## 4 Conclusions  
In this paper, the interaction between vehicles and an unsignalized mid-block raised crosswalk was studied using computational simulation. A pedestrian-vehicle cellular automaton model was developed representing open-boundary conditions with rates \(\alpha\) for injection and \(\beta\) for extraction, whilst pedestrians enter from a waiting zone to the crosswalk at rate \(\alpha_{p}\). Taking traffic flow as the order parameter, the phase diagram was constructed identifying four phases: maximum current, jamming, congestion, and gridlock. It was observed that the crosswalk becomes a bottleneck due to the pedestrians' influx, producing a vehicles reservoir that acts as an alternative injection rate that prevents the emerging of a free-flow phase, even when \(\beta\) is much greater than \(\alpha\). Indeed, in this system, there are free-flow conditions only during the maximum current phase. However, the maximum current phase drops with the increase in \(\alpha\), while the gridlock phase is reached when the pedestrian entrance rate \(\alpha_{p}\) is greater than 0.8. The CO\({}_{2}\) emission and the energy dissipation were also evaluated, and it was found that the maximum values were observed during the jamming phase due to the queue formation of stop-and-go vehicles all along the lane. Conversely, the minimum values were located in the gridlock phases where traffic is at a complete standstill. The carbon dioxide emissions show the same  
Figure 9: Analyzing the effects of an unsignalized zebra mid-block crosswalk for \(\alpha=0.4\); (**a**) traffic flow as a function of \(\alpha_{p}\) and \(\beta\), (**b**) phase diagram in the plane \((\alpha_{p},\beta)\), (**c**) CO\({}_{2}\) as a function of \(\alpha_{p}\) and \(\beta\), and (**d**) energy dissipation as a function of \(\alpha_{p}\) and \(\beta\). features such as the energy dissipation, as both of them have a relationship with speed variation. Along the same lines, the instantaneous energy dissipation was evaluated. It was observed that although the maximum current phase has free-flow conditions, speed changes caused by the crosswalk, and the lane's exit induces energy dissipation peaks. One of the implications of our study is to reveal that always giving priority to pedestrians over vehicles can worsen the traffic flow situation and induce gridlock. The results also provide an insight that raised crosswalks are not suited for roads intended for high traffic volumes; therefore, their installation must be performed according to the road hierarchy. In this sense, the main contribution of this work is to provide a novel reference framework to depict the traffic physics involved with raised crosswalks, so that showed results can motivate the development of microscopic simulation tools or forecasting guidelines for urban planning. This study also was complemented with a brief analysis of a zebra crosswalk, where it was glimpsed that to achieve a fair comparison against a raised crosswalk a more dedicated study is needed, incorporating additional qualitative and quantitative parameters, such as safety factors or accident rates. Further extensions of this work would consider the incorporation of additional variables to improve the model towards mimicking more realistic scenarios. In this sense, the future work will be focused on exploring the effects of multi-lane roads as well as the analysis of drivers yielding when combining with overtaking maneuvers. Conceptualization, J.R.P.C. and N.L. ; methodology, J.R.P.C. and N.L. ; software, J.R.P.C. and J.C.P.S; validation, J.R.P.C., N.L., J.C.P.S. and J.L.Z.L. ; formal analysis, J.R.P.C., N.L., J.C.P.S. and J.L.Z.L. ; investigation, J.R.P.C., N.L. and J.L.Z.L. ; writing--original draft preparation, J.R.P.C., N.L., J.C.P.S. and J.L.Z.L. ; writing--review and editing, J.R.P.C., N.L., J.C.P.S. and J.L.Z.L. ; visualization, J.L.Z.L. ; supervision, J.R.P.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding.