# Adaptive Multi-Channel Clustering in IEEE 802.11s Wireless Mesh Networks +
## 6 Experimental Validation
### Clustering in Static Topologies
#### 6.2.1 Estimation of Clustering Duration
method required for eliminating all nodes with lower metrics is summarized as \(T_{KO}\) in Figure 11. It also depends on the broadcast propagation time for the respective network size/topology and is a multiple of the broadcast period CENT_PERIOD. Depending on the topology, the period should be chosen large enough to ensure complete broadcast propagation of all nodes  
Figure 11: Time components for estimating the clustering duration. Reprinted from ref. [18]. Figure 12: Estimated clustering duration for parameterization P1 (parameter values given in Table 8). within one round. If all nodes first perform a broadcast before receiving a message, at least two broadcast rounds are required for the K.O. procedure. Additional rounds are caused, e.g., by a too-small choice of CENT_PERIOD or the loss of broadcast messages in the network. In sample experiments using the \(5\times 5\)-node grid topology and a broadcast period of \(500\,\mathrm{ms}\), convergence was observed after up to four broadcast rounds. As a simplification, \(T_{KO}\) was subsequently estimated with a fixed length of (\(4\cdot\text{CENT\_PERIOD}\)). Following the selection of the MCH, it initiates the phase transition by means of periodic broadcast messages. This signaling procedure corresponds to the time requirement (PHASE_TRIES : PHASE_PERIOD). In our evaluation, the same repetition number and transmission period were used for all phase transitions. Thus, the respective duration of the subsequent phases 1-4 was composed of the same announcement duration plus a delay PHASE_DELAY. The MCH considers this delay prior to the initiation of the phase transition to ensure information exchange of all nodes including stabilization of metrics in each phase. In phase 3, an additional waiting time of CH_PERIOD (length of a CH broadcast period) is introduced to ensure robust cluster announcement independent of the PHASE_DELAY parameter. Contrarily, announcement of the transition from phase 5 to phase 6 occurs directly after the channel selection conducted by the CHs and MCH. The time required for the channel selection sequence and its TCP unicast message exchange is summarized by \(T_{SelectChannel}\). Besides the number of CHs, it also depends on the network topology (average distance between CHs) and transmission speed. Hence, as for \(T_{KO}\), a general estimate of \(T_{SelectChannel}\) is difficult. In sample experiments with the \(5\times 5\)-node grid topology, where five CHs were created at a maximum distance of two hops from each other and the WLAN data rate setting MCH 3 (gross data rate of 26 Mbps) was applied, \(T_{SelectChannel}\) stayed below \(1\,\mathrm{s}\). We further simplified its estimation using this upper value. The time \(T_{ConfigIF2}\) theoretically required in phase 6 to configure the nodes' secondary interfaces could be ignored in the experiments, since only the primary interfaces were used. In practice, \(T_{ConfigIF2}\) depends on the device platform used, but usually the configuration of the WLAN channel including network joining requires only fractions of a second [43]. The subsequent transition from phase 6 to distributed cluster operation (\"phase 7\") is always performed independently by all nodes, so there is no additional waiting time.