In this research, a scenario is assumed where periodic real-time jobs are being run on a heterogeneous cluster of computers, and new aperiodic parallel real-time jobs, modelled by Directed Acyclic Graphs (DAG), arrive at the system dynamically. In the scheduling scheme presented in this paper, a global scheduler situated within the cluster schedules new jobs onto the computers by modelling their spare capabilities left by existing periodic jobs. Admission control is introduced so that new jobs are rejected if their deadlines cannot be met under the precondition of still guaranteeing the real-time requirements of existing jobs. Each computer within the cluster houses a local scheduler, which uniformly schedules both periodic job instances and the subtasks in the parallel realtime jobs using an Early Deadline First policy. The modelling of the spare capabilities is optimal in the sense that once a new task starts running on a computer, it will utilize all the spare capability left by the periodic real-time jobs and its finish time is the earliest possible. The performance of the proposed modelling approach and scheduling scheme is evaluated by extensive simulation; results show that the system utilization is significantly enhanced, while the real-time requirements of the existing jobs remain guaranteed∗.