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Power control plays an important role in the design and operation of wireless networks. In this paper, we first define two critical metrics, transport density and channel access time to measure the system performance. The trade-off between these two metrics as a function of the peak power constraint is discussed in two cases, a fixed peak power case and an adjusted peak power case. Our analysis shows that the adjusted peak power constraint outperforms the fixed one in terms of both transport density and channel access time. Based on these observations, a novel and fully distributed energy-efficient MAC scheme with adjusted peak power constraint is proposed to schedule the concurrent transmissions in an efficient way. Better performance can be achieved by balancing between transport density and channel access time. Simulation results confirm the expected gains relative to standard MAC schemes: the transport density is increased by more than 50% compared to CSMA and by about a factor of 3 compared to ALOHA.