## 7 Simulation Results and Performance Analysis
### Effect of the Parameter Variation  
We apply trapezoidal numerical integration [17] on the power consumption curves in order to find the total energy consumption of the network. We find that the MDP-based three state model can reduce approximately 40% energy consumption compared to the 'All BS active' model. However, as one can expect from the power consumption curves, our proposed model is consuming little bit more energy than the MDP-based 2 state model, but this disadvantage is outweighed by the benefits of reduced delay compared to the Combes model. In this section, we vary the different parameters and have shown their effect on the energy consumption of the BS. At first, we vary the coverage range of the BS and find that the energy consumption increases rapidly after a certain range in Figure 8. For the set of parameters we have used as in Table 2, we find that the energy consumption remains almost constant for up to BS range of 1.5 km, however increases very rapidly for higher BS ranges. This scenario is true for all of the models we have used. These results depict that our proposed model consumes less energy than 'All TRC active' model and 'Rangisetti 2 state (active-standby) model', however consumes little more energy than 'MDP-based 2 state (active-sleep) model'. Figure 9 shows the expected delay experienced by the users, from where we can see that 'MDP-based 2 state (active-sleep) model' offers more delay than 'Proposed 3 state model' and 'Rangisetti 2 state (active-standby) model'. As per the proposed MDP-based 3 state model, the users will experience delay only when a base station will have transition from stand-by to active mode. The time needed for the sleeping BS to to go stand-by will not cause delay to the users. Note that as per, Rangisetti model, the delay is also caused by the transition between stand-by to active mode. That is why the delay for 'Rangisetti 2 state model' and 'proposed 2 state model' are the same. As expected the delay increases with the BS range; however after a certain range when most of the BSs are active then the activation delay reduces. Please note that different ranges of BSs represent different types of BS (Pico, Femto, Micro, Macro etc). Figures 8 and 9 provide us a good evidence to claim that our proposed model offers a fair share of energy efficiency and wake-up delay for any type of BSs.  
We also observe the effect of different pathloss exponent and shadowing variance on the energy consumption (for macro BS as an example) and expected delay and the results are shown in Figures 10-12 respectively. As we can expect, energy consumption of the BS increases with the path loss exponent and shadowing variance, which is clearly depicted in the figures. Figure 12 depicts that 'MDP-based 2 state (active-sleep) model' offers higher delay than 'Proposed 3 state model' and 'Rangisetti 2 state (active-standby) model'. All of these results again show that our proposed model is an efficient model which offers a fair share of reduced energy consumption as well as reduced wake-up delay.  
Figure 10: Effect of varying pathloss exponent.  
Figure 9: Delay experienced by users.