# Deep Validation of Spatial Temporal Features of Synthetic Mobility Models
## 4 The Proposed Metric: The Mobile Neighbors Range
We deduce that mobile neighbors range remedies the defects of all previously proposed metrics by curing their weaknesses via verifying all nodes of all mobility models during the whole simulation. ## 5 Mobility Metrics Global Intention

Based on these mobility metrics, we can predict the performance of the mobility models without the need to implement a real wireless mobile network as most of the tests do to carry out performance analyses. These validations aim to summarize several parameters into 18,126 different scenarios with an average of 486 validated files corresponding to the six mobility models. The validation details are displayed in Table 6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Mobility Metrics**} & \multicolumn{5}{c}{**Mobility Models**} & \multicolumn{5}{c}{**Total Validations**} \\ \hline  & RWPMM & MGMM & RPGMM & NCMM & SLAW & SMOOTH & \\ \hline \multirow{2}{*}{Speed decay problem} & 50 nodes & 50 nodes & 50 nodes & 50 nodes & 50 nodes & 50 nodes & \multirow{2}{*}{6000} \\  & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times \\ \hline Density wave phenomenon & 20 times & 20 times & 20 times & 20 times & 20 times & 20 times & 120 \\ \hline \multirow{2}{*}{Average neighbor percentage} & 50 nodes & 50 nodes & 50 nodes & 50 nodes & 50 nodes & 50 nodes & \multirow{2}{*}{6000} \\  & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times \\ \hline \multirow{2}{*}{Spatial node distribution} & 1 & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{2}{*}{* Mobile neighbors range} & 50 nodes & 50 nodes & 50 nodes & 50 nodes & 50 nodes & \multirow{2}{*}{6000} \\  & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times & * 20 times \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Validation details; * Proposed metric. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mobility Metrics**} & \multicolumn{3}{c}{**Validation Features**} \\ \cline{2-4}  & **Parameters Inspected** & **Precision Level** & **Limitations** \\ \hline \multirow{3}{*}{Speed decay problem} & \(+\)All nodes & Low & Nodes’ \\  & \(+\)Whole Time & \(\text{Low}\) (speed only) & neighboring \\  & \(+\)Average models & & Other nodes \\ \hline \multirow{3}{*}{Density wave phenomenon} & \(-\)One node & \(+\)Whole time & Medium & + \\  & \(+\)Average models & & Speed \\ \hline \multirow{3}{*}{Average neighbor number} & \(-\)One node & \(\text{Under}\) & Other nodes \\  & \(+\)Whole time & \(\text{Medium}\) & + \\  & \(+\)Average models & & Speed \\ \hline \multirow{3}{*}{Spatial node distribution} & \(+\)All nodes & \multirow{3}{*}{Low} & Other models \\  & \(-\)Specific time & & +Time \\ \cline{1-1}  & \(-\)Specific model & & +Speed \\ \hline \multirow{3}{*}{\({}^{\star}\) Mobile neighbors range} & \(+\)All node & \multirow{3}{*}{High} & \multirow{3}{*}{Speed} \\  & \(+\)Whole time & & \\ \cline{1-1}  & \(+\)Average models & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mobility metrics comparison, + favor, \(-\) flaw, * Proposed metric. An exhaustive analysis with the details in this paper leads to a good understanding of the accurate behaviors of mobility models by displaying the ability of every pattern to deal with certain topology changes and to ensure network performances. We conclude that they can be classified according to their results as summarized in Table 4. The best outcomes are shown by 1 and 2 cells, acceptable shifts are shown by 3 and 4 cells, and the worst results are shown by 5 and 6 cells. According to the previously discussed validated metrics, we deduce the following:

* The density wave phenomenon is only obtained for a unique node during the simulation. It inspects one node to only reflect the fluctuation of the number of neighbors of the validated node. Verifying this property for all mobile nodes used in the simulation would be a worthless task. * The average number of mobile nodes denotes the average number of neighbors of a specific node during the simulation.