# Spiral Mobility Based on Optimized Clustering for Optimal Data Extraction in WSNs
## 6 Experiments and Simulation Results
### Spiral Mobility vs. Random and Grid Mobility  
In this section, we compare the proposed spiral mobility pattern with the random and grid mobility pattern. In order to provide a better comparison, we compare the results with existing routing protocols ZEEP and TARS, which contain the random and the grid mobility pattern, respectively. Figure 6 shows the comparison of the average energy consumption with respect to the network lifetime for all four algorithms, ZEEP, TARS, SMOC and M-SMOC. From Figure 6, it is noticed that the mobility pattern in the proposed algorithm gradually extends the network lifetime as compared to the random and grid mobility. The obtained result clearly shows that the proposed algorithm greedily dissipates energy, and this is because spiral mobility covers the whole network area, which provides transmission between sensor nodes and the mobile sink at a shorter distance. It can be seen clearly that the SMOC and M-SMOC algorithms achieve higher performance with better network lifetime. This average energy consumption is linearly and inversely proportional to the network lifetime, with the M-SMOC algorithm achieving quite better performance due to the four mobile sinks in the network. Figure 5: Comparison of the proposed mobile sink with existing static sink over network lifetime  
Figure 6: Comparison of the network lifetime in terms of energy consumption. Figure 7 shows the graph of the energy consumption in the ZEEP, TARS, SMOC and M-SMOC approaches, respectively. The proposed techniques select more CHs in non-hot-spot areas and balances the energy dissipation throughout the network; this is because the proposed routing protocols completely used the residual energy of sensor nodes in order to select CHs and reduced the network distortion. Figure 8 shows the comparison of end-to-end packet delay between ZEEP, TARS, SMOC and M-SMOC. It is observed that the average delay per round of the proposed protocols is 8.64 and 8.24 ms respectively, because the proposed mobility pattern covers the whole region of the sensor field and collects the data from the sensor nodes at a shorter distant. It is clearly seen that the delay of SMOC is higher than M-SMOC due to the multiple sinks in the sensor field of the M-SMOC approach, where mobile sinks are closer to the sensor nodes. Figure 9 shows the residual energy of sensor nodes in the network with respect to every passing round. It is noticed that the proposed routing protocols SMOC and M-SMOC extend the network lifetime by dividing the network load among all the sensor nodes that are closer to the mobile sink, which helps them to increase network stability and results in better network lifetime. This proves that the proposed spiral mobility pattern is more energy efficient than other random and grid mobility patterns, because it allows the sensor nodes to work with full functionality for a longer period of time. This means that the proposed algorithm successfully eliminates the energy hole problem from the network and provides better performance in terms of network lifetime and network stability. Figure 8: Comparison of the end-to-end delay with respect to the number of rounds. Figure 7: Comparison of the average energy consumption with respect to the number of rounds. When a sensor node transmits its data to the sink, it is supposed that all the data packets are transmitted and received by the sink successfully without any loss. However, in reality, due to reflection, noise, attenuation and interference, some data packets of sensor nodes are dropped. We use the uniform random distribution model to calculate the packet drop ratio [36]. The probability of packet drop varies because of changes in the distance \((D_{i,b})\) of the sink from the node, which is mentioned in Equation (15). If the probability is smaller than \(P_{drop}\), then the packet will be dropped; otherwise, it will be successfully delivered. \[P_{Drop}= \begin{cases}1&\text{if }D_{i,b}>100\\ 1/80\times(D_{i,b}-20)&\text{if }20\leq D_{i,b}\leq 100\\ 0&\text{if }0\leq D_{i,b}<20\end{cases}