## 6 Model Validation and Performance Evaluation
### Criteria to Minimize Delay and Energy Consumption
Indeed, even though the value of \(t_{absorption}\) tends to a constant value when the frame length increases, a higher number of slots per frame yields a greater delay. Since \(\overline{T_{CR}}\) in Equation (12) is proportional to \(t_{absorption}\) (constant) and to the frame length (increasing), the value of \(\overline{T_{CR}}\) increases linearly with the frame length, as shown in Figure 4a. In addition, the coordinator has to listen to the channel in every frame for longer periods of time, yielding greater energy consumption. Figure 4: (**a**) Average delay (in seconds) required to terminate a data collection round over the frame length; and (**b**) average energy consumed by the coordinator in a data collection round over the frame length. Therefore, the frame length has to be tuned in RFSA and FSA to its optimum value, depending on the number of end-devices, taking into account that: (i) a frame length greater than the optimum has a cost in terms of average delay and energy consumed by the coordinator; and (ii) both the average delay and energy consumption increase dramatically when the frame length is much lower than the optimum value. Consequently, since the increase in delay and energy after the optimal point show a very small slope, when the number of end-devices is not known _a priori_, it is better to over-dimension the frame length in order to guarantee that the delay and energy consumption are kept low. Of course, synchronization issues may arise when the frame length is very long. This deserves further research to improve the accuracy of the internal clocks in wireless transceivers so that very long frames can be executed. The average energy consumed per end-device in a data collection round (\(\overline{E_{1-ed}}\)) is represented in Figure 5 as a function of the frame length (from five to 50 slots) for RFSA and FSA considering \(n=25\), 50 and 100 end-devices. As could be expected, the average energy consumed per end-device using RFSA and FSA tends to infinity when the frame length is very small. Indeed, the more frames required to complete a data collection round, the higher the energy consumed per end-device. In addition, the average energy consumed per end-device in FSA is always greater than in RFSA. This is due to the fact that in FSA, an end-device has to contend independently to transmit each one of its \(L\) data packets, and contrarily, in RFSA, an end-device has only to contend to transmit its first data packet and uses a reserved slot to transmit its other \(L-1\) packets, yielding less energy consumption per end-device. Results show that the average energy consumed per end-device tends to a minimum value when \(m\geq n/2\) and \(m\geq n\) using RFSA and FSA, respectively. Indeed, although a longer frame length leads to longer standby and sleep periods in the end-devices, the use of low power standby and sleep modes (as shown in Table 1) yields reduced energy consumption. Therefore, the frame length has to be adjusted according to the number of contending end-devices in order to minimize the average energy consumed per end-device. Figure 5: Average energy consumed per end-device in a data collection round over the frame length.