Desynchronized Pfair Scheduling on Multiprocessors

Pfair scheduling, currently the only known way of optimally scheduling recurrent real-time tasks on multiprocessors, imposes certain requirements that may limit its practical implementation. In this paper, we address one such limitation - which requires processor time to always be allocated in units of fixed-sized quanta that are synchronized across processors - and determine the impact of relaxing it. We show that if this requirement, which may lead to wasted processor time, is relaxed, then under an otherwiseoptimal Pfair scheduling algorithm deadlines are missed by at most one quantum only, which is sufficient to provide soft real-time guarantees. This result can be shown to extend to most prior work on Pfair scheduling: in general, tardiness bounds guaranteed by previously-proposed suboptimal Pfair algorithms are worsened by at most one quantum only.