Providing QoS and performance guarantees to arbitrarily divisible loads has become a significant problem for many cluster-based research computing facilities. While progress is being made in scheduling arbitrarily divisible loads, current approaches are not efficient and do not scale well. In this paper, we propose a linear algorithm for real-time divisible load scheduling. Unlike existing approaches, the new algorithm relaxes the tight coupling between the task admission controller and the task dispatcher. By eliminating the need to generate exact schedules in the admission controller, the algorithm avoids high overhead. We experimentally evaluate the new algorithm. Simulation results demonstrate that the algorithm scales well, can schedule large numbers of tasks efficiently, and performs similarly to existing approaches in terms of providing real-time guarantees.