# Scenario-Based Emergency Material Scheduling Using V2X Communications
## 4 Experiment
### Parameters
#### 4.2.1 Fairness Analysis
The related results of the enhanced Theil model are shown in Figure 7 and Table 13.  
\[F^{\prime}=\sum\limits_{j=1}^{J}\sum\limits_{k=1}^{K}\frac{\alpha_{jk}^{p}}{ \sum\limits_{j=1}^{J}\sum\limits_{k=1}^{K}\alpha_{jk}^{p}}\ln(\frac{\alpha_{ jk}^{p}}{\sum\limits_{j=1}^{K}\sum\limits_{k=1}^{K}\alpha_{jk}^{p}}/\frac{x_{ ijk}^{p}}{\sum\limits_{i=1}^{J}\sum\limits_{k=1}^{K}x_{ijk}^{p}}) \tag{12}\]  
where \(F\) is fairness of the enhanced Theil model; \(\alpha_{jk}^{p}\) and \(x_{ijk}^{p}\) are defined in Equation (4). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{3}{c}{**Chengdu**} & \multicolumn{3}{c}{**Shifang**} & \multicolumn{3}{c}{**Jiangyou**} \\ \cline{2-10}  & **G** & **T** & **W** & **G** & **T** & **W** & **G** & **T** & **W** \\ \hline Amt & 3744 & 10,100 & 17,324 & 9701 & 1910 & 52,578 & 6643 & 0 & 10,276 \\ Sat Rate & 0.6528 & 0.9187 & 0.9371 & 0.9701 & 0.4281 & 0.9701 & 0.8572 & 0 & 0.8382 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Scheduling plan for the Gini model. Figure 8: Iterative curve for SEMS scheduling time optimization. Figure 9: Iterative curve for the enhanced Theil scheduling time optimization. Thus, we compared the scheduling plan with the maximum SEMS fairness, the Gini model and the enhanced Theil model, and then made the following conclusions based on Tables 11-13:  
(1). Comparison between the Gini model and SEMS model. As shown in Table 8, the tent demand for Jiangyou is 149, Shifang 4462, and Chengdu 10,993. The tent demand for Jiangyou is very small and that for Chengdu is large. As shown in Table 12, the optimized solution to the Gini model ignores the demand for Jiangyou and its scheduling amount and demand satisfaction rate are both 0. In the Gini model, for Shifang, the tent demand satisfaction rate is only 0.4281. However, that of the SEMS model is 0.9620. For Chengdu the tent demand satisfaction rate is 0.9187, whereas it is 0.6644 in the SEMS model. This states that the Gini model only meets the disaster depots with a high demand, while ignoring the depots with low demand, although the SEMS model can provide a fairer solution. Table 11 presents the optimized SEMS solution, where the demand satisfaction rate of Jiangyou attains 0.8187, and that of Shifang is 0.9620. Compared with the Gini model, the SEMS considers the disaster depots with low demand. Even though the demand for some material of a disaster depot is very low, it can still receive some emergency materials when the relief supplies are insufficient. (2). Comparison between the enhanced Theil model and SEMS model. As shown in Table 8, the tent demand for Chengdu is higher than Shifang, whereas the scenario coefficient for Chengdu is 0.057, less than that of Shifang 0.157. It means the tent demand for Shifang is more urgent than that for Chengdu. As shown in Table 11, the demand satisfaction rate for Chengdu is 0.6644 in the SEMS model, and lower than that of Shifang 0.9620, whereas the enhanced Theil model is the opposite. Therefore, the SEMS model considers the urgency of emergency material for disaster depots and can guarantee the demand with a high scenario coefficient, so it is closer to the actual situation. In summary, compared with the Gini model and the enhanced Theil model, the proposed SEMS model considers the low demand for disaster depots and guarantees the emergency materials with a high scenario coefficient.