Integrated IP over wavelength division multiplexed (WDM) networks, with generalized multiprotocol label switching (GMPLS) control and management capabilities, are promising candidates for the next generation optical Internet networks. By using a unified control plane, such networks make more efficient use of network resources both at the IP layer and the WDM optical layer. We consider prioritized routing of bandwidth-guaranteed label switched paths (LSPs) providing service differentiation between classes of high and normal priority traffic. The QoS delay requirements are assumed to be translated into bandwidth and opto-electronic-opto (OEO) conversion requirements. We develop a graphical representation of the integrated network state which is different from other conventional graphical representations in that it models the cost of usage of ports and OEO conversions in addition to the usage of wavelength and bandwidth resources. We then develop a threshold-protection-based routing algorithm which admits high-priority LSPs in preference over normal-priority LSPs and satisfies the bandwidth and OEO constraint requirements. Through extensive simulation experiments, we demonstrate the service differentiation and effectiveness of our algorithm.