Competitive dynamic multiprocessor allocation for parallel applications

In this paper we use competitive analysis to study preemptive multiprocessor allocation policies for parallel jobs whose execution time is not known to the scheduler at the time of scheduling. The objective is to minimize the makespan (i.e., the completion time of the last job to finish executing). We characterize a parallel job, J_i , by two parameters: its execution time, l_i, and its parallelism, P_i, which may vary over time. The preemption and reallocation of processors can take place at any time. We devise a preemptive policy which achieves the best possible competitive ratio and then derive upper and lower bounds for scheduling N parallel jobs on P processors