A system and method are provided to allow real-time processes to overrun on a single processor or on a multiprocessor until either the latest start time of another real-time process has been reached or their own deadlines have been reached, and effectively utilize multiple processor resources by allowing process executions to be selectively preempted by other process executions and migrate from one processor to another processor at any time at run time to provide greater flexibility in utilizing any unused processor capacity and meeting deadlines, thus increase the chances that real-time processes will still be able to complete their computations despite overrunning, while guaranteeing satisfaction of important predetermined timing constraints, and increase both processor utilization and system robustness in the presence of inaccurate estimates of the worst-case computation times of real-time processes on a single processor or multiprocessor in a real-time system.