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ABSTRACT. In earlier work we have proposed the concept of the dynamic group maximum matching for grouping the system graph into groups of different sizes according to the tasks arriving at the system. Also, we have developed a more efficient hardware fault-tolerant technique called the Hardware Fault-Tolerant (HFT) technique, where processors and communication channels are subject to failures. Also, we have studied the effect of the HFT technique on the reliability of a task.
In this work, we propose three hardware fault-tolerant scheduling algorithms called the Hardware Fault-Tolerant (FCFS + Smallest Fits First) (FCFSSFF) scheduling algorithm, Hardware Fault-Tolerant (FCFS + Largest Fits First) (FCFSLFF) scheduling algorithm, and Hardware Fault-Tolerant (FCFS + First Fits First) (FCFSFFF) scheduling algorithm. These algorithms are based on the dynamic group maximum matching concept and the HFT technique.
1. INTRODUCTIONHardware fault-tolerance has been studied in [1] - [3]. Examples of commercially available fault-tolerant systems are Tandem, Stratus, and Sequoia computers [4]-[6].
In an earlier work [17] we have introduced a more efficient new hardware fault-tolerant technique called the Hardware Fault-Tolerant (HFT) technique, where processors and communication channels are subject to failures.
In the following subsections we discuss the work.
1.1 Dynamic Group Maximum Matching ConceptThe maximum number of hardware faults that a system can tolerate with respect to a task Ti is defined as the task hardware reliability degree ti. As a task hardware reliability degree increases, more redundancy is used. In [8, 9], the researchers assumed that all the tasks running in the system have equal hardware reliability degree t, and they partitioned the system into groups of size (t + 1).
The concept of group maximum matching has been introduced by Hosseini in [8], which is a generalization of the classical maximum matching concept. The concept of the classical matching problem is used to group nodes of a graph into 2-node disjoint groups. A generalization to the classical matching is to group the nodes into (t + 1)-node disjoint groups. In classical maximum matching problem, 2-node nodes are grouped such that the number of groups is maximum. Similarly, the generalization maximum matching problem, nodes are grouped (each group is of size (t + 1)) such that the number of groups is maximum. Also, the researcher has proposed the Group Maximum Matching (GMM) algorithm for finding the group maximum matching. In [9], the researchers have shown that the GMM algorithm most of the time generates a maximum number of groups and rarely generates one group less than the maximum number. One drawback of the group maximum matching concept relates to the system performance where the system resources may not be utilized efficiently because less critical tasks (tasks with hardware reliability degree ti < t) will use more resources than what they need to maintain their reliability requireme./0ABDĂłƂ&'(89;ăŃƃwxمڅ܅
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