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IP over WDM networks has been receiving much attention as a promising approach to building the next generation Internet since it can reduce complexities and overheads associated with the ATM and SONET layers. Provision of quality of service (QoS) is one important topic in next generation Internet. An optical burst switching scheme to support basic QoS at the WDM layer, the offset-time-based QoS scheme, was proposed by Yoo, Qiao and Dixit (2000, 2001) (YQD scheme). In this paper, we propose a union bound method to estimate the loss probability for different priority services, which is an extension of the bounds given by Yoo, Qiao and Dixit. It is proved that the proposed union bound is tighter than that given by Yoo, Qiao and Dixit. Meanwhile, based on the conservation law, we also present a method to estimate the required maximum delay length of fiber delay lines (FDLs) if FDL buffers are employed in the YQD scheme in IP over wavelength division multiplexing (WDM) networks. Some numerical results on the effect of fiber delay lines on the system performance and the required maximum delay length of FDLs for different service classes are presented.