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Survivability is a very important issue in telecom networks. Many previous works discuss availability-guaranteed and service-differentiated provisioning for survivable network design. Our work makes two new contributions. First, our work proposes a novel provisioning algorithm to explore the effect of link sharing among primary and backup paths. Second, the solution approach applies multi-backup protection scheme for those services which have extremely high availability requirements (relative to the network component availabilities). We develop a mathematical model to quantify a connection's availability with N (Nges1) backup paths with k-link (kges1) sharing between primary and backup paths. Based on the model, we propose a provisioning algorithm for dynamic connections with differentiated availability requirements. A connection can be either unprotected, or protected with N backup paths. The algorithm intelligently explores link sharing among primary and backup paths of a connection to target availability guarantee and resource efficiency. The illustrative numerical examples show that our scheme achieves better performance in both availability satisfaction and network resource utilization, compared to a traditional availability-constrained 1+1 provisioning strategy.