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We consider an IP/MPLS over WDM network, in which label switched routers (LSRs) in the IP/MPLS layer are interconnected through optical cross-connects (OXCs) in the optical core network (WDM layer) providing an end-to-end wavelength routing capability. In this paper, we study a dynamic label switched path (LSP) provisioning problem for the three different network models of the IP/MPLS over WDM network, namely, overlay, augmented, and peer models. For the overlay model, we propose an algorithm, called MLH_OVLY, in which a network finds a path with the minimum number of logical hops for an LSP request. We also propose, for the augmented model, a simple and efficient dynamic LSP provisioning algorithm, called CAPA_AUG, utilizing summarized capacity information from the WDM layer. We compare the proposed algorithms with the existing algorithms available for the overlay and peer models, and also provide an in-depth analysis of the algorithms. The algorithms are compared and evaluated using two key performance measures: LSP blocking probability and network (lightpath) utilization. Simulation results show that at low loads with a limited number of ports available in the network, CAPA_AUG achieves an order of magnitude better blocking performance and outperforms all other algorithm. Considering the small amount of information that is exchanged between the layers in the augmented model, these results suggest that the augmented model can be a practically good compromise between the overlay and peer models.