# Bell-X, An Opportunistic Time Synchronization Mechanism for Scheduled Wireless Sensor Networks
## 6 Results
### Power Consumption  
The main objective of Bell-X mechanism is to speed up the connection process while the energy consumption that is related to the advertising traffic is reduced. Equation (2) is proposed to be able to compare the different simulated configuration in terms of energy. In the numerator, the number of beacons transmitted during a bell cycle is obtained, while the total time of a bell cycle is calculated in the denominator. This equation allows for the average EB per second to be calculated using all of the configuration parameters detailed in Table 2.  
Figure 16 shows the values obtained from the proposed model for two different configurations in which the \(\mathrm{V_{F}}\) and \(\mathrm{P_{F}}\) configuration parameters are modified. It can be seen how when the value of \(\mathrm{P_{F}}\) increases, the number of beacons transmitted decreases, because the peak zone of the bell is longer. Nevertheless, if the value of \(\mathrm{V_{F}}\) is greater, the bell spends more time at its minimum value, so a greater number of beacons is sent. Using this model, a user could choose an energy optimized configuration, which ensures that nodes connect faster in valley zones than in other configurations.  
\[EB/sec=\frac{V_{F}+2\cdot(D-1)\cdot S_{F}+P_{F}}{V_{F}\cdot I_{min}+2\cdot S_{ F}\cdot\sum_{i=1}^{D-1}I_{min}\cdot 2^{i}+P_{F}\cdot I_{min}\cdot 2^{D}} \tag{2}\]  
Figure 17 shows the quantity of EB messages exchanged for each configuration in order to extract value information regarding the impact of the proposed solution in power consumption. In this case, the Bell-65 achieves the lowest number of beacons/hour, only bested by the Trickle Timer. Nevertheless, the Trickle Timer configuration is dependent on the RPL layer behaviour. This means that the result shown is for the most optimistic case in which the timer is set by the RPL layer just rises to its maximum value of 50 s and stays there. In real conditions, the network condition will change over time, frequently restarting this timer and therefore increasing the number of beacons sent. This means that Bell-65 is the most energy efficient configuration tested regardless of the network condition.  
The effect of the different configurations on the evolution of power consumption, due to beaconing, for a node in the network, also taking into account the scanning phase (this is, the behaviour since the node is powered on), is shown in Figure 18. As can be seen, for higher values of 'X' in the Bell-X configuration (Bell-65), the energy used is rising slower than for the other configurations, leading to a longer node lifetime. Nevertheless, these results must be analysed while taking the possible connection time requirements and connection success rate into account.  
Figure 16: Number of beacons per second for different Bell-X configurations; (a) Fixed parameters SF = 4, \(\mathrm{Imin}=4\), \(\mathrm{D}=4\); (b) Fixed parameters \(\mathrm{S_{F}}=4\), \(\mathrm{I_{min}}=1\), \(\mathrm{D}=8\).  
Figure 17: Comparison of the different simulated configurations in beacons per hour.  
Figure 18: Consumption trend analysis during a month of operation for each configuration.