Bounding the execution time of parallel applications on unrelated multiprocessors

Heterogeneous multiprocessors can offer high performance at low energy expenditures. However, to be able to use them in hard real-time systems, timing guarantees need to be provided, and the main challenge is to determine the worst-case schedule length (also known as makespan) of an application. Previous works that estimate the makespan focus mainly on the independent-task application model or the related multiprocessor model that limits the applicability of the makespan. On the other hand, the directed acyclic graph (DAG) application model and the unrelated multiprocessor model are general and can cover most of today's platforms and applications. In this work, we propose a simple work-conserving scheduling method of the tasks in a DAG and two new approaches to finding the makespan. A set of representative OpenMP task-based parallel applications from the BOTS benchmark suite and synthetic DAGs are used to evaluate the proposed method. Based on the empirical results, the proposed approach calculates the makespan close to the exhaustive method and with low pessimism compared to a lower bound of the actual makespan calculation.