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To analyze and reduce the impact of Machine-to-Machine (M2M) Devices (MDs) on the traditional Human-to-Human (H2H) users for the blending scenario, where both M2M and H2H services coexist in the current Universal Mobile Telecommunication System (UMTS) and perform the Random Access (RA) procedure simultaneously, a comprehensive RA analysis model of RA is proposed in this paper. Further, a power ramping strategy based on the logarithm for M2M is proposed. The efficiency of both the existing and proposed scheme is assessed through a simulation across several metrics, including average target power, throughput, blocking probability, and delay statistics. Numerical results show that the proposed algorithm can ensure a minimal impact on H2H communication while maintaining the throughput of the M2M communication. Meanwhile, because of its low energy consumption, this algorithm has a significant guide value for real-world applications.