Cluster computing systems are currently used to execute high performance applications that exhibit real time characteristics. A high-speed communication networks are used to interconnect the nodes of a cluster. Also, special software is used to allocate and manage the execution of the parallel tasks of the applications on cluster's processors to satisfy real-time requirements and achieve high throughput. In this paper, we present a new algorithm to allocate tasks? workloads in a way that improves the utilization of each cluster's processor. Consequently, a cluster's processor can accept more tasks and results in higher throughput. The idea of the algorithm depends on assigning a variable processing power to the task under consideration to satisfy its deadline instead of rejecting it if a constant processing power cannot be guaranteed. Simulation results reveal that the acceptance rate of submitted tasks to a cluster's processor using the new approach is superior to previous approaches.