Approximate Zero-Variance Importance Sampling for static network reliability estimation with node failures and application to rail systems

To accurately estimate the reliability of highly reliable rail systems and comply with contractual obligations, rail system suppliers such as ALSTOM require efficient reliability estimation techniques. Standard Monte-Carlo methods in their crude form are inefficient in estimating static network reliability of highly reliable systems. Importance Sampling techniques are an advanced class of variance reduction techniques used for rare-event analysis. In static network reliability estimation, the graph models often deal with failing links. In this paper, we propose an adaptation of an approximate Zero-Variance Importance Sampling method to evaluate the reliability of real transport systems where nodes are the failing components. This is more representative of railway telecommunication system behavior. Robustness measures of the accuracy of the estimates, bounded or vanishing relative error properties, are discussed and results from a real network (Data Communication System used in automated train control system) showing bounded relative error property, are presented.