## 7 Evaluation
### Simulation Results  
As described in Sections 5 and 6.4, the standard deviation of Equation (12) is measure of how uniform polling queries are generated during \(T_{M}\) and Equation (13) is our fitness function. Therefore, we calculated fitness values by Equation (13) for evaluation.  
First of all, we confirmed that random selection at the initialization step did not have a big impact on the performance. To evaluate this, we created a network topology and then we generated 200 kinds of schedules for a scenario as shown in Table 3. All the results were converged. Then we show one of the detail results as bellow. The fitness values of the top 20 individuals after the GA-based slot assignment are plotted in Figure 11. As shown in Figure 11, minimum standard deviation at the initial random selection where the number of GA operation is 0, was 0.186 and the final one was 0.049. In this case, our proposal generates a schedule for periodic multicycle data collection after 2000 times GA crossover operations. In contrast, the standard deviation of the conventional scheme [25] is 0.49. From uniforming application traffic of periodic data collection point of view, our proposal is superior to the conventional scheme.  
The mean value of all slot type during \(T_{M}\) is calculated by the Equation (14). \(Sl_{ideal}\) is the ideal value when the polling schedule includes all slot assignment of data transmiss  
\begin{table}
\begin{tabular}{l l r} \hline \hline
**Item** & **Notation** & **Value** \\ \hline The number of nodes in an IWSN & \(N_{all}\) & 10 nodes \\ Data collection cycle 1 & \(T_{1}\) & 2 min \\ Data collection cycle 2 & \(T_{2}\) & 4 min \\ Data collection cycle 3 & \(T_{3}\) & 8 min \\ The least common multiple of collection cycles & \(T_{M}\) & 8 min \\ The number of slots in a QF & \(S_{QF}\) & 10 \\ Slot length & \(\Delta t_{s}\) & 3 s \\ QF length & \(\Delta T_{QF}\) & 30 (\(S_{QF}\times\Delta t_{s}\)) s \\ The number of QFs in a chromosomes & \(N_{QF}\) & 16 (\(T_{M}\div T_{QF}\)) \\ The number of slots in a chromosomes & \(S_{gene}\) & 160 (\(N_{QF}\times S_{QF}\)) \\ The number of individuals & \(N_{indiv}\) & 20 \\ The number of iteration of crossover operation & \(I_{max}\) & 4000 times \\ Packet error rate & \(PER\) & 0–20\% \\ MAX retry count & \(R_{max}\) & 2 \\ Threshold of a path quality & \(Th_{path}\) & 90\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation conditions.  
their retries. As shown in Figure 12, the best schedule in the 20 individuals assigns the ideal number of slots for data transmission and their retries.  
\[SI_{ideal}=\frac{1}{N_{QF}\times N_{all}}\times\sum_{i=1}^{\tau_{g}}(\frac{T_{M}} {T_{i}}\times SI_{i}), \tag{14}\]  
where the sum of slot type of all nodes which belong to group \(i\) is as follows;  
\[SI_{i}=N_{i}+2\sum_{j=1}^{N_{i}}R_{i,j}+3(K_{i}-N_{i}-\sum_{j=1}^{N_{i}}R_{i,j}).\]  
In addition, Figure 13 shows E2E communication \"3\"y of all nodes after the GA-based slot assignment, and average one of all nodes in each individual. The E2E communication \"3\"y is calculated by the left-side hand of Equation (1). The abscissa of the graph represents the ID number of individuals, and the ordinate represents the E2E communication \"3\"ies. The E2E communication \"3\"ies are over 90% as shown in Figure 13. The average success probability is 97.4% and the lowest one is 95.2% where the 5 th individual is selected. The results meet our target requirements, as listed in Table 3.  
Figure 11: Transition of standard deviation slot type value of the top 20 individuals, where \(N_{all}=10\).  
Figure 12: Comparison between the mean value of slot type of all QueueFrames between the best chromosome and ideal value.