# Probabilistic Modeling of Congested Traffic Scenarios on Long-Span Bridges
## 6 Conclusions  
The following conclusions can be drawn from the obtained results:  
1. This study conducted a comprehensive investigation into the characteristics of traffic congestion on long-span bridges. Due to the lack of actual congestion traffic data for the bridge in question, a calibrated CA model was utilized to simulate congested traffic flow, creating samples for modeling extreme response scenarios. The data analysis revealed that during congestion periods, the vehicle weight composition is generally lighter than that observed under normal traffic conditions, and these events occur at a relatively low frequency. Because of this, it may happen that extreme load effects under free-flow traffic may be comparable or even higher than under congested-flow conditions. In fact, the higher presence of heavy vehicles and probability of occurrence of extreme situations (due to the shape of the influence lines of the load effects) in the case of free-flow conditions can result in this possibility for some load effects on long-span bridges. This issue is now under investigation thanks to the simulation capabilities provided by the proposed model, valid for both free- and congested-flow traffic. It also emphasizes the need of models for free-flow traffic on long-span bridges, which almost does not exist currently because congested traffic has been considered the critical situation by most researchers in the field.
2. The application of the extreme-response-scenario probabilistic model previously proposed by the authors for free-flow traffic to the case of congested traffic demonstrated its flexible applicability and broad utility. By accurately modeling extreme response scenarios of congested flow, this approach has proven to be an effective tool for simulating extreme conditions under various traffic conditions on long-span bridges. This significantly contributes to the assessment of the safety performance of long-span bridges under traffic loads, highlighting the model's potential to enhance the understanding and management of bridge safety.
3. Through the refined simulation of extreme congestion response scenarios, this study not only corroborates the robustness of the proposed probabilistic model but also underscores its relevance and significance in facilitating accurate safety evaluations by obtaining the maximum load effects in a simpler and cheaper (in terms of computing time) way. This opens the feasibility of using the proposed model in the automatic and on-line management of existing long-span bridges in operation, giving the possibility of obtaining an expected response of the bridge in actual traffic conditions and comparing it with the experimentally obtained response measured in certain locations. The differences in both responses can warn about possible deficiencies in the normal operation of the bridge, therefore becoming a key aspect of the bridge's preventive maintenance.  
Future research will aim to integrate real congestion data as advances in detection and monitoring technologies permit to further validate and refine the model's parameters, ensuring that the simulated traffic scenarios closely mirror real-world conditions and thereby enhancing the predictive accuracy essential for the structural health monitoring of long-span bridges.  
Conceptualization, X.W. and X.R.; methodology, X.W. and M.Z.; software, X.W.; validation, X.W. and J.R.C.; formal analysis, X.W.; investigation, X.R.; resources, X.R.; data curation, X.W. and M.Z.; writing--original draft preparation, X.W.; writing--review and editing, J.R.C.; visualization, X.W.; supervision, J.R.C.; project administration, J.R.C.; funding acquisition, J.R.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflicts of interest.