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We propose an efficient algorithm based on continuous-time Markov chain to compute the availability of network connections protected by shared recovery schemes in optical networks. The shared schemes are widely used to improve the availability without excessively expending network resources. The basic idea consists to share the recovery resources between two or more connections in order to reduce the amount of extra resources. This approach assumes that only a limited number of simultaneous failures that overlaps may happen in the network. In the presence of overlapping failures that affect simultaneously many connections, some may not be recovered, determining a reduction on their availability. The order in which overlapping failures occur is important because the first affected connection will acquire the shared resources, preventing the remaining connections to activate the recovery. The algorithm proposed in this paper significantly simplifies the calculation of the steady-state vector. We show that our approach is computationally more efficient and more accurate than the traditional approach used in the literature. [ABSTRACT FROM AUTHOR]