Cost Minimization while Satisfying Hard/Soft Timing Constraints for Heterogeneous Embedded Systems

In high-level synthesis for real-time embedded systems using heterogeneous functional units (FUs), it is critical to select the best FU type for each task. However, some tasks may not have fixed execution times. This article models each varied execution time as a probabilistic random variable and solves heterogeneous assignment with probability (HAP) problem. The solution of the HAP problem assigns a proper FU type to each task such that the total cost is minimized while the timing constraint is satisfied with a guaranteed confidence probability. The solutions to the HAP problem are useful for both hard real-time and soft real-time systems. Optimal algorithms are proposed to find the optimal solutions for the HAP problem when the input is a tree or a simple path. Two other algorithms, one is optimal and the other is near-optimal heuristic, are proposed to solve the general problem. The experiments show that our algorithms can effectively reduce the total cost while satisfying timing constraints with guaranteed confidence probabilities. For example, our algorithms achieve an average reduction of 33.0% on total cost with 0.90 confidence probability satisfying timing constraints compared with the previous work using worst-case scenario.