## 7 Simulation Results and Performance Analysis  
The traffic model as presented in Section 3 is used to determine the total number of users in the coverage area of the BS at each decision epoch under the above mentioned  
3-state MDP model referred as 'proposed MDP-based 3 state model'. These models can be defined as below:  
* **All BS Active**: where all of the BSs of the network are always active.
* **Rangisetti 2 State (active-standby) Model**: The BSs are capable of switching between active mode and stand-by mode [5].
* **MDP-based 2 State (active-sleep) Model**: The BSs are capable of switching between active mode and sleep mode [2].
* **Proposed MDP-based 3 State Model**: The BSs are capable of switching among active mode, stand-by mode and sleep mode.  
The plots clearly show that using the proposed MDP model, we can save a significant amount of power than 'All BS active' and 'Rangisetti 2 state model' in low traffic condition. This is because, as per our proposed model, some of the BSs are in active mode, one of them is in stand-by mode and rest of them are in sleep mode; whereas in 'Rangisetti 2 state model' all of the unused BSs are in stand-by mode, which causes higher energy consumption. However, our proposed MDP-based 3 state model consumes bit more energy than the 'MDP-based 2 state model', that is because 'Combes Model' put all of the unused BSs in sleep mode only, which results in less power consumption compared to our proposed model but causes more wake up delay. This wake up delay can cause some call drops for some new users who would need to wait for a sleeping BS to wake up. However, as expected, the power consumption is the same for the two states and three states models in higher traffic condition, as almost all of the BSs needs to be active in order to support the load. In order to see the delay performance of the above mentioned four different models we generate Figure 7, which shows the percentage of the total users experiencing delay (from delay group defined in Table 3) in receiving service within the observation period for the four different models. As expected, all the users in 'All BS active' model will have no delay (delay group-1) at all because all of the BSs are always active for this mode. On the other hand, 'Rangisetti 2 state model' uses stand-by mode for the unused BSs and 'our proposed model' uses standby and sleep mode for the unused BSs. Therefore only a few (around 12%) of the users experience approximately 30 \(\upmu\)s (delay group-2) of delay for both of these models. It is noteworthy that 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 go to stand-by mode 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. On the contrary, these users (around 12%) experience 40 s (delay group-3) of delay in the 'MDP model' as this model implements only sleep mode for unused BSs, and it takes more time for the BSs to go from sleep mode to active mode. Therefore, our proposed model offers a fair share of energy efficiency and delay in low traffic condition.  
Figure 7: Percentage of users experiencing delay.