Abstract: Heterogeneous distributed systems are mixed-criticality systems consisting of multiple functionalities with different criticality levels. A distributed functionality contains multiple precedence-constrained tasks. Mixed-criticality scheduling of heterogeneous distributed systems faces severe conflicts between performance and time constraints. Improving the overall performance of systems while still meeting the deadlines of higher-criticality functionalities, and making a reasonable tradeoff between performance and timing are major optimization problems. The F_DDHEFT(fairness of dynamic dual-criticality heterogeneous earliest finish time) algorithm is to improve the performance of systems. The C_DDHEFT (criticality of dynamic dual-criticality heterogeneous earliest finish time) algorithm is to meet the deadlines of higher-criticality functionalities. The D_DDHEFT (deadline-span of dynamic dual-criticality heterogeneous earliest finish time) algorithm is to allow the lower-criticality functionalities to be processed positively for better overall performance while still meeting the deadlines of higher-criticality functionalities, such that a reasonable tradeoff between performance and timing is made. Both example and extensive experimental evaluation demonstrate significant improvement of the D_DDHEFT algorithm.