Calibrating a dependent failure model for computing reliabilities on telecommunication networks

In this work, we propose a methodology to calibrate a dependent failure model to compute the reliability in a telecommunication network. We use the Marshall-Olkin (MO) copula model, which captures failures that arise simultaneously in groups of links. In practice, this model is difficult to calibrate because it requires the estimation of a number of parameters that is exponential in the number of links. We formulate an optimization problem to calibrate a MO copula model to attain given marginal failure probabilities for all links and the correlations between them. Using a geographic failure model, we calibrate various MO copula models using our methodology, we simulate them, and we benchmark the reliabilities thus obtained. Our experiments show that considering the simultaneous failures of small and connected subsets of links is the key to obtain a good approximation of reliability, confirming what is suggested by the telecommunication literature.