## 9 NS-2 Simulations
### Analysis  
Figures 10-13 presents the results obtained. From Figure 12 it can be observed that the MST requires almost 50 percent more energy than LocalHeur for a single traffic source. As consistent with bounds on stretch and diameter, MST has a longer path length and more number of hops and thus greater is the cost of per packet transmission. LocalHeur outperforms MST for 20 sources too but becomes comparable to MST for 30 sources, where the expected starting time between sources is less than 2.5 seconds, given that CBR traffic is turned on randomly in the first 50 seconds of the simulation. These results are for a packet size of 64 bytes at a rate of 4 packets per second. Thus it can be observed that under the assumption of selfish nodes, for events that has to be sensed below this expected time, Localheur can give a considerable energy gain compared to MST. For more frequent sensing of data, the LocalHeur can still provide a good end-to-end delay performance and a better packet delivery ratio with its energy performance tending towards the MST in the worst case. Also having 30 sources transmitting at less than 2.5 s interval between them will cause a significant MAC level contention especially when there are many sources lying within the interference range of the currently transmitting source. Even though this level of contention is bounded by a maximum degree of 6 for both MST and the heuristics as we noted of  
\begin{table}
\begin{tabular}{|l|l|l|} \hline \multicolumn{3}{|l|}{Worst Case no. of nodes deviating from best-response} \\ \hline No of nodes & power = 1 & power = 2 \\ \hline
100 & 10 & 8 \\ \hline
500 & 62 & 59 \\ \hline
1,000 & 98 & 103 \\ \hline \end{tabular}
\end{table}
Table 1: Count of deviating nodes.  
any Euclidean Nash tree, 802.11 performance is considerably influenced under such levels of contention especially when there are multiple hops to destination [29]. This makes a considerable impact both on energy performance as well as the packet delivery ratio considering the fact that for every failed packet there were 7 attempts to retransmit a packet. Thus the effects of MAC are not fully eliminated at high contention, even though we eliminated the effects of idle listening.  
The forwarding decisions of both LocalHeur and MST are very simple with each node just deciding on the next-hop neighbor thus eliminating the cost of having complex routing tables at the intermediate nodes and also very low route computation costs. LocalHeur will have an initial overhead associated with the discovery of the local neighbors which in turn is very much insignificant compared to the costs of cycle check and global neighbor discovery phase of MST. Thus it can be stated that under the constraints of selfish behavior, LocalHeur shows a good energy performance and a better packet delivery ratio compared with the MST scheme under moderate levels of contention, thus providing a global optimal performance with a minimum deviation from equilibrium condition.  
Figure 11: Plot of PacketDelivery ratio for MST and LocalHeur for 100 nodes and 1,10,20,30 sources.  
Figure 10: Plot of average hopcount to destination for MST and LocalHeur for 50,100,250 nodes.