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In an optical WDM mesh network, different protection schemes (such as dedicated or shared protection) can be used to improve the service availability against network failures. However, in order to satisfy a connections service-availability requirement in a cost-effective and resource-efficient manner, we need a systematic mechanism to select a proper protection scheme for each connection request while provisioning the connection. In this paper, we propose to use connection availability as a metric to provide differentiated protection services in a wavelength-convertible WDM mesh network. We develop a mathematical model to analyze the availabilities of connections with different protection modes (i.e., unprotected, dedicated protected, or shared protected). In the shared-protection case, we investigate how a connection's availability is affected by backup resource sharing. The sharing might cause backup resource contention between several connections when multiple simultaneous (or overlapping) failures occur in the network. Using a continuous-time Markov model, we derive the conditional probability for a connection to acquire backup resources in the presence of backup resource contention. Through this model, we show how the availability of a shared-protected connection can be quantitatively computed. Based on the analytical model, we develop provisioning strategies for a given set of connection demands in which an appropriate, possibly different, level of protection is provided to each connection according to its predefined availability requirement, e.g., 0.999, 0.997. We propose integer linear programming (ILP) and heuristic approaches to provision the connections cost effectively while satisfying the connections' availability requirements. The effectiveness of our provisioning approaches is demonstrated through numerical examples. The proposed provisioning strategies inherently facilitate the service differentiation in optical WDM mesh networks.