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We propose and evaluate fast reservation (FR) protocols for optical burst switched (OBS) networks. The proposed reservation schemes aim at reducing the end-to-end delay of a data burst, by sending the burst header packet (BHP) in the core network before the burst assembly is completed at the ingress node. We use linear prediction filters to estimate the expected length of the burst and the time needed for the burstification process to complete. A BHP packet carrying these estimates is sent before burst completion, in order to reserve bandwidth at each intermediate node for the time interval the burst is expected to pass from that node. Reducing the total time needed for a packet to be transported over an OBS network is important, especially for real-time applications. Reserving bandwidth only for the time interval it is actual going to be used by a burst is important for network utilization efficiency. In the simulations conducted we evaluate the proposed extensions and prove their usefulness.