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In this paper we consider working and protection paths for scheduled and random lightpath demands in an optical transport network without wavelength conversion. As the network resources are limited, the objective is to minimize the rejection ratio. To achieve this goal, we use backup multiplexing techniques to minimize the spare resources required to ensure protection. Scheduled lightpath demands (SLDs) are connection demands for which the set-up and tear-down times are known in advance as opposed to random lightpath demands (RLDs) whose date arrival and holding times are not known in advance and that are established on the fly. We propose and implement two routing algorithms to deal with the routing and spare capacity assignment problem for scheduled and random lightpath demands. The former exploits the a priori knowledge of scheduled lightpath demands to compute the routing and spare capacity assignment for the SLDs before considering the RLDs. The latter considers all the demands simultaneously using a sequential algorithm that computes the routing and spare capacity assignment on the fly, that is, demand by demand. We compare the proposed algorithms in terms of the rejection ratio.