Reliability is an important aspect of operating safety-critical applications of networked systems, such as in avionics. In order to ensure sufficient reliability, one approach is to apply redundancy. However, redundancy may be costly if the degree of redundancy is too high. This paper proposes an optimization-based framework for guaranteeing the desired reliability of any graph-based networked system. It focuses on integrated modular avionics architecture, based on the use of minimally redundant components. This framework consists of two steps. The first is to compute the minimum number of components within the architecture, using a geometric program. The second is to determine the topology with the minimal number of connections between these components, using a signomial program. Finally, the method is illustrated on a small example network and a larger network of the A350 avionics architecture.
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