## 6 Performance Evaluation and Discussion
### Simulation Results
#### 6.2.3. Energy Efficiency and Network Lifetime  
The relationship between energy efficiency, allocated transmit power and the expected battery lifetime is an important one and it is described in Figures 9 and 10 in detail. In the designed simulation environment, the SINR behavior of MTC devices is observed at different densities in the simulated cellular network considering the MFG based optimal power control policy. An increase in average SINR of the MTC users is observed with the increase of user density which can be attributed to increasingly dense network environment causing complex interference to all MTC and HTC users. As already observed, MTC devices tend to increase the allocated transmit power levels to counter this experienced interference. Due to increased MTC user density, the intra-MTC device interference takes the dominant role instead of the HTC device impairments after a certain point in the increasingly dense environment. Hence, an eventual drop in allocated power degrades the averaged SINR specifically for the MTC devices beyond this point in the density SINR graph. This behavior of the coexisting hybrid network environment of HTC and MTC devices ensures that the proposed MFG centered power control scheme can indeed achieve the highest possible SINR for the MTC devices. In comparison to the approaches involving a Markov decision process (MDP) based power control, the proposed MFG-based power control gets a more closely matched average SINR value to the target SINR. One can describe the MDP-based approach as a basic stochastic game design with individual optimal decision policies for each player instead of a global optimal policy for all players. Figure 9 provides a comparison of this MDP-based [42] and MFG-based power control scheme in terms of the averaged SINR according to different MTC device densities and their proximity to the target SINR value. It is clear that the MDP based power control scheme fails to support an increasingly dense MT environment with the expected decrease observed in the average SINR mainly due to increased interference levels. This experiment further highlights the importance of the achievable SINR in different MTC user densities as a key design target to ensure an energy efficient MFG-based power control. The network lifetime of MTC devices using the SIL design was analyzed with respect to the target SINR value \(\Gamma_{th}\). It is clear from Equation (13) that the required value of \(\mathrm{P_{o}}\) is directly related to the value of \(\Gamma_{th}\). Hence, the required transmit power needed by MTC devices to achieve their respective target SINR values directly affects their battery lifetimes. A comparative study of the proposed MFG based optimal power control scheme is done with an MDP-based power control mechanism and the results are shown in Figure 10. A decrease in network lifetime is observed for both of these schemes because of the direct dependence of the transmit power level and the value of the target SINR as expressed by Equation (13). The proposed MFG-based approach outperforms the MDP-based design by prolonging the lifetime of MTCDs by a factor of 3 before the optimal threshold value and by almost twice after the optimal value is attained. This proves the effectiveness of the proposed MFG-based design for battery lifetime enhancement for increasingly dense MTC network environment in coexistence with  
Figure 8: Transmit power with varying battery energy levels. traditional HTC users. The convergence of the coupled system of PDEs using finite difference schemes can converge to an asymptotic NE known as the MFE as discussed in detail in Section 5. Figure 11 depicts the exact behavior when multiple simulations are run using different initial state distributions (or mean field distributions) with the proposed algorithm converging rapidly to MFE within a limited number of iterations. This expected behavior is the premise of MFG and its explained benefits as compared to conventional game designs.