content not delivered by its deadline is lost. We consider the simultaneous goals of 1) minimizing overall loss, and 2) differentiating loss fractions across classes of flows in proportion to relative weights. State-of-the-art policies, like Discriminatory Processor Sharing and Weighted Fair Queueing, use a fixed static proportional allocation of service rate and fail to achieve both goals. The well-known Earliest Deadline First policy minimizes overall loss, but fails to provide proportional loss across flows, because it treats packets as independent jobs. This paper introduces the Earliest Progressive Deadline First (EPDF) class of policies. We prove that all policies in this broad class minimize overall loss. Furthermore, we demonstrate that many EPDF policies accurately differentiate loss fractions in proportion to class weights, satisfying the second goal.