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Future M2M networks are expected to accommodate socially important services such as telemetering and disaster sensing. To construct these networks economically, proposals have been made to use wide-range wireless cells with a radius of more than 1 km and that are capable of accommodating more terminals than the population . We propose that the minimum call rate shall be assured to the terminal groups used for such important services even if all terminals used for other services call simultaneously and keep retrying calls. However, no studies have been done on controlling call traffic as a terminal group under such requirements, and it is difficult to distinguish between collision of random access (RA) call messages and idle signals, so it is also difficult to control RA message traffic. We propose here a fair congestion control method for terminal groups. This method distinguishes between RA collisions and idle signals using media access control (MAC) layer information and also enables RA message traffic and data packet traffic to be controlled. The results of a simulated evaluation are presented.