In this paper, the Behavioral Importance Priority Server (BIPS) algorithm is proposed to schedule sets of hard/soft real-time tasks. The mechanism postpones or advances the execution of the next instance of a task according to the value obtained from a function properly associated to the behavior of the task; as a consequence, there is a flexible adaptation of the bandwidth required by each server. A synchronization method is introduced to prevent deadlocks and priority inversions in the case of sets of tasks sharing resources along with the necessary and sufficient conditions for the schedulability analysis. A software framework proposing an abstract architecture of a system based on BIPS is also presented. The BIPS software framework intends to bridge the gap between theoretical scheduling aspects and the actual implementation of them. Since BIPS is capable of managing very different sets of tasks, it covers a wide variety of applications found in the real world.