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This paper focuses on energy minimization for the mapping and scheduling of real-time workflows under reliability constraints. Workflow instances are input periodically to the system. Each instance is composed of several tasks and must complete execution before the arrival of the next instance, and with a prescribed reliability threshold. While the shape of the dependence graph is identical for each instance, task execution times are stochastic and vary from one instance to the next. The reliability threshold is met by executing several replicas for each task. The target platform consists of identical processors equipped with Dynamic Voltage and Frequency Scaling (DVFS) capabilities. A different frequency can be assigned to each task replica to save energy, but it may have negative effect on the deadline and reliability target. This difficult tri-criteria mapping and scheduling problem (energy, deadline, reliability) has been studied only recently for workflows with arbitrary dependence constraints. We investigate new mapping and scheduling strategies based upon layers in the task graph. These strategies better balance replicas across processors, thereby decreasing the time overlap between different replicas of a given task, and saving energy. We compare these strategies with two state-of-the-art approaches and a reference baseline on a variety of benchmark workflows. Our best heuristics achieve an average energy gain of 60% over the competitors and of 82% over the baseline. • Tri-criteria mapping and scheduling problem for real-time workflows of arbitrary shape. • First general solution without any limitation on the number of replicas used. • Innovative solution based upon layers of the workflow outperforms competitors. [ABSTRACT FROM AUTHOR]