Switch Complexity in Systems with Hybrid Redundancy

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Abstract
The combination of N-modular redundancy (NMR) and standby sparing has resulted in a promising redundancy technique for protecting those portions of a fault-tolerant system whose continuous real-time operation is essential. This technique, known as hybrid redundancy, uses N + Sp identical modules. N of these are connected to a majority voter to form an NMR core. The remaining Sp are used as standby spares. Disagreement detectors instruct a switch to replace with a standby spare any of the N modules that disagrees with the majority consensus. Since the switch and disagreement detector, as well as the modules, must function properly for the system to perform its designed task, the overall system reliability depends on the disagreement detector, switch, and hybrid reliabilities. Hence the overall reliability is a function of switch reliability. A highly reliable, thus simple, switch is desirable. First, strategies where every spare can be switched into every voter position (totally assigned) are considered. An optimal strategy is developed where the number of states in the switch is the criterion used for optimality. Formulas for the switch state count for the various strategies are derived and the strategies compared. Next, partially assigned switching strategies, strategies where every spare need not be capable of occupying every voter position, are examined. It is shown that designs where all spares are assigned to the same t + 2 of the 2t + 1 voter positions have as good reliability as the more complex totally assigned switching strategy.

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