## 8 Simulation Assessment
### Results and Discussion
The SOA-SDA scheme presents a much smaller number of discarded messages due to buffer overflows  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Unconditioned Scenario**} & \multicolumn{3}{c}{**Conditioned Scenario**} \\ \hline
**Depths** & **Load/Nodes-SDA** & **SOA** & **STA** & **SDA** & **Load/Nodes-SDA** & **SOA-SDA** & **STA-SDA** \\ \hline Depth 1 & 98 & 200 & 200 & 98 & 200 & 200 \\ Depth 2 & 47 & 200 & 200 & 39 & 200 & 200 \\ Depth 3 & 24 & 200 & 200 & 19 & 200 & 200 \\ Depth 4 & 20 & 200 & 200 & 15 & 200 & 200 \\ Depth 5 & 17 & 200 & 200 & 12 & 200 & 200 \\ Depth 6 & 12 &(4%-5% of messages), as it considers the adjustment of the superframe durations according to the depth of each cluster-head in the cluster-tree network. These results clearly highlight that an equal allocation of the superframe durations is not adequate for cluster-tree networks, as it does not consider the tree topology effects of the network. Considering that both STD-SDA allocation schemes have discarded messages, it is important to check where those messages were discarded. Figure 15 illustrates the average number of discarded messages for the STD-SDA allocation scheme, as function of the CHs' depth. As expected, the number of discarded messages is higher for cluster-heads located at depth 1, followed by cluster-heads of depth 2, and so on. In fact, as convergecast traffic is forwarded through the cluster-tree towards the PAN coordinator, the trend is that cluster-heads near the PAN coordinator will be more congested, where the network performance will be substantially affected. This behaviour is observed for both unconditioned and conditioned scenarios. Figure 16 illustrates the average number of discarded messages as function of the CHs' depth for the SOA-SDA allocation scheme. It can be observed that, this scheme adequately allocated superframe duration values for the clusters located closer to PAN coordinator, but not for the deepest clusters. This problem could be solved by increasing superframe duration values for leaf cluster-heads. However, as the SOA-SDA allocation scheme defines that the duty-cycle of a parent cluster-head must  
Figure 14: Average discard message rate due to buffer overflows: (**a**) Unconditioned Scenario; (**b**) Conditioned Scenario. Figure 15: Average message discard rate (per depth) due to buffer overflows for the STD-SDA scheme: (**a**) Unconditioned Scenario; (**b**) Conditioned Scenario. be greater or equal to the sum of duty-cycles of child cluster-heads, increasing the allocation values for the leaf cluster-heads could lead to the non-fulfilment of the overall protocol constraint (Equation (10)). Finally, Figure 17 illustrates the total message loss rate (considering both message collisions and message discards due to buffer overflows) for each of the defined allocation schemes. As it can be observed, the number of discarded messages due to buffer overflows strongly influences the number of lost messages, decreasing the number of successfully delivered messages. Comparing results of Figures 14 and 17, it is clear that the message loss rate due to message collisions is around 22%-28% for the all allocation schemes. The main reason for this high number of message losses is due to the (default) CSMA/CA parameters used for the simulation assessment. As previously shown in [9; 36], the default parameter values used for _macMinBE_, _macMaxBE_ and _CW_ (Contention Window) can easily lead to a high number of message collisions, for a number of sensor devices as low as 6 devices per cluster-head. According to this simulation assessment, it becomes clear the importance of defining adequate active communication periods and buffer sizes for the cluster-heads. An adequate allocation of superframe durations for the different clusters can significantly improve the network behaviour. We have also assessed the average end-to-end delay for convergecast traffic, in order to evaluate the influence of the buffer sizes and superframe allocation schemes.