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As the survivable mapping is critical in IP-over-wavelength-division-multiplexing (WDM) network to guarantee the restorability of IP layer, provisioning survivability in network with dynamic traffic is essential. However, survivable mapping problem for dynamic traffic shows more complexity than that for static traffic: 1) How to guarantee a survivable mapping since the lightpath is established and released dynamically; 2) how to make a balance between the cost of maintaining the survivable mapping and network utilization efficiency; 3) what kind of algorithm could be employed as an efficient online algorithm with acceptable computing complexity and scalability. In this paper, two schemes, dynamic routing and logical topology remapping, are proposed to keep a survivable mapping from logical topology to physical topology in dynamic traffic scenario. In addition, two different cutset-searching methods are presented in order to support the proposed online survivable mapping algorithm. At the end, a series of experiments employing regular networks and some special topologies with different connectivity have been carried out in order to evaluate the efficiency and scalability of our approach, in terms of the blocking probability, resource utilization, critical link holding time, and the restoration rate for random single failures. Generally, our results show that this new approach offers great degree of survivability for IP layer, but with acceptable resource cost and complexity.