## 8 Simulation Assessment
### Results and Discussion  
Firstly, we present some information about the cluster-tree network formation for each of the defined scenarios. Table 5 shows the average number of generated clusters during the cluster-tree formation, the average maximum depth of the cluster-tree network, and the average number of children per cluster. The main target of the proposed proportional SDA schemes is to allocate adequate communication resources (superframe durations and buffer sizes) for the cluster-heads, in order to avoid network congestion and message discards due to buffer overflows. Therefore, the buffer occupancy is an important performance metric to evaluate the proposed allocation schemes. Table 6 shows the considered buffer sizes for the cluster-heads at each depth of the cluster-tree (average values for the different cluster-heads located at each level of the different tree branches). Load-SDA and Nodes-SDA schemes define buffer sizes for cluster-heads that are proportional to the number of descendant nodes, according to the defined buffer constraint (Equation (12)). As STD-SDA and SOA-SDA allocation schemes do not provide any mechanism to define buffer sizes, we have set the length of internal buffers to a value equal to the total number of sensing nodes (200). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Information** & **Unconditioned Scenario** & **Conditioned Scenario** \\ \hline Average number of clusters & 45 & 47 \\ Average maximum depth & 9 & 8 \\ Average number of children per cluster & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Information about the network formation. Table 7 illustrates the average SO parameter values for cluster-heads, considering their depths in the cluster-tree network. Note that, as both SOA-SDA, Load-SDA and Nodes-SDA schemes allocate superframe durations based on the imposed traffic, allocations are proportional to depth: clusters closer to the PAN coordinator have higher superframe durations. The difference between these three schemes is that in Load-SDA scheme, superframe durations are based on the traffic load of the cluster itself and of its descendant nodes, while Nodes-SDA scheme only considers the number of descendant nodes. Instead, SOA-SDA allocation scheme imposes that a parent cluster-head must have duty-cycle greater or equal to the sum of duty-cycles of its child cluster-heads, leading to slightly different values for the allocations. Finally, STD-SDA scheme allocates the same superframe duration for all cluster-heads. Figure 14 illustrates the average rate of discarded messages due to buffer overflows for the overall network, when applying the four allocation schemes to the defined scenarios. It can be observed (Figure 14) that both Load-SDA and Nodes-SDA schemes behave adequately for both communication scenarios, considering the defined set of message streams. All CHs were able to forward their messages and no messages were discarded due to buffer overflows. This behaviour highlights one of the major advantages of the Load-SDA and Nodes-SDA allocation schemes, where both superframe durations and buffer sizes are dimensioned according to the network load and number of nodes of each of the branches of the cluster-tree network, respectively. On the other hand, the STD-SDA scheme discarded 30%-35% of the messages due to the allocation of inappropriate superframe durations and also due to the inability of the cluster-heads to temporarily store the accumulated messages in their internal buffers, despite the larger number of allocated buffer resources.