# Energy Efficient Policies for Data Transmission in Disruption Tolerant Heterogeneous IoT Networks
## 5 Results
This results in increments of expected energy cost up to 30% for cells that lie in the vicinity of LP-PAN base stations. Similarly, Figure 3c presents the MPE between the \(J_{\text{MP}}\), the horizon discounted cost for the Myopic Policy, and \(J_{\text{OPI}}\). The myopic policy performs poorly in general, with increments in energy cost as high as 80%. This is mainly due to its short term energy conserving policy that focuses entirely on saving energy at the current stage and completely disregards the potential transitions to cells with only LP-WAN connectivity or no connectivity at all at subsequent stages. Actually, transmissions occur only when the policy is forced to do them, i.e., when the backlog has more than six packets, and this will often result in packet drops at an excessive cost. Figure 3d presents the MPE between the \(J_{\text{RP1}}\), the horizon discounted cost for the policy derived by the Rollout Algorithm with one policy improvement step, and \(J_{\text{OPI}}\). As described previously in this section the Rollout Algorithm with one policy improvement step is only slightly different from the OPI policy. This is reflected in the low values for \(\text{MPE}_{\text{RPI, OPI}}\), presented in Figure 3d, compared to the previous two policies. For \(\text{MPE}_{\text{RP1, OPI}}\), increments in energy cost are mainly due to transmitting a larger number of packets, compared to the approximately optimal policy, in cells such as (1,1), (1,20), (20,1) and (20,20). This increment in the number of transmitted packets does not actually  
increase energy consumption, since in all these cells an LP-PAN is available and packet transmission are conducted with the minimum energy expense. However, we observe an increment in energy cost because the Rollout Algorithm with one policy improvement step disregards the effect of the discounting factor \(\gamma\) on energy cost. The OPI policy will favor delayed packet transmissions, whenever this does not lead with high probability to energy inefficient packet transmissions or packet drops in future stages, because future energy costs are _discounted_. To assess the energy efficiency of all the aforementioned policies in a variety of base station topologies we conducted two thousand numerical experiments for a surveillance area of \(20\times 20\) cells that includes five LP-WAN base stations and five LP-PAN base stations. In each numerical experiment the base stations were placed randomly within the surveillance area. Other than the number and the placement of the base stations the configuration is identical to that of the illustrative example presented above. Figure 4 presents MPE in energy consumption for the four policies, calculated as follows,  
\[\text{MPE}_{P}=\frac{1}{|S|\cdot L}\left(\sum_{l\in L,s\in S}\frac{J_{\text{P} }^{l}(s)-J_{\text{OPI}}^{l}(s)}{J_{\text{OPI}}^{l}(s)}\right)\cdot 100\;( \%), \tag{10}\]  
where \(L\) is the number of numerical experiments, \(|S|\) is the cardinality of the state space and \(J_{\text{P}}\) is one of \(J_{\text{BEP}}\), \(J_{\text{MP}}\), \(J_{\text{RP1}}\) and \(J_{\text{RP2}}\). In Equation (10) the mean value for the percentage error is calculated over all states of the system and, subsequently, over all experiments. Figure 4 depicts that the Myopic and Empty-Backlog policies result in a significant increment in energy consumption compared to the OPI policy. On the other hand, the Rollout algorithm with one policy improvement step significantly reduces the energy cost compared the myopic policy, its base heuristic policy, and achieves  
Figure 3: Mean Percentage Error (MPE) in energy consumption for each suboptimal policy compared to the horizon discounted cost for the Optimistic Policy Iteration (OPI) policy \(J_{\text{OPI}}\). an approximately optimal energy cost with just two policy improvement steps. The results of Figure 4 exhibit the significance of the network availability map and localization information in devising energy efficient packet transmission policies for mobile nodes in DTNs.