# Deep Validation of Spatial Temporal Features of Synthetic Mobility Models
## 4 The Proposed Metric: The Mobile Neighbors Range  
In this section, in order to overcome the limitations shown by other metrics, we suggest a novel metric that offers multiple advantages to represent an accurate behavior of mobility model steadiness for all simulated nodes during the test time. Whatever the expected node and the targeted instant, we can easily depict the range of neighbors for each mobility model. The validation of this property is effective at all simulation instants. At the same time, this metric highlights the strengths and weaknesses of each mobility issue, which has been verified previously. * **Principle:** We assess a set of synthetic mobility models of each pattern in order to define the range of the number of neighbors for all mobile nodes within the simulation. We generate all mobility models with a propagation range of 150 m. For this reason, a threshold setting (150 m) is present in our new metric to exactly reflect the correct outcomes. Then, we remove the lowest and highest values of the total number of neighbors recorded. Therefore, this metric makes it possible to inspect a total predefined propagation range based on all the mobility parameters, whatever the inspected node, the targeted model, and the time instant are. This property is calculated using the following Algorithm 1. ``` Result: Mobile neighbors range during the simulation Input : Mobility models Output : Mobile neighbors range of each instant
1\(t\gets 0\)s
2\(step\gets 10\)s
3\(T\leftarrow\)Validation_time
4 whilet <=Tdo
5 foreachtime range [t, t+step]do
6 foreachMM[0, Max]do
7*Calculate the distance between current node and other nodes */
8 foreachnode[id_0, id_Max]do
9 foreachneighbor[id_0, id_Max]do
10 if(id_node == id_neighbor)then
11 Skip
12 elseif(distance between node and neighbor > propagation range of node)then
13 Skip
14 elseif(distance[node, neighbor] or[neighbor, node] already verified)then
15 Skip
16 else
17 Save as a neighbor
18
19
20 end if
21 Save neighbors of each node
22
23 end if
24
25 Save neighbors of each mobility model
26
27 end if
28
29 Save neighbors of each time range
20
21 end for
23
24 Define the [min, max] neighbors for each time range of all mobility models;





* **Validation and results:*
* The validation results are depicted in Figure 6. We observe that:
* Based on Figure 6a,b, the RWPMM and the MGMM represent the worst mobility models according to this property, as they suffer dramatically from variation in the number of neighbors with time. However, the MGMM shows convenient oscillatory fluctuations of 0-9 with an obvious and regular gap, but with many instants in which there are no neighbors. This is in strong agreement with the results of previous metrics, such as the density wave phenomenon. * SLAW and the RPGMM show average performances with ranges of [0,14] and [0,19], respectively, according to Figure 6e,c. The RWPMM shows an irregular gap during the simulation within a moderate range. Some acceptable instants with no neighbors were recorded. * Figure 6d,f show that the NCMM and SMOOTH have few instants with no neighbors, and the range promptly converges to benefit the most possible from all deployed nodes. The NCMM peaks at 49 neighbors, which means it is the best model due to the correlated strategy of belonging to a single group with one leader for all mobile nodes (49 + the leader = 50 applied nodes (Table 2). nodes. This reflects the fact that the validated mobility model is more stable and steady with time that will lead to satisfactory outcomes in the performance analysis [3]. According to the features of the proposed metric, we deduce that it shows an obvious and effective neighborhood. It strongly endorses the results obtained by other existing metrics, such as the spatial node distribution, density wave phenomenon, and average neighbor percentage. From Table 5, the suggested novel metric provides a high precision compared to the others. This result inspects all the deployed nodes that change with time to show us more apparent movement behaviors of all mobility patterns.