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We propose a service differentiation scheme for optical burst switching (OBS) with scheduling algorithm horizon. In addition to the latest horizon used in the conventional horizon, we introduce the second latest horizon. Burst priority is perfectly controlled according to the burst class information informed by its control packet if the starting time of the burst transmission is later than the second latest horizon and earlier than the latest horizon. Therefore, the proposed scheme can guarantee burst class order between the two horizons even in the multi-hop networks, while the conventional extra-offset-time-based scheme does not guarantee it. We assume a multi-hop network with ring topology where bursts traverse five intermediate nodes, and evaluate the end-to-end and hop-by-hop burst blocking probabilities of the network. Simulation results show that the proposed scheme can achieve service differentiation with smaller blocking probability than the conventional scheme with horizon. Furthermore, we show that the proposed scheme preserves service differentiation even in the multi-hop environments.