# 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  
Designing the initial cluster formation as a phase sequence also brings benefits for its practical analyzability. For example, the time required for the phase sequence can be estimated in advance, since it is largely determined by the parameterization of the algorithm. Basically, the parameters are chosen as a compromise between low overhead (clustering duration and number of control messages sent) and required robustness (high delivery probability of the information required for clustering). In practice, the parameterization depends, for example, on the expected network size and link quality as well as the processing speed of the mesh nodes. For a detailed description of all CHaChA parameters, we refer to Section 4.2, Table 5.  
The clustering duration results, to a large part, from fixed waiting times before phase transitions as well as periodic retransmissions of broadcast messages, which mainly concern the phase announcements of the MCH. Figure 11 shows the general estimation of the clustering duration as a composition of the temporal contributions of all phases. Here, it is assumed that all nodes start executing the phase sequence simultaneously. In practical scenarios, we expect the clustering phase sequence to be triggered by network operators after initial node commissioning. Depending on the parameterization of the algorithm (i.e., granting up to several seconds \"slack\" per phase), only a loosely synchronized start of CHaChA on all nodes is required. Triggering a new clustering run will likely be done via the mesh network's base channel, instead of a separate Ethernet control channel as in our testbed. Apart from that, also a loosely synchronized system time (e.g., achieved by using NTP on the base channel) would allow for planning the start of future clustering runs directly on the nodes. Figure 12 shows a specific time estimation, applying CHaChA parameterization variant P1 (described later in Section 6.2.3) to the general estimation given in Figure 11. P1 served as initial parameterization for the practical assessment of the prototype (also see Table 8). It represents a generous choice of the time constants and thresholds to ensure robust clustering, resulting in an estimated duration of 130 s.  
The time requirement in phase 0 (network entry and MCH election) is composed of four components. When the CHaChA prototype is started, it first waits a fixed time INIT_DELAY to create objects and data structures for the network interfaces and fill them with information from the operating system. This parameter is thus not part of the clustering algorithm, but depends on the implementation and hardware/software platform. Adjusted to the test environment, a value of 2 s was selected for INIT_DELAY. After its initialization, a node checks whether clusters already exist and the phase sequence can be skipped. To do this, it waits for CH_THRESH transmission periods of length CH_PERIOD for the reception of CH broadcast messages. If new messages of previously unknown CHs arrive before this time is exceeded, the timer is reset. The delay that can be caused by getting to know new CHs is summarized as \(T_{NeuCH}\). It depends not only on the time offset of the CH broadcasts, but also on their propagation time in the network. The clustering experiments described below were always started in a newly initialized network on the base channel, so \(T_{NeuCH}\) could be neglected. If no CHs are available, MCH election is started. All nodes periodically announce their CENT metric via broadcast in the network at intervals of CENT_PERIOD. Upon receiving a higher CENT value, nodes are eliminated according to the K.O. principle. The node with highest metric wins the race after CENT_THRESH consecutive broadcasts without receiving a message in return. The convergence time of the K.O.