Probabilistic schedulability analysis of harmonic multi-task systems with dual-modular temporal redundancy

To improve reliability of real-time control systems, various fault-tolerance methods have been designed and implemented. We propose a highly reliable control system using modular and temporal redundancy, called dual-modular temporal redundancy (DMTR). Assuming that transient faults occur and recover with exponential probability distributions, we analyze the probabilistic schedulability of DMTR for multiple tasks with harmonic periods (DMTR-HP). After formulating a discrete-time reliability model for DMTR-HP, we formulate an efficient recursive computation algorithm for rapidly obtaining the probabilistic schedulability of the overall system. Considering the overhead for checkpointing in a DMTR-HP control system, we obtain the optimal number of subslots for maximum reliability using our DMTR-HP reliability model. In addition, we compare the reliabilities of DMTR-HP, DMTR using GCDP scheduling (DMTR-GCDP), and conventional dual-modular redundancy (DMR).