# Deep Validation of Spatial Temporal Features of Synthetic Mobility Models
## 3 Validation of Mobility Models
### Spatial Node Distribution  
This property describes how mobile nodes are spatially localized within the simulation field. It is mainly related to the fact that the initial positioning of the nodes is typically taken from what is established based on a uniform distribution; the mobility model may change this distribution during the simulation. This behavior usually occurs if the simulation area has borders. If we are not aware of how the used mobility model changes the node distribution, simulation results may be misinterpreted. [PERSON] et al. [6] validated this metric for the RWPMM. They recognized a non-uniform spatial distribution of this mobility model. When it reaches the steady state, mobile nodes gather at the center and move away from the boundaries, as observed in Figure 5a. In our validation, we choose to verify the final state (at t = 1000 s) of this property. From Figure 5, we can interpret the results obtained for the last two metrics, and it is worth remarking the following:  
* Figure 5c,f provide insufficient results due to nodes gathering near the leaders in the RPGMM or in populated locations in SMOOTH. If the groups are sparsely located, the mobility model will show the worst performance if any intermediate neighbor is reached during transmission. This results in a more fragile network that is highly partitioned with many free simulation spaces.
* Based on Figure 5b,e, we remark that SLAW and the MGMM are slightly more distributed in the simulation field compared to the RWPMM, SMOOTH, and the RPGMM. Due to the area division in the MGMM, the mobile nodes are located at the boundaries with few empty spaces compared to the RWPMM in Figure 5a. This later represents the worst spatial distribution, being mainly based on totally random movement decisions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Mobility Models**} \\ \hline \multirow{2}{*}{**Mobility Metrics**} & \multicolumn{2}{c}{**Entity**} & \multicolumn{2}{c}{**Correlated**} & \multicolumn{2}{c}{**Human**} \\ \cline{2-7}  & **RWPMM** & **MGMM** & **RPGMM** & **NCMM** & ** SLAW** & **SMOOTH** \\ \hline Speed decay problem & 3 & 2 & 4 & 1 & 5 & 6 \\ \hline Density wave phenomenon & 5 & 6 & 3 & 2 & 4 & 1 \\ \hline Average neighbor percentage & 6 & 5 & 4 & 1 & 3 & 2 \\ \hline Spatial node distribution & 6 & 5 & 3 & 1 & 4 & 2 \\ \hline \multicolumn{7}{l}{* Mobile neighbors range} & 6 & 5 & 3 & 1 & 4 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mobility metrics strengths and weaknesses; * Proposed metric.  
Figure 5d shows the best results, with all mobile nodes being located within one area which is governed by a nomadic leader while moving. This proves that all the nodes belong to just one reference point. The outcome of Figure 4d is exemplary with nearly 98% of nodes gathering together due to the concentrated spatial distribution of all nomadic nodes in one specific area.  
We conclude that, if a mobility model shows a non-uniform spatial node distribution during the simulation, then nodes will also suffer from an unstable density wave phenomenon and a disturbed average neighbor percentage, as depicted in Figures 3 and 4, respectively. These three mobility flaws are mainly related to each other.  
Given the limitations of these metrics, a novel synthetic mobility metric is proposed to overcome such problems. This metric, which has several validated parameters with few limitations, is called the \"_mobile neighbors range_\" and is described in the next section.  
Figure 5: Spatial node distribution at \(t=1000\) s. (**a**) The RWPMM; (**b**) the MGMM; (**c**) the RPGMM; (**d**) the NCMM; (**e**) SLAW; (**f**) SMOOTH.