# Clustering-Based Channel Allocation Method for Mitigating Inter-WBAN Interference
## 5 Performance Evaluation
If a WBAN moves out of the area \(\mathcal{S}\), a new WBAN is added so that the number of WBANs in \(\mathcal{S}\) is the same all the time. When a new node is added to \(\mathcal{S}\), its location is randomly selected in \(\mathcal{S}\). In Figure 8, we depict the variations of the modularity of the interference relationship graph over time. The term 'now' in this figure represents the modularity of a graph at the start of a time slot \(t\), and the term'move' represents the modulat  
Figure 5: Comparison of the interference experienced by a WBAN (\(|N|=100\)). the WBANs at the end of the time slot \(t\). The results shown as \"recluster' in this figure are obtained when our adaptive module is applied right after'move'. Since WBANs can randomly move around, their locations change over time. Thus, the cluster membership made based on the set of WBANs at the beginning of a time slot may not faithfully reflect the interference relationship graph formed by the set of WBANs at the end of the time slot. Therefore, the modularity of a graph reduces at the end of a time slot. Since our adaptive module rectifies the cluster membership of each WBAN distorted by its movement, it increases the modularity of the graph constructed based on the set of WBANs at the end of the time slot. To examine the effectiveness of the adaptive module, in Figure 9, we compare the distributions of \(\gamma_{i}(t)\)s obtained when only the base module is used with those obtained when both the base module and the adaptive module is used over time. When both modules are used, the base module is called at the time slots 7, 8, 10, and 11 when \(|N|=100\). When \(|N|=200\), the base module is called at the time slots 1, 3, 4, 5, 8, and 9. We can observe that the differences between these two cases are marginal for all the time slots. Figure 8: Variations of the graph modularity over time. The term ‘now’ represents the modularity at the start of a time slot \(t\); ‘move’ represents the modularity of the graph at the end of the time slot \(t\). The results shown as ‘recluster’ are obtained when our adaptive module is used right after ‘move’. Figure 7: Comparison of the data rate among the clusters when \(|N|=100\). To further investigate the validity of our method, we compare the average data rate achieved by our method with those obtained by the stochastic learning algorithm (SLA) proposed in [10]. We show the result in Figure 10. We can observe that the data rate increases gradually when SLA is used. This is attributed to the manner that SLA determines a channel to use. When SLA is used, each WBAN learns a channel selection probability distribution and exploits it to select a channel to use in a stochastic manner. Whenever a WBAN uses a channel, it measures the data rate of the intra-WBAN communication. Using the measured data rate, the WBAN modifies its channel selection probability distribution. Since the learning process inevitably involves an exploration phase, it takes time for a WBAN to predict the best channel in a given network topology. Therefore, during the exploration phase, the data rate of a WBAN is low because a WBAN does not select the channel that gives it the maximum data rate. When our method is used, a server collects necessary information from the WBANs and allocates channels for them without an iterative process. We note that the performance of our method is comparable to that of SLA in a stable state. When we inspect the differences between the data rates obtained by our method and those obtained by SLA in a converged state, the differences are less than 8.1% for all \(|N|\)s. We evaluate the channel decision time with a computer that is equipped with an AMD Ryzen 3700x whose CPU clock is 36 GHz. The size of a RAM is 16 GB, and Python version 3.10.3 is used to measure the channel decision time. When \(|N|=100\), it takes 49.78 s for SLA to converge to a stable point. Our base module decreases the channel decision time to 2.69 s (i.e., 94.6% reduction).