Schedule Dynamic Multiple Parallel Jobs with Precedence-Constrained Tasks on Heterogeneous Distributed Computing Systems Computer systems tend to be heterogeneous parallel and distributed computing systems, which are characterized by having various types of computational units interconnected via networks for executing multiple parallel jobs precedence-constrained tasks. Scheduling multiple jobs, which arrive at different instants, on such systems for fastest execution is a well-known NP-hard optimization problem. In order to achieve high-performance of systems, two important factors can be improved. One factor is the heterogeneity. Most algorithms use the upward rank value for ordering tasks and the earliest finish time for assigning processors. These two criteria can be improved to permit creating accurate and efficient schedules in heterogeneous distributed computing systems. Another factor is the fairness, existing algorithms are for static scheduling, and failed to make full use of the fairness in dynamic environments, such that obvious unfairness to longer-makespan jobs or shorter-makespan jobs can be caused. A dynamic multiple parallel jobs scheduling algorithm called F DMHSV (Fairness of Dynamic Multiple Heterogeneous Selection Value) is proposed to address the above problems to achieve high-performance of systems in this paper. Both example and extensive experimental evaluation demonstrate significant improvement of the F_DMHSV algorithm.