Scheduling for Flow-Time with Admission Control

We consider the problem of scheduling jobs on a single machine with preemption, when the server is allowed to reject jobs at some penalty. We consider minimizing two objectives: total flow time and total job-idle time (the idle time of a job is the flow time minus the processing time). We give 2-competitive online algorithms for the two objectives and extend some of our results to the case of weighted flow time and machines with varying speeds. We also give a resource augmentation result for the case of arbitrary penalties achieving a competitive ratio of using a speed processor. Finally, we present a number of lower bounds for both the case of uniform and arbitrary penalties.