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Realizing machine-to-machine (M2M) communications requires to construct and to manage scrupulous connections (logically and physically) from devices controllers to an enormous number of devices. By leveraging existing cellular infrastructures providing higher layers connections, the most challenging task is to efficiently manage massive accesses on the air interface. Consequently, in this letter, a massive access management (MAM) is proposed, which provides the most critical guarantees of quality-of-service (QoS), for devices. By deriving sufficient conditions of QoS guarantees, we show that the proposed MAM can effectively satisfy diverse QoS requirements, thus enabling the M2M communications over 3GPP scenarios.