# Location-Based Lattice Mobility Model for Wireless Sensor Networks
## 5 Discussion of Results  
The state-of-art research on WSNs depends on energy consumption for maintaining QoS provisioning. The energy consumption due to effect of the mobility model has been significant trade-off that has not fully been explored. The LMM produces better residual energy because of the memory less model, which supports the sensor nodes due to their low battery power. Furthermore, LMM has a marginal chance of breaking the links and MAC failure.  
Based on the results, we demonstrate the performance of LMM and show in Table 4 its comparison with other mobility models: CMM, WMM and RWMM. The overall results validate that LMM has minimum average delay 0.030 and 0.008 at 25 and 50 event ranges that is much lower than CMM, WMM and RWMM models. LMM consumes less power (1.21 \(\times\) 10\({}^{-6}\) and 2.28 \(\times\) 10\({}^{-6}\) at 25 and 50 m  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Mobility Models** & **Time Complexity Derivations** \\ \hline \hline \multirow{8}{*}{**LMM**} & \(T(n)=at(\frac{n}{p})+O(n)\) \\  & Model uses finite set of inputs and time complexity remains constant ’\(n\)’ \\  & \(T(n)=t(\frac{n}{2})+O(n)\) \\  & \(T(n)=t(\frac{n}{2})+n\) \\  & \(T(n)=t(\frac{n}{2})+n\) \\  & As, we know that \(n=k\)\(\&\)\(k=log\)\(n\) \\  & Thus, time complexity is \(O(log\)\(n)\) \\ \hline \hline \multirow{8}{*}{**CMM**} & \(T(n)=at(\frac{n}{p})+O(n)\) \\  & Model uses finite set of inputs and time complexity remains constant ’\(n\)’ \\  & \(T(n)=t(\frac{n}{2})+O(n)\) \\  & \(T(n)=t(\frac{n}{2})+n+n\) \\  & \(.\) \\  & \(.\) \\  & \(.\) \\
**WMM** & \(.\) \\  & \((n)=t(\frac{n}{p})+n+n\) \\  & \(T(n)=t(1)+n+n\) \\  & \(T(n)=t+n+n\) \\  & Ignore \(t^{\prime}\) \\  & \(T(n)=n+n\) \\  & \(N=k\)\(\&\)\(k=log\)\(n\) \\  & substitute single ’\(n\)’ then we get: \(O(log\)\(n+n)\) \\ \hline \hline \multirow{8}{*}{**RWMM**} & \(T(n)=at(\frac{n}{p})+O(n)\) \\  & The model divides the task into parts with different size \\  & \(T(n)=t(\frac{n}{5})+t(\frac{2n}{3})+O(n)\) \\  & \(T(n)=t(\frac{n}{5})+t(\frac{2n}{3})+O(n)\) \\  & \(T(n)=t(\frac{n}{5})+t(\frac{2n}{3})+n+n\) \\  & \(T(n)=2t+2n\) \\  & \(T(n)=logn\) \\  & \(T(n)=O(nlog(n))\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time complexity for SDAAA and contending algorithms.  
event ranges) as compared with other contending mobility models. Once nodes change the locations using LMM at 10 m/s and variable velocities, then minimum time is required as compared to other competing mobility models. LMM produces lower drop rate that is 0.78% from 0 to 18 m/s velocities. The mobility affects the performance of the network because nodes start dropping the energy, as the result, throughput is reduced. The LMM is not highly affected that is reason, it possesses the better residual energy 3.7, 3.51 and 3.32 joules with 10%, 25% and 50% mobility rates respectively as compared to other contending mobility models. The LMM overcomes the shortcomings of competing mobility models by providing the better results in the state-of-the-art performance-metrics. As, LMM deals with the node and sink mobility synchronously. Furthermore, it reduces the control packets and pause time to obtain higher throughput performance. The LMM is suitable for those applications where events are required mobility-supported sensor nodes to accomplish the tasks specially disaster-recovery, battlefield, cool-mining monitoring, animal movement detection etc., Based on the overall result, LMM has edge over other competing mobility models. Table 5 demonstrates the improvement of LMM over CMM, WMM and RWMM mobility models.