## 4 Simulation Assessment of the ARounD Communication Scheme
### Results and Discussion  
Table 3 illustrates the results obtained from the network formation process (_Scenarios 1_ and _2_), concerning 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. One important result is that all the communication environment was fully covered, meaning that all nodes were associated with a particular cluster-head (no orphan nodes). Regarding the source-to-destination communication, Table 4 presents some relevant information about nodes 1 (source) and 2 (destination), and the source-to-destination message stream. Note that, as expected for _Scenario 1_, the ARounD path is significantly shorter than the cluster-tree path. This is basically due to the selection of the shortest inter-cluster path between the source and destination nodes. For _Scenario 2_, the difference between the cluster-tree and ARounD paths is smaller, as the PAN coordinator is located between source and destination nodes. However, even though cluster-tree and ARounD paths are equivalent in the number of hops, the main advantage of ARounD is that it prioritises leaf nodes to build the routing path, allowing to save energy of cluster-tree nodes. Figure 20 illustrates one of the physical topologies for _Scenarios 1_ and \(2\). Note that both ARounD paths are composed mostly of leaf nodes. Although the ARounD paths are usually smaller than cluster-tree paths, the main target of these simulations is to evaluate the performance of the message stream using the ARounD scheme compared to the IEEE 802.15.4/ZigBee standard cluster-tree routing, regarding end-to-end delays and successfully received data messages. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Information** & **Scenario 1** & **Scenario 2** \\ \hline Average depth of Node 1 & 3 & 4 \\ Average depth of Node 2 & 3 & 4 \\ Average number of hops of the standard paths & 8 & 8 \\ Average number of hops of the ARounD paths & 4 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information about source-to-destination message stream, considering the scenarios 1 and 2. \begin{table}
\begin{tabular}{l c} \hline \hline
**Information** & **Value** \\ \hline Average number of clusters & 59 \\ Average maximum depth & 5 \\ Average number of children per cluster & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Information about the network formation. Within this context, and according to the application perspective, Figure 21 shows the average end-to-end delay of the source-to-destination message stream for simulation _Scenario 1_ (five physical topologies, under different background and source-to-destination data rates). The ARounD approach provides a smaller end-to-end delay compared to the IEEE 802.15.4 standard tree routing (Standard approach) for all background and source-to-destination data rates. This is due not just to the shorter inter-cluster path between the source and destination nodes; the main reason is that an ARounD path is scheduled within just one beacon interval, whereas a standard path is scheduled over several beacon intervals. This is one of the major disadvantages of cluster-tree path scheduling, where either a top-down or a bottom-up approach is used for scheduling the traffic (but not both). It is well-known that bottom-up scheduling approaches favour upstream traffic (from sensors to the PAN coordinator), while top-down approaches favour downstream traffic [39]. Moreover, the contention and transmission attempts of the CSMA-CA algorithm also impact the end-to-end communication delay in more congested areas of the wide-scale cluster-tree (near the PAN coordinator) [19]. It can be also observed that, as the background data rate increases, the average end-to-end delay for the standard cluster-tree approach also increases. This is mainly due to the accumulation of  
Figure 21: End-to-end Delay for ARounD Approach vs. Standard Approach considering Scenario 1, with different data rates for the background traffic.