Optimal task execution times for periodic tasks using nonlinear constrained optimization

Abstract

Designing real-time systems is a challenging task and many conflicting issues arise in the process. Among them, the most fundamental one is the adjustment of appropriate values for task parameters such as task periods, deadlines, and computation times that directly influence the system feasibility. Task periods and deadlines are generally known at design stage and remains fixed throughout, however, task computation times fluctuates significantly. For a better quality of service or higher system utilization, higher task computation values are required, while this flexibility comes at the price of system infeasibility. To the best of our knowledge, no optimal solution exists for extracting the optimal task computation times in a given range so that the overall system remains feasible under a specific scheduling algorithm. In this paper, we present a generalized bound on the task schedulability defined as a nonlinear inequality h i ?0 in the space of the execution times c i . Based on this bound, the adjustment problem of tasks execution times, which determines the optimum c i for a better system performance while still meeting all temporal requirements, is addressed by solving the standard nonlinear constrained optimization problem. Simulations on synthetic task sets are presented to compare the performance of our work with the most celebrated result, i.e., LL-bound by Liu and Layland in (J. ACM 20(1):40---61, 1973).