Online Scheduling of Jobs for D-benevolent instances On Identical Machines

We consider online scheduling of jobs with specic re- lease time on m identical machines. Each job has a weight and a size; the goal is maximizing total weight of completed jobs. At release time of a job it must imme- diately be scheduled on a machine or it will be rejected. It is also allowed during execution of a job to preempt it; however, it will be lost and only weight of completed jobs contribute on prot of the algorithm. In this paper we study D-benevolent instances which is a wide and standard class and we give a new algorithm, that ad- mits (2m + 4)-competitive ratio. It is almost half of the previous known upper bound for this problem.