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This paper considers the problem of establishing dependable connections (D-connections) for fast failure recovery in wavelength-routed wavelength-division multiplexed (WDM) networks with dynamic traffic demand. A D-connection is realized by a primary lightpath and one or more backup lightpaths. Real time applications usually require timeliness and fault-tolerance. It is not a difficult task to guarantee timely delivery of messages in WDM networks, as a lightpath with its entire bandwidth is dedicated to an application. However providing fault-tolerance is an important issue to be solved in these networks. In this paper we focus on backup multiplexing based, primary-backup lightpath routing in WDM networks. We present different methods to assign wavelengths to backup lightpaths, for a given primary lightpath. They are broadly classified into primary dependent backup wavelength assignment (PDBWA) and primary independent backup wavelength assignment (PIBWA) schemes. The PDBWA is further classified into PDBWA-S and PDBWA-D, depending on whether the wavelength of the backup lightpath is the same as that of the primary lightpath or not. All the above methods differ in their computational complexity and performance. To improve fairness among the connections with and without fault-tolerant requirements, we propose a method called backup threshold. We conduct extensive simulation experiments to study the performance of the proposed methods.