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Long-reach Passive Optical Networks (LR-PONs) aim to combine the capacity of metro and access networks by extending the reach and split ratio of the conventional PONs. LR-PONs appear as efficient solutions having feeder distances around 100km and high split ratios up to 1000-way. On the other hand, transmission of the signals in long distances up to 100km leads to increased propagation delay whereas high split ratio may lead to long cycle times resulting in large queue occupancies and long packet delays. Before LR-PON becomes widely adopted, the trade-off between the advantages and performance degradation problem which is resulting from long reach and high split ratio properties of LR-PONs needs to be solved. Recent studies have focused on enhancing the performance of dynamic bandwidth allocation in LR-PONs. This article presents a comprehensive survey on the dynamic bandwidth allocation schemes for LR-PONs. In the article, a comparative classification of the proposed schemes based on their quality-of-service awareness, base-types, feeder distances and tested performance metrics is provided. At the end of the article, a brief discussion on the open issues and research challenges for the solution of performance degradation in LR-PONs is presented.