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Description:
Task parameters in traditional models, e.g., the generalized multiframe (GMF) model, are fixed after task specification time. When tasks whose parameters can be assigned within a range, such as the frame parameters in self-suspending tasks and end-to-end tasks, the optimal offline assignment towards schedulability of such parameters becomes important. The GMF-PA (GMF with parameter adaptation) model proposed in recent work allows frame parameters to be flexibly chosen (offline) in arbitrary-deadline systems. Based on the GMF-PA model, a mixed-integer linear programming (MILP)-based schedulability test was previously given under EDF scheduling for a given assignment of frame parameters in uniprocessor systems. Due to the NP-hardness of the MILP, we present a pseudo-polynomial linear programming (LP)-based heuristic algorithm guided by a concave approximation algorithm to achieve a feasible parameter assignment at a fraction of the time overhead of the MILP-based approach. The concave programming approximation algorithm closely approximates the MILP algorithm, and we prove its speed-up factor is (1+delta)^2 where delta > 0 can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. Extensive experiments involving self-suspending tasks (an application of the GMF-PA model) reveal that the schedulability ratio is significantly improved compared to other previously proposed polynomial-time approaches in medium and moderately highly loaded systems.