## 4 System Model
### Gedpar
Here, 0 indicates the minimum PAR and 1 represents maximum PAR. In our scenario, during PAR calculation it is noticed that PAR of GEDAR, LMPC, E2 EVHR and GEDPAR is about 0.6, 0.8, 0.93 and 0.95, respectively. These statistics clearly show that GEDPAR and E2 EVHR perform best among the comparing ones. Figure 11: Throughput. Figure 10: Depth adjustment. Delay is calculated in terms of time duration which is required by a packet to reach from source to destination node. Basically, calculation of delay starts from the time when the first packet is transmitted from the source node. The calculation of delay continues until the last data packet is received at a sink. In addition, delay contains total duration from the generation of the first packet at a source node to the reception of the last packet at the sink node. E2 EVHR takes more time at start due to the necessary calculations for source to sink path finding procedure. When it finds the complete path by ensuring that there is no void node in the route then it transfers the packets directly from selecting paths. On the other hand, GEDPAR involves more calculations and the reason is that it takes more time to the comparing schemes. Delay of the comparing schemes is presented in Figure 13. Moreover, Figure 13 also shows the trade-off and this trade-off authenticates the simulation results. This means that for getting minimum energy consumption and throughput, we have to compromise on computational time. In Figure 14, the comparison among the different routing protocols with respect to energy consumption is presented. From the Figure 14, GEDPAR consumes less energy as compared to the GEDAR and LMPC. GEDAR consumes more energy then counterparts because it focuses on depth adjustment during the void hole avoidance. Depth adjustment takes 1500 mJ energy for one meter while transmission range enhancement takes less energy than depth adjustment (adapted from [22]). Figure 14 is also representing the average energy consumption of all comparing schemes. Simulations are performed multiple times to check the average results. LMPC uses multiple transmissions for one packet which resulted in energy dissipation. The proposed routing protocol (GEDPAR) consumes less energy because it covers the void holes by increasing the transmission range. GEDPAR only changes the depth when no forwarded node is found even by increasing transmission range. Figure 12: Packets received at sink. Figure 13: Delay. ## 6 Feasible Regions

Feasible region is the area where all possible solutions of a particular problem exists. In this section, mathematical formulation using linear programming is used to find the feasibility of the proposed protocol. To achieve the optimal solutions, we define some constraints (listed below). By defining these constraints, the coordinates of feasible regions are calculated. In this work, we have calculated the coordinates for three feasible regions according to the proposed schemes (GEDPAR and E2 EVHR). In Figures 15-17, we annotate the feasible regions as P1, P2, P3 and P4. Figure 15 presents the feasible region of energy consumption versus throughput. Figure 16 illustrates the feasible region (energy consumption versus PAR) for the GEDPAR routing protocol. While in Figure 15, the feasible region of energy consumption versus delay is presented. In Figures 18-20, we annotate the feasible regions for E2 EVHR as P1, P2, P3 and P4. Figure 18 presents the feasible region of energy consumption versus throughput, whereas the Figure 19 illustrates the feasible region of energy consumption versus PAR, for the E2 EVHR routing protocol. In Figure 18, the feasible region of energy consumption versus delay is presented.