# Deep Validation of Spatial Temporal Features of Synthetic Mobility Models
## 1 Introduction  
Mobility models (MMs) are aimed at describing the movement patterns of mobile users (nodes) and how their mobility parameters (position, speed, and acceleration) change during the observation period. Hence, mobility models attempt to emulate displacement patterns in real-life environments with high accuracy. They are relevant in view of the fact that they are applied to measure the performance of network protocols. Thus, mobility modeling represents a thriving field of research for mobile networks given throughput improvements, which can be achieved by using accurate models. So far, several synthetic mobility models which are mainly based on mathematical equations have beenproposed. In other cases, they are described by physical motion laws. This category always attracts interest among the researcher community because these synthetic MMs can deploy an arbitrary number of nodes over a large simulation field in order to mimic a specific movement behavior in the presence of many network constraints. Recently, this category has shown magnificent progress, especially for sociality/human-based mobility models. Indeed, numerous synthetic patterns are presented to represent movements under diverse situations of mobile networks, for example military operations, disaster relief systems, and rescue events. Mobility management in ad hoc wireless networks faces many challenges. It represents the set of mechanisms providing a time-varying mapping between the identifier of a mobile node and its location with respect to the network structure [1]. Mobility constantly causes the network topology to change. In order to keep accurate routes, the routing protocols must dynamically readjust to such changes. Thus, routing update traffic overhead is significantly high. Different mobility patterns have in general different impacts on specific network protocols or applications [2]. The performance of mobile networks is remarkably impacted by several factors that further govern network performances: the packet delivery ratio, the average end-to-end delay, and throughput [3]. The mobility model represents one of these influential factors which shape the adopted motion strategy. A set of metrics is used to quantify the mobility features. Each inaccuracy of the model produces one or several mobility problems that indicate serious flaws, such as imbalance in the average speed during simulation, a non-uniform distribution of mobile nodes within a defined field, or unacceptable fluctuation in the number of neighbors. These model validations have already been verified for the random waypoint mobility model (RWPMM), for example:  
* the speed decay problem, described by [PERSON] et al. [4] and then in [5],
* spatial node distribution, introduced by [PERSON] et al. [6], later discussed in [7] for random networks and in [8] for the outage probability in wireless networks,
* the density wave phenomenon, reported by [PERSON] et al. [9] and later in [10; 11], for wireless networks. * the average neighbor percentage, investigated by [PERSON] et al. [12] and then in [13]. Based on those stochastic properties, it is possible to perform a precise analysis and simulation of a mobility model and the issues that can affect performances without needing to implement it on a real mobile wireless network. Network analysis is mainly done to verify the entire simulation process using appropriate performance metrics that only display a general perspective. Furthermore, a proper mobility validation can accurately detect the causes of network deterioration without needing to implement a mobility pattern to analyze the performances of the real mobile network. For these reasons, in this paper, we first validate the previously suggested mobility metrics for some popular synthetic mobility models that have not been verified until now. Then, we propose a novel mobility metric called the \"node neighbors range,\" which reveals the imbalance of mobility models during the simulation. The remainder of this paper is organized as follows.