# 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  
Based on the results obtained with the conservative parameterization P1 in the \(5\times 5\)-node grid, topologies of different grid sizes were investigated. In advance, the parameterization P2 given in Table 9 was determined experimentally in the \(5\times 5\)-node grid. The objective was to reduce the clustering duration while maintaining the reproducibility of the previously obtained clustering results. Therefore, we gradually decreased parameters relevant to the duration and verified that no negative effects on the clustering result occurred. First, the time required in phase 0 was lowered. On the one hand, the initial check for already existing clusters was deactivated (CH_THRESH\(=0\)), since a synchronous execution of all devices was ensured in the experiments, and this fixed waiting time could thus be omitted in contrast to real scenarios. On the other hand, the threshold for consecutively received CENT messages was halved (CENT_THRESH = 10), which reduced the time required by the K.O. competition for MCH election. Additionally, the delay before phase transitions (PHASE_X_DELAY) was reduced from 10 to 2 s. Likewise, the number of retransmissions (PHASE_X_TRIES) of the associated announcement messages was halved. Both parameters significantly determine the duration of the individual phases (see estimation in Section 6.2.1). Due to the shorter phase duration, the transmission intervals for NC and CH messages were reduced accordingly to ensure timely delivery within their respective phases. With parameterization P2, the average clustering duration was reduced to just under 40% of the time required with parameterization P1 (55.6 s vs. 135.5 s). The previously most frequently generated cluster constellation (see Figure 13a) could still be reproduced in nine of ten measurements. The parameter values listed in Table 9 are specific to our testbed Mini-Mesh and its device platform [42]. It can be assumed that even lower times can be achieved with more powerful hardware. In the following paragraphs, clustering results obtained with parameterization P2 for different network sizes are discussed. We considered grid topologies with \(2\times 2\) to \(5\times 5\) nodes. The practical procedure was unchanged from the experiments described in Section 6.2.2. However, for the trend analysis as main focus, we conducted only 10 measurements per topology and averaged their results. First, the generated cluster constellations are discussed and their formation is explained in the context of the algorithm. This is followed by a comparison of the scenarios with respect to clustering duration and communication overhead. \(2\times 2\)-node grid:In the smallest topology, the constellation with two clusters shown in Figure 14 was formed consistently in all measurements. Although no central node position existed in the \(2\times 2\) setup, node 6 was always chosen as MCH in phase 0 due to a slightly higher CENT metric. It is calculated from the ALM distances of all mesh paths and small ALM differences caused the preference of one node. In phase 1, the three remaining nodes were applied as PCHs since they shared the same NC and PCHNC metrics. Of these candidates, node 7 reproducibly remained as final CH in phase 2. Again, this was due to a slightly higher CENT metric, which serves as weighting factor in the WNPR metric. Our current concept allows CHs to emerge in close proximity to the MCH but not to each other. This is motivated by applications where the MCH serves administrative purposes even beyond cluster formation. Use cases include, e.g., the retrieval of status information (monitoring) of all nodes, which we outlined in a previous case study [17]. Here, on the one hand, proximity to the MCH is desirable for efficient data synchronization. On the other hand, the coverage of individual network regions by the  
Figure 14: Cluster constellations in the \(2\times 2\)-node grid for parameterization P2 (cluster channels (“C#”) highlighted in color; occurrence rate given in %). Reprinted from ref.