## 6 Conclusions  
In this work, we discuss the performance of vehicular networks in terms of the metric Delta Network [29]. The Delta Network characterizes the connectivity of the vehicular network through the percentage of travel time in which vehicles are connected to roadside units. In summary, this article reviews the concept of the Delta Network and extends its study through the presentation of a general heuristic in Algorithm 1, which is based on the definition of _scores_ to identify areas of the road network that should receive coverage under different objectives. We consider the Vehicular Mobility Trace of Cologne, Germany, with the road network partitioned into a grid-like structure  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Strategy** & **Score Computation** & **Style of Coverage** \\ \hline _balanced_ & select cell maximizing the area under the Delta curve & moderate density around the epicenter of traffic \\ _direct_ & select cell prioritizing vehicles with high coverage & high density around the epicenter of traffic \\ _inverse_ & select cell prioritizing vehicles with low/no coverage & low density around the epicenter of traffic \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of strategies.  
Figure 12: (**a–c**) Present the Delta Network in a single plot for the three proposed strategies: _balanced_ (blue), _direct_ (red), and _inverse_ (green). (**d–f**) Present the Differential Delta Network. In these figures, the red curve indicates the value _“balanced_ minus _direct_”, while the green curve shows _“balanced_ minus _inverse_”.  
of dimensions 100 \(\times\) 100, resulting in urban cells of dimension 270 m \(\times\) 260 m, holding more than 75 thousand vehicles.  
After defining the general heuristic, we show how small changes in the _score_ computation can generate very distinct (and interesting) patterns of coverage, each one suited to a given coverage objective. The definition of the _score_ is based on the number of vehicles meeting coverage in relation to the distance traveled. In particular, when we consider the same weight for all travel classes (strategy _balanced_), we obtain as a result the maximization of the area under the Delta curve. On the other hand, when we consider the score directly proportional to the percentage of the trip that vehicles travel with coverage (strategy _direct_), we obtain a pattern that privileges the coverage of vehicles with high connectivity, resulting in increasing the share of vehicles experiencing high coverage, where the resulting layout of roadside units becomes more condensed around the traffic epicenter.  
However, when we consider scores inversely proportional to the percentage of the trip that vehicles meet coverage, we get a more inclusive pattern where new vehicles get the opportunity to meet coverage. In such a case, we have the least concentrated roadside units layout when considering all experiments performed along this study (strategy _inverse_). Finally, for all strategies evaluated, the layout of roadside units follows a circular pattern around the traffic epicenter.  
Conceptualization, C.M.S.; methodology, C.M.S.; software, C.M.S. and L.A.L.S.; validation, C.M.S., L.D.S., J.F.M.S. and L.A.L.S.; formal analysis, C.M.S., J.F.M.S. and A.P.; investigation, C.M.S. and J.F.M.S.; resources, L.D.S., L.A.L.S. and A.P.; data curation, C.M.S., L.D.S.; writing--original draft preparation, C.M.S.; writing--review and editing, C.M.S. and A.P.; visualization, A.P.; supervision, A.P.; project administration, A.P.; funding acquisition, A.P. This research was partially funded by CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico), CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior), FAPEMIG (Fundacao de Amparo a Pesquisa do Estado de Minas Gerais), and the Federal University of Sao Joao del-Rei. The authors declare no conflict of interest.