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In the next generation Internet, connection requests will be arriving and departing at high rates with a non-uniform traffic pattern. An appropriate WDM network control scheme must be implemented to set up lightpaths for each request in an efficient manner. Most previous dynamic wavelength routing algorithms were based on accurate link state information. However, maintaining and distributing such information requires complex WDM network control signaling and management overhead. Moreover, the frequent changes in data traffic raise the difficulty of maintaining accurate wavelength availability information. An adaptive alternate routing is proposed for multi-fiber WDM network by using approximate congestion information. Simulation results show that the proposed routing scheme can achieve similar performances to the fixed-paths least-congestion (FPLC) algorithm, but with much less control overhead.