# Optimal Routing for Time-Driven EH-WSN under Regular Energy Sources
## 6 Numerical Results  
In order to validate the theoretical results and demonstrate the impact of the routing strategy on the average duty cycle of nodes, several simulation experiments were conducted by varying the network size from 100 to 1000 sensor nodes (in steps of 100). The data, shown in Table 1, which correspond to TinyOS sensor nodes, were used. Correspondingly, the transmission range (\(r\)) was set to 250 m. The sensor field consisted of a square region of 1 km\({}^{2}\), with the left lower corner and the base station respectively located at coordinates \((0,\ 0)\) and \((1000,\ 500)\) (in meters). As for the regular energy source, solar radiation was considered. As stated in Section 3, the solar energy-harvesting model proposed in [44] was used, with the meteorological data taken from the NASA POWER Project database for the city of Madrid and the month of September: \(D_{month}=4.87\) kWh/m\({}^{2}\)/day and \(STDHOURS=12.5\) hours [40]. Three routing protocols were considered in the evaluation: A routing protocol based on the MHC criterion, the well-known Collection Tree Protocol (CTP) and a generic location-based or Geographical Routing Protocol (GRP). CTP has been adopted in this evaluation because of its extended use in both, battery-powered and energy-harvesting wireless sensor networks. An example is the case of TinyOS-based sensor networks, where CTP runs on top of a duty-cycled LPL-based MAC protocol. To be more precise, La-CTP should be considered, but since a duty-cycled LPL protocol was supposed to be running at the MAC layer, loops could not happen and, consequently, it could be expected that La-CTP provided the same results as CTP. In CTP, the expected number of transmissions (ETX) is adopted as the routing metric, and then Shortest Path Routing (SPR) is applied to determine the least cost path from every node to the base station [46]. Note that the number of transmission tries is a magnitude that depends on both the quality of the link that connects the two nodes and the asynchrony between their duty periods (recall Figure 1). Since the purpose of this simulation is to compare the intrinsic effects of MHC, CTP and GRP on the average traffic workload, it has been assumed that all feasible links are in good quality conditions. Accordingly, the only factor determining the number of transmission tries is the asynchrony between duty periods. As stated in [14], the number of transmission tries between a transmitter and a receiver (parent) node is a fixed value extracted from a quasi-uniform distribution between 1 and a maximum value that depends on the duty cycle of the receiver (parent) node. Note that this introduces a \"snake biting its tail\" problem when dealing with CTP routing in the context of EH-WSN, in which the duty cycle varies from node to node: The number of tries required by a given node depends on the duty cycle of its parent node, which in turn depends on the routing topology created by CTP based on the number of tries. In fact, this is a typical behavior observed in CTP: It enters an initial transient period during which a connected network is progressively built, and after that the routing topology becomes practically fixed, consistently with the regular traffic conditions imposed by time-driven applications. In such a steady-state regime, the traffic load and duty cycle of each node becomes stable, at least during long periods of time. Based on the data shown in Table 1, the simulation experiments performed in [14] and the large network densities managed in the current simulation (note that a large network density means a large number of nodes distributed over a relatively small number of layers), a uniform distribution between 1 and 10 becomes sufficiently representative to characterize the number of tries throughout all feasible links in the network. Finally, another important category of routing protocols for sensor networks encompasses those based on location information [47; 48].