Network resiliency pertains to the vulnerability of telecommunication networks in the case of failures and malicious attacks. With the increasing capacity catering of network for the booming multi-services in Next Generation Networks (NGNs), reducing recovery time and improving capacity efficiency while providing high quality and resiliency of services has become increasingly important for the future network development. Providing network resiliency means to rapidly and accurately reroute the traffic via diversely routed spare capacity in the network when a failure takes down links or nodes in the working path. Planning and optimization for NGNs require an efficient algorithm for spare capacity allocation (SCA) that assures restorability with a minimum of total capacity. This dissertation aims to understand and advance the state of knowledge on spare capacity allocation in network resiliency for telecommunication core networks. Optimal network resiliency design for restorability requires considering: network topology, working and protection paths routing and spare capacity allocation. Restorable networks should be highly efficient in terms of total capacity required for restorability and be able to support any target level of restorability. The SCA strategy is to decide how much spare capacity should be reserved on links and to pre-plan protection paths to protect traffic from a set of failures. This optimal capacity allocation problem for survivable routing is known as NP-complete. To expose the problem structure, we propose a model of the SCA problem using a matrix-based framework, named Distributed Resilience Matrix (DRM) to identify the dependencies between the working and protection capacities associated with each pair of links and also to capture the local capacity usage information in a distributed control environment. In addition, we introduce a novel ant-based heuristic algorithm, called Friend-or-Foe Resilient (FoF-R) ant-based routing algorithm to find the optimal protection cycle (i.e., two node-disjoint paths between a source-destination node pair) and explore the sharing ability among protection paths using a capacity headroom-dependent attraction and repulsion function. Simulation results based on the OMNeT++ and AMPL/CPLEX tools show that the FoF-R scheme with the DRM structure is a promising approach to solving the SCA problem for survivable routing and it gives a good trade off between solution optimality and computation speed. Furthermore, for the SCA studies of survivable networks, it is also important to be able to differentiate between network topologies by means of a robust numerical measure that indicates the level of immunity of these topologies to failures of their nodes and links. Ideally, such a measure should be sensitive to the existence of nodes or links, which are more important than others, for example, if their failure causes the network’s disintegration. Another contribution in this dissertation is to introduce an algebraic connectivity metric, adopted from the spectral graph theory, namely the 2nd smallest eigenvalue of the Laplacian matrix of the network topology, instead of the average nodal degree, to characterize network robustness in studies of the SCA problem. Extensive simulation studies confirm that this metric is a more informative parameter than the average nodal degree for characterizing network topologies in network resiliency studies.