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Massive Machine-Type Communication (mMTC) is expected to be strongly supported by future 5G wireless networks. Its deployment, however, is seriously challenged by the high risk of random access (RA) collision. A popular concept is to reduce RA collisions by clustering mMTC devices into groups, and to connect group members with device-to-device (D2D) links. However, analytical models of this method and discussions about the reliability of D2D links are still absent. In this paper, existing grouping-based solutions are reviewed, an analytical model of grouped RA collision is proposed. Based on the analytical model, the impact of D2D reliability on the collision rate is also investigated. Afterwards, an efficient grouped RA procedure is designed to extend the state-of-the-art with an efficient local group update mechanism against D2D link exceptions.