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Barrera, J., Moreno, E., Munoz, G., & Romero, P. (2022). Exact reliability optimization for series-parallel graphs using convex envelopes. Networks, 80(2), 235–248.
Abstract: Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem-to find a network with the best possible reliability under multiple constraints-presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.
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Jimenez, D., Barrera, J., & Cancela, H. (2023). Communication Network Reliability Under Geographically Correlated Failures Using Probabilistic Seismic Hazard Analysis. IEEE Access, 11, 31341–31354.
Abstract: The research community's attention has been attracted to the reliability of networks exposed to large-scale disasters and this has become a critical concern in network studies during the last decade. Earthquakes are high on the list of those showing the most significant impacts on communication networks, and simultaneously, they are the least predictable events. This study uses the Probabilistic Seismic Hazard Analysis method to estimate the network element state after an earthquake. The approach considers a seismic source model and ground prediction equations to assess the intensity measure for each element according to its location. In the simulation, nodes fail according to the building's fragility curves. Similarly, links fail according to a failure rate depending on the intensity measure and the cable's characteristics. We use the source-terminal, and the diameter constrained reliability metrics. The approach goes beyond the graph representation of the network and incorporates the terrain characteristics and the component's robustness into the network performance analysis at an affordable computational cost. We study the method on a network in a seismic region with almost 9000 km of optical fiber. We observed that for source-terminal that are less than 500 km apart the improvements are marginals while for those that are more than 1000 km apart, reliability improves near a 30% in the enhanced designs. We also showed that these results depend heavily on the robustness/fragility of the infrastructure, showing that performance measures based only the network topology are not enough to evaluate new designs.
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