Abstract

There have been many task designs for modelling real-time embedded systems in order to capture real-world problems. The traditional approach is when each task has a hard deadline, so all tasks are equally treated when considering the scheduling problem. A recent design is for a task set to have (<tex>$m, k$</tex>)-firm deadlines, namely at least <tex>$m$</tex> out of any <tex>$k$</tex> consecutive tasks must meet their deadlines. Another related model may be defined when a task is allowed to execute in multiple feasible intervals, for which a miss happens when the task does not execute in any of the feasible intervals. Other existing models are represented by soft real-time (SRT) systems, but do not require any deadline to be met. Instead SRT systems require bounded tardiness, where jobs are allowed to miss deadlines as long as the extent of miss is bounded. This paper describes a new task model, similar yet different from all previous existing models, for scheduling single-instance non-preemptive tasks on a multiprocessor platform by considering both a soft and a hard deadline for each task in a given task set. Our motivation is that tasks that finish before their soft deadlines achieve their best performance. Finishing before the hard deadline implies an acceptable and a safe performance, while missing a hard deadline leads to harmful situations. In addition, our paper defines a measure for the feasibility of a task set, where meeting a soft deadline counts twice as much as meeting just a hard deadline of that task. This paper also describes a scheduling algorithm for soft-hard single-instance non-preemptive tasks together with some examples reaching a feasible schedule.

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