Fog computing technology has emerged to handle a large amount of data generated by the Internet of Things (IoT) terminals and cope with latency-sensitive application requests by allocating computation and storage resources at the edge of the Internet. In many IoT applications, the data acquisition procedures must apply the Directed Acyclic Graph (DAG) to get real-time results. The principal goal of DAG scheduling is to reduce total completion time without breaking priority constraints by properly allocating tasks to processors and arranging task execution sequencing. In this paper, we propose a bandwidthaware workflow allocation (BW-AWA) that schedules tasks by priority to the resource and optimizes the total execution time (Makespan) in the entire computing system. The task allocation process needs to consider the dependency between tasks. The proposed approach is tested with a monitoring application case study, and the results are compared to well-known approaches to demonstrate its effectiveness in optimizing the Makespan.