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Traffic grooming in wavelength division multiplexing (WDM) optical networks routes and consolidates sub-wavelength connections onto lightpaths, to improve network utilization and reduce cost. It can be classified into static or dynamic, depending on whether the connections are given in advance or randomly arrive/depart. In this paper, an analytical model is developed for dynamic traffic grooming, allowing heterogeneous data rates for sub-wavelength connections, arbitrary alternate routing in both logical and physical topologies, and arbitrary wavelength conversion. The accuracy of the model has been verified by numerical results from simulation.