# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 4 Case Analysis
### Experimental Process and Result
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Indicator Name** & **Line 1’s \(w_{j}\)** & **Ranking** & **Line 139’s \(w_{j}\)** & **Ranking** \\ \hline Bunching (E2) & 7.59 & 5 & 7.995 & 4 \\ Big interval (E3) & 1.15 & 10 & 2.19 & 8 \\ Punctuality rate (D1) & 0.63 & 11 & 3.4 & 7 \\ Actual departure interval (A1) & 1.485 & 8 & 1.885 & 9 \\ Actual arrival interval (A2) & 1.475 & 9 & 1.785 & 10 \\ Card swiping passenger volume (B1) & 39.265 & 1 & 38.77 & 1 \\ On schedule departure rate (C1) & 0.205 & 12 & 0.25 & 12 \\ Load factor (B3) & 9.45 & 4 & 5.65 & 5 \\ Landing volume (B2) & 20.65 & 2 & 22.43 & 2 \\ Number of online operating vehicles (C2) & 2.43 & 7 & 1.325 & 11 \\ Bus single-trip time (E1) & 3.08 & 6 & 10.465 & 3 \\ OD passenger flow (B4) & 12.595 & 3 & 3.855 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Weight ranking results. and trend terms. If the p-value of the ADF test for the period \([t_{test},t_{E}]\)\((t_{test}>t_{L})\) is less than 0.05, it indicates that the subset of data is stationary, and the steady-state time is defined as \(t_{SS}=t_{test}\) and the steady-state value as \(y_{S}=y(t_{test})\). After obtaining \(t_{SS}\) and \(y_{S}\) for each indicator, the resilience factors \(\theta\), \(\rho\), \(\lambda\), \(\sigma\), \(\tau\), and the overall resilience \(R_{l}\) are calculated. The volatility coefficient \(\sigma\) is computed using the raw indicator data, denoted as \(y_{raw}(t)\), and the smoothed data obtained through STL decomposition, denoted as \(y_{s}(t)\). The resilience factors and overall resilience for the seven analyzed routes, in this case, study are shown in Table 9.  
Figure 16: Trend of line passenger flow index after STL decomposition (x-axis: serialized time). Figure 17: Trend of stop passenger flow index after STL decomposition (\(v\)-axis: serialized time). From the observation of Figure 18 and the comparison of experimental results, it can be concluded that among the seven analyzed routes, Route 40 exhibits the highest resilience. This is mainly attributed to its higher values of the absorption factor \(\lambda\) and the recovery factor \(\rho\). These factors indicate that Route 40 has better absorption and recovery capabilities during the resilience cycle, resulting in an overall enhancement of resilience. On the other hand, Route 60 has the lowest resilience value, primarily due to its weaker absorption capability during the resilience cycle and higher sensitivity of indicators to disruptive events. Among the thirteen analyzed stations, the Chaoneixiaojie station demonstrates the highest resilience value. This is also because it possesses higher absorption and recovery capabilities, as indicated by \(\rho>1\), indicating that the indicator values exceed the initial values when reaching the steady state. By comparing the smoothed data in the plots, it is evident that the trend of Route 40 is significantly less affected by the disruptive event within the \([t_{S},t_{SS}]\) interval compared to Route 60. The comparison between the two stations further emphasizes this point, as the passenger volume at Chaoneixiaojie station during the resilience cycle is minimally affected by the disruptive event, showcasing its superior recovery and absorption capabilities compared to Langjiayuan station. Based on this case analysis, it can be concluded that the proposed resilience analysis model based on resilience cycles effectively and accurately assesses the resilience of bus routes affected by disruptive events. The resilience values calculated for the bus routes in this section will serve as inputs for the overall resilience analysis of the bus network. These values will be used to compute the overall resilience of the bus network.