A robust maximum completion time measure for scheduling

One popular measure for evaluating the performance of scheduling algorithms, is the maximum response time of any job (makespan). Typically the objective is to find a schedule that minimizes the maximum response time over all jobs. One drawback of this measure is that a relatively small number of jobs in the request set could cause the maximum response time to be very high. Thus, this measure reflects local rather than global properties of the request set. In this paper we consider a robust generalization of this measure. Our goal is to minimize T, such that a given fraction of jobs can be scheduled with a response time of at most T. We demonstrate the applicability of this measure in the context of broadcast scheduling. We show that in the online setting no constant factor online approximation is possible for the problem of minimizing the maximum response time for a given fraction of jobs in the context of broadcast scheduling. We give a factor 5, polynomial time offline approximation algorithm for the problem of minimizing the maximum response time for a given fraction of jobs in the context of broadcast scheduling.