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The problem of dynamic routing in a multifibre time-slotted wavelength routed WDM network is considered. Requests to establish a connection are dynamic and each connection requests an integer multiple of some basic unit. Each wavelength has the capacity of carrying a multiple of these channels, where each channel is represented by a time-slot as in TDM networks. The network is represented as a layered graph model with multiple layers, where each layer represents a specific wavelength. Each link in the layered graph has one or more fibres and an associated cost. The cost of layered graph links could be a function of the loading state of the respective wavelength across the available fibres. Algorithms are proposed for fibre selection and for setting link costs, and a modified Dijkstra algorithm on the layered graph is used to select a route on the layered graph for a new connection request. The selected route on the layered graph represents the physical path and the selected wavelength. The performance of these algorithms is evaluated for a realistic mesh network topology for various combinations of the number of wavelengths, the number of fibres per link, the number of time-slots per wavelength, and the offered load for both uniform and non-uniform traffic loads. The best performing fibre selection and link cost update methods are identified. The proposed algorithm for routing and wavelength assignment in mesh optical WDM grooming networks outperforms previously proposed work in the literature.