# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 3 Methodology
### Transport Lines Resilience Analysis Model Based on Resilience Theory  
The resilience of bus routes mainly focuses on reflecting the dynamic resilience of the bus network system, which refers to the ability of the line performance to gradually degrade and recover to a steady state before the disturbance when the public transportation network system is interfered with due to sudden events such as traffic accidents, natural disasters, large-scale social activities, etc. The occurrence of sudden events in the environment where bus routes are located is a prerequisite for the disturbance of the bus network. The performance of bus routes is the external manifestation of the network operation status. For example, the line performance can be represented by the average speed of the line, passenger volume, and one-way running time of the line. The sudden event changes the network performance by affecting the working status of the bus routes themselves. Therefore, this section analyzes the resilience of bus routes by using the key indicators obtained in the previous section as the line performance. Based on the resilience cycle theory, a resilience analysis model is constructed by analyzing the change curve of the key indicators under the impact of sudden events. 1. Model construction. As shown in Figure 7, in the event of a sudden incident, the performance indicators of a bus route usually exhibit a trend of initially declining and then rebounding over time. In existing resilience research, the resilience cycle theory is typically used to segment this trend, with the adaptation phase being from the start of the incident until the system performance begins to decline, the absorption phase being from the start of system performance decline until it reaches the lowest point, and the recovery phase being from the start of system performance recovery until it reaches the expected stable level. The Y-axis represents the measurement of public transit performance over time. \(t_{S}\) represents the time when the sudden event occurs, while \(t_{D}\) represents the time when the transit system performance starts to decline. In general, \(t_{S}\) is not equal to \(t_{D}\), because the change caused by the sudden event and the spread of negative effects may delay the decline of performance. For example, the impact of a traffic accident on a bus route may not be evident until congestion or traffic control measures appear, while a relatively major sudden event, such as a natural disaster, can quickly bring negative effects to the transit system. \(t_{L}\) represents the time when the transit system performance reaches its lowest point, and \(t_{SS}\) represents the time when the transit system performance stabilizes again. According to the resilience cycle theory, the resilience response of a public transit route can generally be divided into three stages after a sudden event occurs: first is \(t_{S}\to t_{D}\), where due to the absorption capacity of the route's resilience, the decline in performance caused by the sudden event is not immediately apparent. Second, is \(t_{D}\to t_{L}\), during which the decline in performance caused by the sudden event will reach its maximum, and the peak value of performance decline is determined by the route's adaptation capacity. Finally, \(t_{L}\to t_{SS}\), which is the recovery stage of the route's resilience, where the system performance will gradually recover to the stable level before the sudden event occurred, and the recovery rate is determined by the route's recovery capacity. The resilience of public transit routes in these three stages is difficult to measure using a single dimension. Therefore, a unified quantitative research method is proposed to comprehensively evaluate the resilience of public transit routes in response to various unexpected events.