# Deep Validation of Spatial Temporal Features of Synthetic Mobility Models
## 3 Validation of Mobility Models
### Speed Decay Problem  
This property represents the degree of respecting the attributed speed that is allowed before generating the mobility model. Speed decay problem represents one of the most widely affronted issues. A mobility model suffers from speed decay when the average nodal speed decays to a steady-state level that falls below the initial average nodal speed. Such speed decay can have a dramatic influence on the measured performance and overhead. Consequently, one cannot present time-averaged metrics during this period of decay, as the underlying process is not stationary. This metric was introduced by [PERSON] et al. (2018) for the RWPMM. Randomness contradicts the famous RWPMM assumption that the same average speed is maintained throughout the simulation, which is adequately tested in Figure 2a. We observe that the velocity suffers strong fluctuations when the experiment begins. It then adjusts to approach the attributed speed, showing scattered fluctuations before the simulation ends. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of nodes & 50 \\ \hline Speed & 5 m/s \\ \hline Pause time (s) & 0 \\ \hline \multirow{3}{*}{Mobility models} & RWPMM, MGMM (Entity models) \\  & RPGMM, NCMM (Correlated MMs) \\  & SLAW, SMOOTH (Human MMs) \\ \hline \multirow{3}{*}{Mobility metrics} & Speed decay problem \\  & Spatial node distribution \\  & Density wave phenomenon \\  & Average node neighbor percentage \\ \hline Area & 1030 m \(\times\) 1030 m \\ \hline Simulation time & 1000 s \\ \hline Iterations & 20 times \\ \hline Implementation tool & MATLAB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Validation parameters. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
\begin{tabular}{c} PD on set \\ destinations \\ \end{tabular} & NA & TPL & TPL & P \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mobility models. C: Constant, HB: History Based, UD: Uniformly Distributed, PD: Probabilistically Distributed, P: Periodic, PL: Truncated Power Law, NA: Not Applicable. Meanwhile, Figure 2 shows the average speed fluctuation of other synthetic mobility models during the simulation. We observe the following:  
* From Figure 2e,f, we conclude that human models suffer heavily from the speed decay problem and show the worst average speed. Even in the case where a specific speed is fixed, it will not be deployed by these models because it is lower than 5 m/s during the whole simulation period. This problem mainly relates to the non-attributed speed, acceleration, and deceleration in these models, as strictly reported by the settings of these models in Table 3.
* Figure 2c shows that the RPGMM presents a speed that fluctuates with time, starting from the specified speed and then oscillating between 0 and 5 m/s. This is due to the correlated strategy of mobile nodes. The nodes form several groups and each group has a leader that takes all mobility decisions. Sometimes, a node changes group and follows another group leader with a different speed. Table 3 also highlights that speed is based on reference points, while this validation metric precisely indicates that speed is uniformly distributed according to the reference points. * In Figure 2b, the MGMM represents a nearly stable speed during the entire simulation. MGMM fluctuates in an acceptable margin between 5 and 5.25 m/s. This allows it to be steadier due to the adopted movement strategy, which is based on a uniform division of the simulation field with a constant or uniform speed, as depicted in Table 3.
* According to Figure 2d, we remark that the NCMM presents the best average speed out of all the validated models that keep the same speed during the simulation. This result mainly does not agree with the principal methodology of using the non-attributed speed, acceleration, and deceleration as shown in Table 3. Therefore, a relevant outcome of this research and this validation is that the NCMM showed a constant speed during the experiment since all MNs belong to a single leader.