## 4 Results and Discussion  
### Risk Analysis and Calculations  
The basic theme of applying DEA method was to analyze the comparative safety levels of motorway segments to rank them for prioritizing safety improvements and financial decision making for implementation. High-risk segments could easily be identified but an additional sensitivity analysis method of cross-risk calculation helped in prioritizing the segments for ranking. A standard of 1 served as the benchmark, and an increasing trend indicated the distance from the safety ideal, so the far-most are considered the most dangerous ones. Thus, after applying model (2) for calculating risk (R\({}_{0}\)) in accident data analysis and management field, the lowest level must be measured as the frontier of safety. As described above, for ranking purposes, the cross-risk technique [20] has been adopted to obtain the best ranking, as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**DMU** & \multicolumn{5}{c}{**Rated DMU**} \\ \hline  & 1 & 2 & 3 &... &... & \(n\) \\ \hline DMU1 & \(R_{11}\) & \(R_{12}\) & \(R_{13}\) &... &... & \(R_{1n}\) \\ DMU2 & \(R_{21}\) & \(R_{22}\) & \(R_{23}\) &... &... & \(R_{2n}\) \\ \(DMUn\) & \(R_{n1}\) & \(R_{n2}\) & \(R_{n3}\) &... &... & \(R_{nm}\) \\ Mean & \(\overline{R}_{1}\) & \(\overline{R}_{2}\) & \(\overline{R}_{3}\) &... & \(\overline{R}_{n}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A cross-efficient risk matrix (CERM). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Seg.ID** & **Km** & **V/C** & **VKT** & **VHT** & **NOA** & **NOAP** & **DEA-Risk** &
\begin{tabular}{c} _RARI_ \\ **(CE-Risk)** \\ \end{tabular} & **Rank** \\ \cline{3-10}  & **Post** & _Input I1_ & _Input I2_ & _Input I3_ & _Output O1_ & _Output O2_ & & & \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: Road accident risk index (RARI) calculation mechanism using DEA. DEA has a major advantage of not having any specific functional form. Additionally, it can deal with various sources of information and different yields. DEA has a few other advantages as it does not require a presumption of a utilitarian structure relating contributions to yields; DMUs considered in DEA are directly looked at against peers or blend of peers. Inputs and yields utilized in DEA can have diverse estimation units. In this investigation, number of accidents (NoA) and number of affected/influenced people injured or killed (NoAP) are considered as two yields, while presentation factors--volume/capacity (V/C), vehicle kilometers traveled (VKT), and vehicle hours traveled (VHT) were considered as three sources of info. The idea of hazards considered in the ideal of hazardous fragments begins with esteem 1, in view of Model (1); its range started at 1 and continues with increment up to 21.81. Portions with the closest incentives to 1 are viewed as protected and the highest value is considered in danger. In the Table 3, a comparative ranking using the cross-risk method [20] to rank the risky segment by prioritization can be seen. The ranking of DMUs was designated to evaluate the risk level of all segments: the risk value of 21.81 was the largest value in the Table 3 and was ranked first (i.e., the riskiest segment). Priority of treatment can also be decided based on this ranking. GIS-based spatial map of the motorway section is shown in Figure 6. Dark red colored segments highlight the risky segments. Comparative analysis if calculated risk and Number of accidents (NOA) has been shown in Figure 7.  
Figure 6: Risk map of motorway (M-2). By applying DEA in combination with GIS, provides a series of benefits. For a 100-km long road, which in fact becomes 200 segments due to one-way traffic (both sides), only 99 problematic segments were studied. By further focusing on the problematic segments and taking the opportunity to identify riskiest segments, DEA helped in locating those segments. CERM helped as an extension to DEA to prioritize the risky road segments based on severity.