## 5 Simulations
### Discussion of the Results  
In this subsection, we discuss the results for the two categories of data gathering trees with respect to each of the performance metrics and explore the dependence of the aggregation delay on metrics such as the diameter, number of child nodes per intermediate node and the fraction of nodes as leaf nodes. We also discuss the impact of node density on the performance of the two data gathering trees. To begin with, we observe the diameter of the bottleneck node-weight based DG trees to be significantly smaller than the diameter of the bottleneck link-weight based DG trees. The diameter of the bottleneck link-weight based DG trees is about 100-270% larger (for networks of moderate-high node density) and 120%-370% larger (for networks of high-very high node density) compared to that of the bottleneck node-weight based DG trees. With increase in node density, the diameter of the bottleneck link-weight based DG trees increases by about 30-50%, whereas the diameter of the bottleneck node-weight based DG trees increases only by at most 20% with increase in node density. To vindicate the diameters observed for the bottleneck node _vs._ bottleneck link-weight based DG trees, the average hop count per path for both the categories of DG trees is about half the diameter values observed for the DG trees (for a given node density and transmission range). The smaller diameter and the correspondingly smaller average hop count per path incurred with the bottleneck node weight-based DG trees augurs well for real-time reporting of data by any sensor node to the root node of the DG tree (_i.e._, one-to-one communication between a sensor node and the root node). As a consequence of incurring a smaller diameter, the average number of child nodes per intermediate node for the bottleneck node-weight based DG trees is significantly larger (by factors of two to five in networks of moderate-high node density and by factors of 3 to 10 in networks of high-very high node density) than the average number of child nodes per intermediate node incurred with the bottleneck link-weight based DG trees. On the other hand, the fraction of nodes as leaf nodes is more than 0.7 (and could be as large as 0.94 in networks of very high node density) for the bottleneck node-weight based DG trees, whereas the fraction of nodes as leaf nodes is at most 0.42 for the bottleneck link-weight based DG trees. We observe the minimum aggregation delay for the bottleneck node weight-based DG trees to be lower than that of the bottleneck link weight-based DG trees when the network is operated under moderate transmission range values (of 25 m and 30 m) in networks of moderate-high node density and at 25m transmission range in networks of high-very high node density. As the diameter values are moderate (and not too low) and the average number of child nodes per intermediate node is not too high for the above said conditions, we observe the minimum aggregation delay to be relatively lower for the bottleneck node weight-based DG trees compared to that incurred with the bottleneck link weight-based DG trees (for which the impact of a larger diameter could be felt at these operating conditions). However, as the node density increases with increase in the transmission range and the number of nodes in the network, the minimum aggregation delay for the bottleneck node weight-based DG trees starts increasing significantly and becomes much larger than the minimum aggregation delay incurred with the bottleneck link weight-based DG trees. With increase in node density, the reduction in the tree diameter and a concave-up pattern of increase (_i.e._, the rate of increase increases with increase in node density) in the number of child nodes per intermediate node significantly impact the aggregation delay of the bottleneck node weight-basedDG trees.