# Two-Component Bayesian Hierarchical Models for Cost-Benefit Analysis of Traffic Barrier Crash [PERSON]
## 6 Cost-Benefit Analysis  
For conducting any optimization process, the benefits and costs of any policy need to be carefully weighted. Welfare maximization has been highlighted as the objective of cost-benefit analysis [17].  
The cost-benefit analysis relies on the Pareto-criterion for checking whether a project increases welfare or not. The idea states that the ideal welfare scenario would be achieved when an improved change makes some people better off while nobody would experience a loss. However, in practice, some projects make some people better off, while others would be worse off. Thus, the economists pledge to a less demanding state, stating that a project satisfies the criterion when those who benefit from a project compensate those who lose from it [17]. The same concept was implemented in this study: if, overall, the total benefit is positive, optimizing traffic barriers would be cost-effective, and a higher priority should be given to a higher benefit based on cost-benefit analysis. A period of 10 years was considered in this study for cost-benefit analysis, and the benefit could be written as follows:  
\[\begin{array}{rl}\mathit{Benefit over}\ 10&\mathit{year}\\ &=\sum\limits_{i=1}^{10}\left(\mathit{predicted\ cost\ with\ no\ barrier\ enhancement}_{i}-\left(\mathit{Reset\ cost}\right.\\ &\left.+\mathit{predicted\ Future\ cost}_{i}\right)\end{array} \tag{14}\]  
where \(i\) is a measurement for every year. In the above equation, costs would be estimated based on various years for various traffic count. Major costs, including reset or new barrier cost, would be executed in the first year. It should be noted that, for the incorporated barriers, box-beam and W-beam barriers heights can be reset, while for concrete barriers, the removal and rebuilding of concrete barriers would be needed to optimize heights.  
Based on the last 10-year historical traffic data, the traffic on the state highway system was almost constant, while the traffic on interstate system increased by a rate of 4% in 10 years.  
EPDO based on recommended WYDOT values for different crash types would be written as:  
\[\begin{array}{rl}\mathit{EPDO\ rate}=\mathit{Fatal\ crashes}+\mathit{ suspected\ serious\ injury}+\mathit{suspected\ minor\ in\ jury}+\\ \mathit{possible\ injury}+\mathit{Unknown}+\mathit{PDO}\end{array} \tag{15}\]  
The above equation after converting every crash severity level to PDO, in order, follows:  
\[\begin{array}{rl}\mathit{EPDO\ rate}=277\times\mathit{PDO}+13\times\mathit{ PDO}+4\times\mathit{PDO}+4\times\mathit{PDO}+4\times\mathit{PDO}+1\times\mathit{PDO}\end{array} \tag{16}\]  
In summary, the methodological steps taken in this study could be highlighted as follows:  
1. Identify all the barriers with crashes across highway and interstate systems in Wyoming.
2. Identify the barrier which did not experience any crashes but are below/above recommended heights.
3. Aggregate the crash data, data in steps 1 and 2, with traffic barrier dataset based on milepost, and roadway ID.
4. Filter the data to include those barriers that are not based on standard heights, as \"newdataset\".
5. Identify the best distribution with a lowest DIC based on data in step 3.
6. Convert the best fit model in step 5 into an equation.
7. Implement a trained model in step 6 on dataset being based on current barrier geometric characteristics, and for each year an increase in traffic for interstate system only.
8. Optimize the barriers to optimum height values based on the literature review, and conduct step 7 with the difference that an optimum value of barriers would be used.
9. Based on step 8, convert EPDO into a cost and sum up the expected barriers crash cost for every year for barriers with optimum values and add the cost of height reset.  
Based on step 7, Convert the EPDO into a cost and sum up expected barriers crash cost for every year for barriers with no enhancement, and no cost of reset.
* Measure the difference between steps 9 and 10.
* Report the total of saving.
* Sort barriers based on highest benefits and report it.