In future, a massive number of devices are expected to communicate for pervasive monitoring and measurement, industrial automation, and home/building energy management. Nevertheless, such Machine-to-Machine (M2M) communications are prone to failure due to depletion of machines energy if the communication system is not designed properly. A key step in building energy-efficient protocols for large-scale M2M communications is to assess, model or characterize a network energy consumption profile. To meet this need, we develop a theoretical and numerical framework to evaluate the cumulative distribution function (CDF) of the total energy consumption by fully exploiting the properties of stochastic geometry.
Unlike the other existing approaches, we model the transmission energy as a function of transmission power, packet size, and link affordable capacity that is a logarithmic function of experienced Signal to Interference plus Noise Ratio (SINR). Since it is very difficult, if not impossible, to derive a closed-form expression for the CDF, we derive numerically computable first- and second-order moments of energy consumption. Applying these moments we then propose Log-normal and Log-logistic distributions to approximate the CDF. Our simulation results show that Log-logistic almost precisely approximates the exact CDF.