# Energy Efficient Policies for Data Transmission in Disruption Tolerant Heterogeneous IoT Networks
## 5 Results
Their main difference is a small reduction in the number of packets to be transmitted when in cells that lead with high probability to a neighboring cell that offers LP-PAN network connectivity, e.g., cells (1,1), (1,20) and (20,1), and cells that lead with low probability to an area with no network connectivity, e.g., cell (5,1). A major result of this work is that the policy derived by the Rollout algorithm with two policy improvement steps is identical to the policy derived with the  
Figure 2: Packet transmission policies for the scenario of Figure 1 for the set of states with \(m=6\), i.e., with six packets stored in the backlog. The policy produced by the Rollout algorithm with two policy improvement steps is identical to the policy produced by the optimistic policy iteration (OPI) algorithm. OPI algorithm. The importance of this result is that we may attain an approximately optimal policy by utilizing a computationally efficient suboptimal algorithm. Finally, although we do not present the relevant figures here due to lack of space, we note that when the number of packets in the backlog is less than six all four policies will retain their form, as presented in Figure 2, although the number of transmitted or dropped packets in each cell will decrease. Obviously, when the backlog is empty no packet will be transmitted at any cell for all policies. On the other hand, when the mobile node has more than six packets in its backlog then it is obliged by the queue management policy to transmit or drop packets in each cell so that there is room for \(W_{m}^{\max}\) packets in the backlog. Thus, for the case of seven, eight and nine packets in the backlog all four policies will retain their previous form, as presented in Figure 2, although the number of transmitted or dropped packets in each cell will increase respectively by one, two and three. Figure 3 presents results related to the expected energy cost over an horizon for all policies presented in Figure 2. More specifically, Figure 3a presents \(J_{\text{OPI}}\) the expected discounted cost over an horizon for each state of the mobile node when the approximately optimal OPI policy is used. The figure includes nine surface plots, one for each state of the backlog \(m\), that cover the whole state space \(S\). The surface plot that lies on top of all others corresponds to the case where \(m=9\), i.e., the expected energy cost is maximized when the backlog is full. As the number of packets in the backlog decreases we get lower values for the expected energy cost in all cells and the minimum is attained when the backlog is empty. Furthermore, Figure 3a indicates that the expected energy cost is small for cells that lie in the vicinity or within the service area of a LP-PAN, increases for cells in the vicinity or within the service area of a LP-WAN and becomes maximum for cells that lie outside the communication range of any base station. Figure 3b presents the mean percentage error (MPE) [35] between \(J_{\text{EBP}}\), the horizon discounted cost when the Empty-Backlog Policy is used, and \(J_{\text{OPI}}\) calculated as  
\[\text{MPE}(x,y)=\frac{1}{M}\sum_{m=0}^{M}\frac{J_{\text{EBP}}(x,y,m)-J_{\text{ OPI}}(x,y,m)}{J_{\text{OPI}}(x,y,m)}\cdot 100\ (\%). \tag{9}\]  
Equation (9) is well defined because \(J_{\text{OPI}}\) is a positive real number. Furthermore, the quantity in the MPE sum represents the percentage _increment_ in cost due to using a suboptimal policy since \(J_{\text{EBP}}\geq J_{\text{OPI}}\) for all states. Finally, in Equation (9) we average over all possible backlog values in order to avoid presenting a different surface plot for each state of the backlog as we did in Figure 3a. Now, Figure 3b indicates that the Empty-Backlog Policy does not utilize the heterogeneity of the available networks within the surveillance area. Instead, the mobile node blindly transmits all packets in the backlog whenever it enters a cell with LP-WAN coverage disregarding the fact that neighboring cells may offer a more energy efficient network service such as LP-PAN.