ReTMiC: Reliability-Aware Thermal Management in Multicore Mixed-Criticality Embedded Systems

As the number of cores in multicore platforms increases, temperature constraints may prevent powering all cores simultaneously at maximum voltage and frequency level. Thermal hot spots and unbalanced temperatures between the processing cores may degrade the reliability. This paper introduces a reliability-aware thermal management scheduling (ReTMiC) method for mixed-criticality embedded systems. In this regard, ReTMiC meets Thermal Design Power as the chip-level power constraint at design time. In order to balance the temperature of the processing cores, our proposed method determines balancing points on each frame of the scheduling, and at run time, our proposed lightweight online re-mapping technique is activated at each determined balancing point for balancing the temperature of the processing cores. The online mechanism exploits the proposed temperature-aware factor to reduce the system’s temperature based on the current temperature of processing cores and the behavior of their corresponding running tasks. Our experimental results show that the ReTMiC method achieves up to 12.8°C reduction in the chip temperature and 3.5°C reduction in spatial thermal variation in comparison to the state-of-the-art techniques while keeping the system reliability at a required level.

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A Simple Sum of Products Formula to Compute the Reliability of the KooN System

Reliability block diagram (RBD) is a well-known, high-level abstract modeling method for calculating systems reliability. Increasing redundancy is the most important way for increasing Fault-tolerance and reliability of dependable systems. K-out-of-N (KooN) is one of the known redundancy models. The redundancy causes repeated events and increases the complexity of the computing system’s reliability, and researchers use techniques like factorization to overcome it. Current methods lead to the cumbersome formula that needs a lot of simplification to change in the form of Sum of the Products (SoP) in terms of reliabilities of its constituting components. In This paper, a technique for extracting simple formula for calculating the KooN system’s reliability in SoP form using the Venn diagram is presented. Then, the shortcoming of using the Venn diagram that is masking some joints events in the case of a large number of independent components is explained. We proposed the replacement of Lattice instead of Venn diagrams to overcome this weakness. Then, the Lattice of reliabilities that is dual of power set Lattice of components is introduced. Using the basic properties of Lattice of reliabilities and their inclusion relationships, we propose an algorithm for driving a general formula of the KooN system’s reliability in SoP form. The proposed algorithm gives the SoP formula coefficients by computing elements of the main diagonal and elements below it in a squared matrix. The computational and space complexity of the proposed algorithm is θ ((n – k) 2 /2) that n is the number of different components and k denotes the number of functioning components. A lemma and a theorem are defined and proved as a basis of the proposed general formula for computing coefficients of the SoP formula of the KooN system. Computational and space complexity of computing all of the coefficients of reliability formula of KooN system using this formula reduced to $\theta (n-k)$ . The proposed formula is simple and is in the form of SoP, and its computation is less error-prone.

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