On-line Scheduling with Partial Job Values

Abstract

We consider a new form of on-line preemptive scheduling problem in which jobs are not required to completed to get the value: instead they get partial value proportional to the amount processed. This problem first arises as a quality-of-service problem in transferring multimedia content over a narrowband network. Previous heuristics for this problem are 2-competitive. In this paper we propose a new heuristic that achieves an improved competitive ratio when the importance ratio is bounded. Specifically, for job weights within the range[1..B], our heuristic is (2[lgB]+3)/([lgB]+2)-competivitive,and the bound is tight.