## 5 Simulation Results
### Simulations of algorithm EBH  
In Figure 10, we compare the average remaining energy per node with different lifetime definitions of networks. We compare EBH with DIRECT and HBH. The node number is 20 and the internode distance is 100 m. The energy grades \(m=45\) computed by Equation (15). We have modified the DIRECT algorithm where each node has the ability transmitting data directly to the sink in order to compute different lifetime of the network. The figure shows that DIRECT has the highest energy wasted, all above 60% remaining energy with three different lifetime definitions. HBH wastes less energy than DIRECT but higher than EBH. EBH has less than 2% energy wasted for all three lifetime definitions. Figure 11 shows the network's lifetime for different schemes. We vary the node number from 10 to 25, and the internode distance is 100m. Observed from the Figure 11, the networks's lifetime of three algorithms decreases as the number of nodes increases. The DIRECT's lifetime is determined by the farthest node from the sink. So, as the number of nodes increases, the farthest node has longer distance which decreases the network's lifetime. As to HBH, the node nearest to the sink determines the lifetime of network. That means, as the node number increases in the network, the node nearest to the sink will relay more packets which lead to decrease of the network's lifetime. Because of EBH is a hybrid transmission scheme of DIRECT and HBH, the network's lifetime decreases as the number of nodes increases in the network. We also observe that with different lifetime definitions, the lifetime of EBH is almost the same. The reason is that as each node dissipates energy evenly in EBH, they are out of function almost at same time. The figure also shows that EBH gives the best performance with different number of nodes, because it combines the advantages of both DIRECT and HBH. Figure 12 compares the network lifetime with different internode distance. We assign each node with initial energy of 6 J. We observe from the figure that as the internode distance increases, the lifetime difference between EBH and HBH decreases. The reason is that when we fix the node number, larger internode distance means larger direct transmission energy consumption for EBH, therefore the advantage of EBH decreases. Fixing the internode distance, as the total number of nodes increases, the lifetime difference between EBH and HBH decreases. The reason is the same, for larger number of nodes means larger direct transmission distance for EBH. Figure 10: The average remaining energy per-node. Figure 13 shows the relationship between energy grades \(m\) and network lifetime. The total number of nodes is 20 and \(r\) is 100 m. From Figure 13, we observe that the network lifetime increases rapidly when the energy grades initially increase; then there is a section of area where the network lifetime is more or less constant. Finally in the last sectors, the network lifetime decreases slightly as the grades increase. This can be explained that as the energy grades initially increasing, the nodes dissipate more evenly, thus the network lifetime's increases rapidly. However, as the grades increase too much, the node's mode is changing more frequently which incurs too many control messages. Meanwhile the nodes are in DIRECT transmission mode more frequently, so the network lifetime decreases. Figure 13 also shows that Equation (15) is a reasonably good approximation of energy grades, because the computed energy grades (\(m\) = 45) based on Equation (15) fall in the highest network lifetime areas where the network lifetime is almost constantly high. Figure 11: Network Lifetime for different routing schemes. Figure 12: Network Lifetime with different internode distance. Figure 14 illustrates how well EBH achieves energy balance among individual sensors. We set 25 nodes in the linear network and \(r\) is 100 m. From Figure 14, it is shown that all 25 nodes dissipate energy evenly which is the reason for longer network lifetime.