Analysing Vehicular Mobility Structure under a 1 Temporal Perspective 2

In recent years, Vehicular Networks have received much attention 7 because they can contribute to solving several problems of urban scenarios. 8 An interesting perspective to characterize these urban problems is to study 9 vehicles’ mobility records to increase our knowledge about them. Thus, an al- 10 ternative is to model these records as graphs enabling us to apply algorithms 11 and graph theory to design new solutions for vehicular networks. This work 12 explores three diﬀerent strategies to model vehicular networks and analyzes 13 two real well-known traces from Rome and San Francisco. We perform a study 14 on the network aspect, measuring metrics that portray some network charac- 15 teristics and proprieties. We highlight the advantages and limitations of each 16 approach evaluated. Also, we present some applications and future directions 17 for the knowledge extracted with this analysis. 18

generated because it considers that one edge remains during the whole time, 137 which leads the analysis to interpret that this contact exists during the entire 138 time. 139 When we analyze traces, the temporal aspect is essential. Thinking about  In this section, we discuss the methodology used to perform this work. We 169 present details about the datasets, the graph models used to capture the trace 170 interactions, and the metrics applied to evaluate the results. interval. Second, we define G A = (V, E), we V is the set of nodes that contain 186 all the nodes that make up the network during the period, and E is the set 187 of edges that includes all the edges that appeared in the network during the 188 time interval. In this work, a period of 15 minutes was used to generate the 189 aggregate graph. This time was chosen because it is often used in related work.    The microscopic metrics define individual values for the node. We compute 231 the metrics for all the nodes, and we present the average value over time.

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Average Node Degree: node degree is the number of edges connected 233 to the node. We calculate the average of all node's degrees in the network. (2) where d(v, u) is the shortest-path distance between v and u, and n is the 246 number of nodes in the graph.

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Average Clustering Coefficient: for unweighted graphs, the clustering 248 of a node u is the fraction of possible triangles through that node that exists, where T (u) is the number of triangles through node u and deg(u) is the degree   and San Francisco traces. We evaluated the influences of these models in nine 277 metrics of complex networks.

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Although the Instantaneous graph's purpose is to analyze a mere instant 279 of the total time, we decided that it would be more just that it was generated Therefore, Temporal analysis can portray these patterns more realistically.

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Other metrics that show the impacts of different modeling types are the Clus-312 tering Coefficient, the Betweenness Centrality, and the Closeness Centrality.  Concerning the Figure 5-  Initially, we analyzed the behavior of vehicle connections in San Francisco.

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As observed in Figure 6-(a), the average of contacts occurred only once an hour.   Many are the applications for the knowledge extracted with our analysis.

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In literature, we found many works and new branches to explore our work.

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In this section, we present these works and some challenges in applying our results. We divided this section into five subsections. In these subsections, we

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The proposed protocol presented the best performance in terms of signaling 510 overhead. In scenarios with higher traffic demand, the number of messages 511 generated by the proposed protocol was lower than other related protocols.

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The first way to validate a new data dissemination protocol is to run sim-513 ulations of protocols to compare them. For this, it is necessary to explore the 514 communication among them. As we saw in our results, the type of graph used to model mobility can directly influence vehicles' communication. Therefore, 516 our study reinforces the need to perform careful data modeling, so avoiding the 517 simulations favor a specific protocol and explore a scenario closer to reality.

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Also, it is very suggested to use real vehicular traces to improve the accuracy 519 of the evaluation.