A swarm robotic system is a system in which multiple robots cooperate to fulfill a macroscopic function. Many swarm robots have been developed for various purposes. This study aims to design swarm robots capable of executing spatially distributed tasks effectively, which can be potentially used for tasks such as search-and-rescue operation and gathering scattered garbage in rooms. We propose a simple decentralized control scheme for swarm robots by extending our previously proposed non-reciprocal-interaction-based model. Each robot has an internal state, called its workload. Each robot first moves randomly to find a task, and when it does, its workload increases, and then it attracts its neighboring robots to ask for their help. We demonstrate, via simulations, that the proposed control scheme enables the robots to effectively execute multiple tasks in parallel under various environments. Fault tolerance of the proposed system is also demonstrated.