# Sink-Type-Dependent Data-Gathering Frameworks in Wireless Sensor Networks: A Comparative Study
## 4 Quantitative Performance Comparison via Simulation
### Delay Model  
To analyze the delay, we only consider the sink mobility delay of the proposed algorithm. The data propagation delay is less significant compared to the sink mobility delay. To compute the delay, we consider the model expressed by the following equation:  
\[\sum_{r_{n}=1}^{R_{n}}\Bigg{(}\frac{1}{V_{du}}\Bigg{(}\Delta_{(S,P_{1})}+ \Delta_{(P_{|p|},S)}+\sum_{i=1}^{|P|}\Delta_{P_{i}P_{i+1}}\Bigg{)}\Bigg{)}, \tag{10}\]  
where \(V_{du}\) is the default velocity of the mobile sink, \(\Delta_{(S,P_{1})}\) is the distance between the first position \(P_{1}\) and the starting position in the ROI (S), \(\Delta_{(P_{|p|},S)}\) is the distance between the final position of the UAV, and \(\Delta_{P_{i}P_{i+1}}\) is the distance between two consecutive positions on the mobility model of the sink. The sensor node deployment scenario for the protocols differs from one another other, and the deployment paradigm followed was based on the scenario discussed in the original paper. This was done because our intention was to compare the performance metrics between planned deployment and random deployment. Figure 7 illustrates the energy consumption scenario of the compared protocols. Based on the data shown, it can be seen that the IoJHR protocol performed better than the other two methods. This outcome was expected, as the IoJHR protocol follows a planned deployment, and the distance from the planned route of the sink is uniform. The CHs transmit data only when the sink is in close proximity. The main problem with NDCMC is that it does not optimize altitude with the sensor position. As a result, the transmission distance was comparatively higher with the IoJHR protocol. It should be noted that when the CH fails, the VHs and other sensor nodes are able to send data to the sink directly. Cluster range is an important factor in the energy consumption of the NDCMC protocol. If the cluster range is reduced, the intra-cluster distance is similarly reduced; consequently, the energy consumption due to data transmission will be lower. However, the amount of energy consumed by the HEED protocol was interesting. Based on the setup adopted in the simulation of this study, the HEED protocol exhibited a sink in the middle of the ROI. However, this may be due to a long transmission distance in the case of the CH, but not for the CMs, as the CHs are selected based on their lowest transmission power. The HEED protocol consumes more energy because it transmits the control packets for electing the CHs as distinct from the other protocols. Figure 8 shows an analysis of the number of dead nodes compared to the number of rounds. The terminology rounds state the dissemination procedure of a specific number of data packets from sensor point of view. The static sink-based solution simply disseminates the specific amount of data to the sink. However, in case of mobile sink-based solution, a round ends when the mobile sink completes a single round of data collection tour and collects the same number of data that is supposed to be disseminated in the static sink-based solution. In every round, the CH selection process is initiated. The graph clearly shows that NDCMC outperforms the other frameworks. According to the graph, the nodes in the IoJHR protocol die linearly. Among the compared protocols, nodes died significantly in the HEED protocol, and the energy of the majority node was reduced to zero before the 70 th round. This situation occurred because of the transmission distance from the sensor nodes to the CH or from the CH to the sink. The IoJHR and HEED protocols cannot directly transmit data to the sink. However, with NDCMC, the transmission distances are smaller, and after the death of a CH, no further CH is selected, and the data are sent directly to the sink node. Therefore, the extra burden of the CH has little impact on NDCMC. The protocol also introduced VHs to solve the problem of long-distance messages from the CMs to the CHs.