In this paper, a novel availability-constrained survivable routing algorithm, called Generalized Dedicated Protection (GDP), is introduced for circuit switched mesh networks. The goal of the algorithm is minimizing the cost of reserved bandwidth for protection purposes while a predefined connection availability is guaranteed. The paper gives a formal description of the working and dedicated protection paths/segments allocation problem with connection availability constraints. Firstly, a connection availability evaluation method is proposed for modeling dependent or independent failures based on state enumeration. Secondly, it is shown that GDP is NP-complete even when splitting the traffic on multiple routes is allowed, and formulated as an Integer Linear Program (ILP). Finally, simulation is conducted to verify the proposed availability evaluation method, and the GDP protection algorithms with their existing counterparts.