## 5 Experimental Evaluation
### Clustering and Routing Mechanism Evaluation  
A visualisation module is developed for the dynamic illustration of the clustering process and the distribution of the CHs within the WSN. It is noticed that the clusters' distribution improves (qualitative metric) over time since the probabilistic techniques used tend to homogenize the size and form of the created clusters and thus distribute the clustering overhead among the elected CHs. Two indicative screenshots are presented in Figure 12 where clusters are distinguished. Figure 11: Deviation in the estimation of the (a) density and (b) size of the WSN. Figure 12: Cluster Visualisation. In Figure 13, the comparison of the number of CHs that are elected in the simulation environment with the theoretical ones according to the \(P_{clust}\) (refer to Equation 1) is shown. As it is expected, the theoretical and simulation results are closely related. An important characteristic for the optimisation of the clustering process is the adaptation of the clusters' size according to the changes in the network topology. In cases of more dense networks, it is desirable the creation of larger (in size) clusters since nodes are close (in number of hops) to each other. The existence of less CHs with small distances from their members improves the energy efficiency of the WSN (refer also to Section 5.3). In Figures 14(a)-(c), the average size of the clusters that are created is presented for fixed and variable probability (refer to Equation 1). In the latter case, the trend is the creation of larger in size clusters in dense networks in opposition to the first case where the cluster size remains stable. Self-optimisation of the clustering process is therefore achieved. However, more optimal equation for the \(P_{clust}\) probability may be selected, in case that smaller clusters are desirable in dense networks. Furthermore, great variation is present in small-scale networks (Figure 14(c)) due to the impact that has the probability in the cluster size, as the number of the elected CHs significantly affects the average cluster size. This variation is decreased as the period that NEURON is applied in the WSN increases since probabilistic techniques follow an optimal behaviour. Figure 14: Cluster Size for (a) \(P_{clust}=1\%\), (b) \(P_{clust}=4\%\) and (c) variable \(P_{clust}\). Figure 13: Theoretical and Practical number of elected CHs. The average number of route entries that are stored on each node's routing cache after the cluster formulation process is shown in Figure 15. This number is critical since sensor nodes may present memory constraints. \(P_{clust}\) is variable according to Equation 1. It is shown that the number of route entries increases slightly as the size and the density of the network increases. However, this number remains bounded, even for large networks. In sparse networks, an average routing cache has 50 entries, while in dense networks an average routing cache with 150 entries is needed. Since the maximum size of a routing entry is 45 bytes (refer to Section 3.4), 15 kB of routing cache size is adequate for all the sensor nodes. In addition to the number of route entries, a qualitative metric is the percentage of the total route entries that exists in the CH's routing caches since these entries are used from the routing functionality in NEURON. This metric is depicted in Figures 16(a)-(c) for fixed and variable probability. As the number of CHs increases in the network, the percentage of the total routing entries that exist in their routing caches also increases. This is shown in Figures 16(a,b), where the selection of larger value for the stable probability results to higher percentages of routing cache entries in the CHs. When this percentage is smaller, intra-cluster communication is facilitated since the nodes that are not CHs have  
Figure 14: _Cont._  
Figure 15: Average entries in each node’s routing cache. available routes for other nodes within the cluster and do not need to communicate with their CH for establishing a route towards them.