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Overlay routing can be used as a Traffic Engineering (TE) technique to realize efficient resource utilization and load balancing in the current wired Internet. Conventional overlay routing uses a detour path immediately upon quality degradation of the default path. However, with the widespread use of mobile and wireless communication technologies, conventional overlay routing faces several significant challenges such as intermittent connectivity and high packet loss rate resulting from the instability of network environments. Therefore, this paper proposes a novel TE technique based on overlay routing that has an Acceptable Waiting Time (AWT), which allows the overlay node to await the quality recovery of the default path, instead of employing the detour path immediately upon the quality degradation of the default path. Simulation results show that the proposed scheme can deal with instability of path condition.