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A new online multi-layer integrated routing (MLIR) scheme that combines IP (electrical) layer routing with WDM (optical) layer routing is investigated. It is a highly efficient and cost-effective routing scheme viable for the next generation integrated optical Internet. A new simplified weighted graph model for the integrated optical Internet consisted of optical routers with multi-granularity optical-electrical hybrid switching capability is firstly proposed. Then, based on the proposed graph model, we develop an online integrated routing scheme called differentiated weighted fair algorithm (DWFA) employing adaptive admission control (routing) strategies with the motivation of service/bandwidth differentiation, which can jointly solve multi-layer routing problem by simply applying the minimal weighted path computation algorithm. The major objective of DWFA is fourfold: 1) Quality of service (QoS) routing for traffic requests with various priorities; 2) blocking fairness for traffic requests with various bandwidth granularities; 3) adaptive routing according to the policy parameters from service provider; 4) lower computational complexity. Simulation results show that DWFA performs better than traditional overlay routing schemes such as optical-first-routing (OFR) and electrical-first-routing (EFR), in terms of traffic blocking ratio, traffic blocking fairness, average traffic logical hop counts, and global network resource utilization. It has been proved that the DWFA is a simple, comprehensive, and practical scheme of integrated routing in optical Internet for service providers.