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Novel advance reservation (AR) requests, such as user data replication and grid computing, which are different from immediate reservation requests, allow certain initial-delay during setting up, as long as the resources are allocated before a preset deadline. Empowered by the optical orthogonal frequency-division multiplexing (O-OFDM) technology, the elastic optical networks (EON) support channels operating at heterogeneous line rates by allocating spectral resources in a flexible and dynamic manner. However, in a dynamic traffic scenario, dynamic path setup and teardown operation will inevitably lead to spectral fragmentation. In this paper, to effectively allocate the spectrum in a suitable duration along a better route, we introduce a notion of available time-spectrum consecutiveness (TSC) to describe the spectrum fragmentations along frequency axis and time axis. Based on TSC, three time-aware routing and spectrum assignment (RSA) algorithms are proposed. The novel algorithms retain the TSC as much as possible when establishing a lightpath and reduce the spectrum fragmentation. Simulation results indicate three proposed algorithms achieve lower blocking probability and higher spectrum efficiency.