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In most existing studies of optical burst-switched networks, adaptive routing is based on deflection routing and/or feedback from the past intervals which often introduces excessive transmission delay and architectural complexity. Our proposed novel adaptive routing schemes, however, consider the transient link congestion at the moment when the bursts arrive and have potential to reduce the overall burst loss probability. Moreover, they can utilize the same offset times for the same node pairs implying zero additional transmission delay and simplicity. The proposed hop-by-hop routing schemes also aim to address the intrinsic unfairness defect of existing popular signaling protocols by increasing the effective link utilization. The results show that the proposed schemes generally outperform shortest path routing and depending on the routing strategy involved, the network topology and the traffic load, this improvement can be substantial. We develop analytical loss models to demonstrate the need for such an adaptive routing scheme at each hop and show its effectiveness. We also verify the analytical results by simulation.