# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 2 Related Literature
### Resilience Research in Transportation  
Our society relies heavily on a large number of critical infrastructure systems, such as transportation, water supply, power grids, communication systems, and so on. These  
Figure 2: Comparison of system behaviors. systems work together to provide us with essential goods and services for our daily lives. Over the past few decades, these systems have become increasingly complex and interdependent, making them vulnerable to disruption and difficult to restore. Therefore, unexpected disasters can cause huge losses in terms of human lives and economic damages. The transportation system is one of the most severely affected infrastructure systems by disasters [28; 29]. As the lifeline of urban infrastructure, the transportation network provides access to disaster-affected areas and supports emergency response and long-term recovery efforts after disasters. Therefore, the stable functionality of the transportation network is of significant importance from both economic and safety perspectives [30]. Based on this background, many concepts have been used to study the performance of transportation network systems when facing various disruptions (from frequent daily fluctuations to rare natural disasters), among which the term resilience is increasingly used in the literature. In recent years, resilience theory has been widely studied in transportation networks. The trend of research on transportation network resilience in the past twenty years is shown in Figure 3.  
In the 2009 U.S. National Transportation Recovery Strategy, resilience was proposed as an indicator to enhance the resilience of various community infrastructures and accelerate the recovery of disrupted transportation networks [31]. In terms of the definition and quantification of resilience, the four concepts of \"R4\"--robustness, redundancy, intelligence, and speed--and the \"resilience triangle\" proposed by the multidisciplinary Earthquake Engineering Research Center have been widely used in the study of transportation network resilience in various disciplines [31; 32]. Based on the previous review of resilience theory in various fields and stages, this article will summarize the definition, related concepts and characteristics, and measurement methods of transportation network resilience from the perspectives of definition, relevant concepts, and measurement methods. (1) The definition of resilience in transportation networks:  
[PERSON] was the first to define resilience specifically in the context of transportation networks, rather than general infrastructure systems. He also proposed metrics and measurement methods for resilience. In his research, he identified ten dimensions of resilience, including redundancy, diversity, efficiency, self-organization, strength, collaboration, adaptability, mobility, safety, and quick recovery. However, these ten dimensions are highly complex and interactive, making it difficult to obtain a comprehensive measure of  
Figure 3: Number of studies on transportation network resilience during 1975–2023. resilience [33]. Since then, the concept of resilience has been applied to various studies on transportation network systems. After analyzing the concept of resilience in transportation network systems, [PERSON] and [PERSON] identified four basic dimensions that mainly reflect the resilience of transportation network systems: resistance, recovery, absorption, and transformation [34]. [PERSON] et al. then proposed four attributes of resilience based on these four dimensions: robustness, redundancy, resourcefulness, and rapidity, in their \"R4 framework\" [35]. This framework has been widely used in subsequent resilience research as an application of the resilience cycle theory. Robustness and redundancy determine the performance (loss) of the transportation network system during the disruption phase. Specifically, robustness measures the ability to withstand damage caused by disasters, and redundancy reflects the availability of alternative resources.