Multiprocessors scheduling for imprecise computations in a hard real-time environment

This paper discusses the problem of scheduling multiprocessors in a hard real-time environment allowing imprecise computations. The computation of tasks can be divided into mandatory and optional parts; In a feasible schedule, the mandatory part of every task has to be completed before the deadline of the task. The optional part refines the result produced by the mandatory part to reduce the error in the result. The optional parts need not ever be completed. The quality of the result of each job is measured in terms of the average error in the results over several consecutive periods. Thus, given n real-time periodic jobs which has a periodicity and a processing requirement per period, the problem of determining whether there exists a preemptive schedule on m identical or uniform machines which completes the mandatory portion of each job in the time interval in a period is examined. A combination of network flow techniques and convex programming formulation is used to construct a minimum error schedule whenever there exists a feasible schedule. The error produced due to the uncomputed portions of tasks is assumed to be some real-valued convex function of the uncomputed portions