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As the operation of our fiber-optic backbone networks migrates from interconnected SONET rings to arbitrary mesh topology, traffic grooming on wavelength-division multiplexing (WDM) mesh networks becomes an extremely important research problem. To address this problem, we propose a new generic graph model for traffic grooming in heterogeneous WDM mesh networks. The novelty of our model is that, by only manipulating the edges of the auxiliary graph created by our model and the weights of these edges, our model can achieve various objectives using different grooming policies, while taking into account various constraints such as transceivers, wavelengths, wavelength-conversion capabilities, and grooming capabilities. Based on the auxiliary graph, we develop an integrated traffic-grooming algorithm (IGABAG) and an integrated grooming procedure (INGPROC) which jointly solve several traffic-grooming subproblems by simply applying the shortest-path computation method. Different grooming policies can be represented by different weight-assignment functions, and the performance of these grooming policies are compared under both nonblocking scenario and blocking scenario. The IGABAG can be applied to both static and dynamic traffic grooming. In static grooming, the traffic-selection scheme is key to achieving good network performance. We propose several traffic-selection schemes based on this model and we evaluate their performance for different network topologies.