Aperiodic requests with unknown execution times and unknown arrival patterns are dynamically mapped to ratebased execution (RBE) tasks with variable rates and scheduled such that the real-time tasks are guaranteed to meet their deadlines. The aperiodic requests dynamically share the available processor capacity without reserving a fixed processor capacity for any one aperiodic request (or class of requests). This approach was selected over the traditional approach of using a static set of server tasks to process aperiodic requests so that the available processor capacity could be proportionally shared between active aperiodic requests.