## 5 Simulation Results
### Performance Evaluation
It occurs, owing to the fact that the sink motility significantly minimizes the hop number and the distance of the sent data packets to the BS. However, higher mobile sink speed leads to obtaining sink position information. We note that the proposed scheme demonstrates the lowest packet delivery delay among the algorithms compared, as it is able to discover the shortest trajectories. Figure 14: Comparison of the proposed scheme with existing algorithms versus trajectory length travelled by MS: (**a**) Simulation graph for scenario 1; and, (**b**) Simulation graph for scenario 2. Figure 15: Simulation of the mobile sink trajectory. * Throughput: This performance criterion means how accurately the data is transmitted and how accurate the data is delivered from the first bit to the last bit. We have assessed the performances of the algorithm for varying mobile sink speeds from 1 m/s to 8 m/s. The results clearly show that throughput increases with the mobile sink speed up to 5 m/s for all algorithms, as plotted in Figure 16b. However, once the speed of the mobile sink increases more quickly, the throughput value decreases, owing to the fact that MS trajectories change rapidly. The throughput for our proposed algorithm is better than those of other protocols due to the best MS communication with CHs. In this way, MS could gather more accurate data from CHs and deliver it to the BS. * Packet delivery rate: This metric is the ratio of the number of received packets at the mobile sink to the send packets by source nodes. The higher value means that it gives better performance. As illustrated in Figure 17a, the proposed protocol demonstrates the higher packet delivery ratio of 99% with increasing sink speed, especially between 4 and 5 m/s, and this ratio sharply decreases after the speed of the mobile sink increases. This performance validates the benefits of using appropriate mobile sink speed in the network. * Functional overhead: By this performance metric, the number of data packets that is received by the MS is computed. As shown in Figure 17b, the functional overhead of the proposed system is  
Figure 16: Comparison of the proposed scheme with existing algorithms versus packet delivery delay and throughput: (**a**) Packet delivery delay; and, (**b**) Throughput. Figure 17: Comparison of the proposed scheme with existing algorithms versus packet delivery ratio and functional overhead: (**a**) Packet delivery ratio; and, (**b**) Functional overhead. the lowest among the other presented algorithms. This originated because of the clustering of the network and routing to BS with best CH selection in the clusters. This protocol guarantees the single hop communication with BS. On the other hand, it can be observed that functional overhead increases fairly while mobile sink speed increases. * Energy efficiency (\(E_{e}\)): This metric is used for a performance measurement that observes the network life time. It is calculated via assessing the ratio of the total number of transmitted packets to the BS and the overall network's energy consumption during the simulation rounds. The formula of energy efficiency ratio \(E_{e}\) is presented in Equation (17). We have executed the presented algorithms by simulations according to the energy efficiency during the round iterations. Figure 18a demonstrates that the performance results of the IACO, PSO, nCRO-UCRA, BI-DFAMDT, starfish algorithm, and our proposal scheme are given as the ordered level from the least to most energy efficient level. Although it has partially disrupted after the 3100 th round, it has generally demonstrated stable energy efficiency. The proposed algorithm expends less energy thanks to the balanced CH selection algorithm and energy aware routing mechanism in the heterogeneous network.