An increasing number of real-time applications, related to multimedia, adaptive control and videoconference, require greater flexible scheduling than classical real-time systems permit. This paper proposes a novel approach that generates dynamically the upper bounds and the lower bounds of tasks to manage overload in a real-time system. And then we design a very simple stochastic heuristical algorithm to maximize the weighted reward of task set, and analyze the performance of this algorithm. The proposed scheme provides a very simple and efficient mechanism to handle overload in linear time complexity in the presence of rate constraints.