# Optimal Routing for Time-Driven EH-WSN under Regular Energy Sources
## 6 Numerical Results
Though these protocols were developed for battery-powered WSN, they could be perfectly extended to EH-WSN. In essence, these protocols take advantage of location information to make routing more efficient. As indicated in [47], either real or virtual geographical coordinates can be used (in the first case, sensor nodes are assumed to be equipped with a Global Positioning System or GPS). Protocols in this category use location information in multiple forms, depending on how a node holding a packet selects the next-hop node in the route towards the destination (base station). The neighbor which is closest (in terms of Euclidean distance) to the destination, the most distant neighbor that is closer to the destination (most-forward-within-radius technique), the nearest neighbor that is closer to the destination (nearest-forward-process) or the neighbor with the minimum angular distance from the imaginary line that connects the current node to the destination (compass routing), are just some examples. A common feature of these variations is that they introduce intra-layer connections that increase the average traffic workload over the network. Since this is the relevant fact in the present evaluation, a generic geographical routing protocol under the name of GRP has been simulated, leaving aside the peculiarities of each variation. Specifically, in GRP the next-hop node is randomly selected among all feasible intra-layer and forward inter-layer connections of the current node. For each network size and routing protocol, the simulation experiment consisted of 30 simulation runs, each providing two results: The average traffic load and the average duty cycle over the network. Particularly, Figure 6 shows the evolution of the average traffic load as the network size increases, for the three routing schemes considered in the analysis. As it can be noticed, MHC leads to significantly lower traffic load per node compared to the rest of routing criteria; this is because the latter generates an intra-layer, in addition to forward inter-layer connections, whereas the former only gives rise to forward inter-layer connections. Moreover, MHC also exhibits a practically flat behavior of around two forwarded packets per node on average, meaning that it is the routing metric that best distributes the overall traffic load across the network. Therefore, MHC is substantially more scalable in terms of network size than the rest of criteria. The results in terms of the duty cycle of nodes are shown in Figure 7. This figure is a direct consequence of Figure 6 and Equation (13). Leaving aside the energy-harvesting term, Equation (13) defines the duty cycle of node \(X\) as a function of (1) the duty cycle of its parent node, through the term \(E_{trigger}(X)\), and (2) the number of descendant nodes, through the term \(\sigma(X)\). Accordingly, Algorithm 1 outlines the main steps to calculate the duty cycle of every node in the network. As it can be noticed, this algorithm proceeds by layers, though the concept of layer has been slightly modified here, since it  
Figure 6: Evolution of the average traffic load with regard to the network size, for the routing metrics considered in the analysis. The surprisingly small value obtained for MHC is a consequence of the large network densities managed in the simulation. is now based on the spanning tree that results from applying any routing protocol. In other words, for any given spanning tree, the first layer is constituted by the nodes directly connected to the base station; the second layer contains the nodes directly connected to the nodes in the first layer; the third layer groups the nodes directly connected to the nodes in the second layer; etc. So, for instance, a node in the second layer could belong to the first layer according to the concept of layer adopted in Section 4. To conclude the description of Algorithm 1, its computational complexity can be evaluated.