# Adaptive Multi-Channel Clustering in IEEE 802.11s Wireless Mesh Networks +
## 6 Experimental Validation
### Clustering in Static Topologies
#### 6.2.4 Results for Different Grid Sizes
\(5\times 5\)-node grid: As with parameterization P1 (see Section 6.2.3, Figure 13), the same most frequent cluster constellation was also formed with parameterization P2 in 9 of 10 measurements (see Figure 17a). Differences from the previous result existed only in the CH order during channel selection in phase 5, which depends on the ALM cost between the CHs and thus may be subject to slight metric variations. The constellation 2 shown in Figure 17b, which was formed in only one measurement, also resulted from an ALM-based  
Figure 16: Cluster constellations in the \(4\times 4\)-node grid for parameterization P2 (cluster channels (“C#”) highlighted in color; occurrence rate given in %). Reprinted from ref. [18]. decision. Here, node 11 did not consider CH 17 (red cluster) but CH 7 (purple cluster) as closest CH from its point of view in phase 4. Due to the more than doubled number of CHs in the \(5\times 5\) grid, compared to the previous topologies, as well as the majority of nodes being outside the neighborhood of the MCH, the initial phase sequence already formed clusters that differed in size only by a maximum of two nodes. Again, further balancing would lead to equal cluster sizes, as demonstrated for the \(5\times 5\) grid in Section 6.3.1. **Comparison of clustering duration and communication overhead:** Following the functional validation, clustering duration and communication overhead were compared in all scenarios. Table 10 shows the average clustering duration as well as TCP/UDP data size and packet count for each topology. The results for the \(5\times 5\)-node grid using parameterization P1 can be found in the last row of the table for comparison. Figures 18 and 19 show the results for parameterization P2 including their standard deviation. For parameterization P2, the estimation described in Section 6.2.1 resulted in an expected clustering duration of 50 s. It should be emphasized that our estimation uses simplified assumptions for the time components \(T_{NewCH}\), \(T_{KO}\), and \(T_{SelectChannel}\), which are in fact topology-dependent and subject to random processes. Of these, time \(T_{NewCH}\) was omitted (as with parameterization P1) because the phase sequence was always started simultaneously on all nodes. In addition, with parameterization P2, the initial check for existing clusters in phase 0 was disabled. Contrarily, \(T_{KO}\) (convergence time of broadcast-based MCH election in phase 0) as well as \(T_{SelectChannel}\) (time required for CH communication during channel selection in phase 5) were responsible for the clustering duration increasing with network size and CH count. Furthermore, our estimation neglects any execution delays on the devices, and therefore also the impact of message processing times increasing with the number of nodes. In the \(2\times 2\)- and \(3\times 3\)-node grids, the influence and variability of the topology-dependent time components were still low, and the measured average clustering duration of 49.3 s and 50.5 s, respectively, was close to the estimated duration of 50 s (see Figure 19). As the number of nodes increased, the average duration slowly rose above the estimate. Clustering took 52.9 s in the \(4\times 4\) grid and 55.6 s in the \(5\times 5\) grid, respectively. At the same time, the standard deviation increased to approx. 1 s (\(4\times 4\) grid) and 2 s (\(5\times 5\) grid). In terms of communication overhead, the trends shown in Figure 18 were obtained for the TCP and UDP traffic, again showing a standard deviation increasing with node count. As expected, the TCP trend exhibited a nearly linear dependence on the number of nodes. The reason for this is that CHaChA performs reliable information exchange via TCP mainly  
Figure 17: Cluster constellations in the \(5\times 5\)-node grid for parameterization P2 (cluster channels (“C#”) highlighted in color; occurrence rate given in %). Reprinted from ref. [18]. between neighboring nodes.