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Journal of Geographical Sciences >

2024 , Vol. 34 >Issue 8: 1657 - 1674

DOI: https://doi.org/10.1007/s11442-024-2265-4

Research Articles

Travel behavior resilience: Theory, method, and empirical studies

  • HUANG Jie , 1 ,
  • WANG Jiaoe , 1, 2, *
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  • 1. Key Laboratory of Regional Sustainable Development Modelling, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • 2. College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China
*Wang Jiaoe, PhD and Professor, E-mail:

This paper is initially published in Acta Geographica Sinica (Chinese edition), 2023, 78(10): 2507‒2519.

Huang Jie, PhD and Associate Professor, specialized in big data and urban transport geography. E-mail:

Received date: 2024-04-16

  Accepted date: 2024-05-22

  Online published: 2024-08-16

Supported by

National Natural Science Foundation of China(42225106)

National Natural Science Foundation of China(42121001)

Youth Innovation Promotion Association of Chinese Academy of Sciences(2021049)

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Abstract

Resilience studies have long been a focal point in the fields of geography, social science, urban studies, and psychology. Recently, resilience studies from multiple disciplines have scrutinized resilience at an individual scale. As one important behavior in the daily life of human beings, travel behavior is characterized by spatial dependence, spatiotemporal dynamics, and group heterogeneity. Moreover, how to understand the interaction between travel behavior (or demand) and transportation supply and their dynamics is a fundamental question in transportation studies when transportation systems encounter unexpected disturbances. This paper refines the definition of travel behavior resilience based on fundamental theories from multiple disciplines, including ecology, transportation engineering, and psychology. Additionally, this paper proposes a conceptual theoretical framework of travel behavior resilience based on the dynamic equilibrium characteristics of transportation supply and demand. In general, travel behavior has three stages of variation, namely, dramatic reduction, rapid growth, and fluctuation recovery, which have helped capture the travel behavior resilience triangle. Then, we construct a corresponding evaluation methodology that is suitable for multiscale and multidimensional perspectives. We emphasize that the evaluation of travel behavior resilience should be process-oriented with temporal continuity or capture the inflection points of travel behavior. Using multisource big data such as mobile phone signaling data and smart card data, this paper reviews empirical studies on travel behavior resilience, exploring its spatial heterogeneity and group differences. With location-based analysis, we confirm that people show greater travel behavior resilience in places where people engage in various socioeconomic activities. The group-based analysis shows that age and socioeconomic attributes of mobility groups significantly affect travel behavior resilience. Travel behavior resilience can be one pillar, offering geographic perspectives in resilience studies. In the future, the study of travel behavior resilience at multiple scales and from multiple perspectives can explore the spatial heterogeneity of transportation re-equilibrium and travel modal differences, contributing to urban spatial structure studies. Studying travel behavior resilience can provide scientific and technological support for urban management and resilient city construction.

Key words： resilience; residential travel; social group; urban transportation; big data

Cite this article

HUANG Jie , WANG Jiaoe . Travel behavior resilience: Theory, method, and empirical studies[J]. Journal of Geographical Sciences, 2024 , 34(8) : 1657 -1674 . DOI: 10.1007/s11442-024-2265-4

1 Introduction

Resilience, as a pivotal attribute for sustainable systems in the fields of ecology and socioeconomics, encapsulates the capacity for recovery, functional maintenance, and continual adaptation to disturbances. Since its inception, the concept of resilience has been extensively applied across a multitude of disciplines, such as ecology, environmental engineering, management, sociology, and psychology, leading to the development of theories related to equilibrium states, feedback mechanisms, and self-organization. Scholars have globally examined resilience from various spatial-territorial/regional perspectives in the context of regional resilience, urban resilience, and rural resilience (Sun et al., 2017; Li et al., 2021; Yang et al., 2021); based on domain categorization, discussions on the concepts of ecological resilience, economic resilience, social resilience, infrastructure resilience, and institutional resilience have emerged (Holling, 1973; Zhou et al., 2006; Sun et al., 2017). Therefore, resilience studies have emerged as a prominent focus within the field of geography, encompassing investigations in natural geography, economic geography, urban geography, and rural geography (Xiu et al., 2018; Song et al., 2019; Chen et al., 2020; Li et al., 2021; Wang et al., 2021a; Wu et al., 2021). This encompasses investigations into the dynamic adaptability of regional systems’ resource and environmental carrying capacities, disaster prevention, mitigation, and preparedness (Zhou et al., 2019); the self-organizing and adaptive capacity of trade networks during financial crises, economic downturns, and other negative disturbances (Yu et al., 2020; Wang et al., 2021b; Zong et al., 2021); regional economic resilience reflected through recovery, transformation, and renewal abilities following external shocks (Chen, 2017; Sun and Sun, 2017; Tan et al., 2020; Hu et al., 2021); and the examination of urban systems’ dynamic equilibrium and resistance to disturbances from the aspects of social development, the ecological environment, the built environment, and management systems (Huang and Huang, 2015; Wang et al., 2016; Qian et al., 2017; Sun and Zhen, 2019; Yang et al., 2021), as well as discussions on urban network resilience through collaborative efforts and complementary relationships between cities across social domains, including economic engineering aspects and organizational dimensions (Wei and Xiu, 2020; Wei and Pan, 2021). In general, the contemporary trend in resilience studies emphasizes the processual changes experienced by studied subjects during disturbances, analyzing their adaptive capacity within the system from multiple dimensions.
From the functional consistency and systemic approach perspectives, transport systems can be divided into supply and demand sides, with the equilibrium between these two dimensions constituting the foundational conditions for system stability. Existing studies on network robustness and reliability have provided theoretical and methodological frameworks for resilience studies on the transport supply side, facilitating a paradigm shift in transportation system development from an “emphasis on construction” to an “emphasis on maintenance and quality” (Chen et al., 2020). To strengthen China’s transportation infrastructure, there must be a concerted effort to prioritize modernization and high-quality development within transportation systems, enhancing transportation system’s resilience as a crucial research priority. However, limited attention has been devoted to the adaptive capacity of demand-side transportation systems (residential travel) in response to disruptions, specifically travel behavior resilience. The focus of travel behavior resilience research should be on the travelers (individuals or groups), with quantitative methods emphasizing the interplay and interconnectedness between supply and demand, thereby investigating the traveler’s capacity for recovery within the framework of a supply-demand interaction mechanism. In summary, this paper aims to investigate the resilience demonstrated by how residential travel deals with disruptions from a dynamic supply-demand interaction perspective based on variations in travel patterns among different residential travel groups (individuals). This paper endeavors to dissect the conceptual essence of travel behavior resilience and proposes research methodologies for its measurement supplemented by empirical case studies. The theory of travel behavior resilience plays a crucial role in developing the conceptual framework and scope of resilience research and refining the analytical methods for studying transportation system resilience. This contributes to promoting the evolution of transportation systems from a “quality-centric” growth model to a more “people-oriented” high-quality growth model.

2 The structure of travel behavior resilience theory

2.1 Conceptual clarification: From resilience to travel behavior resilience

Resilience, originating from the Latin “Resilio” meaning to return to the initial state, was first defined in psychology as an individual trait, leading to the concept of Behavioral Resilience. Behavioral Resilience refers to an individual’s positive adaptability in the face of socioeconomic crises, significant life events, community crises, and psychological stresses (Bonanno, 2004). In recent research, the focus of behavioral resilience has shifted from individual resilience to resilience at community spatial scales or of social groups (Masten et al., 2004). In terms of national spatial planning, there is increasing emphasis on enhancing territorial functional resilience with a people-oriented and fine management demand orientation (Xiu et al., 2018; Zhou et al., 2019; Yang et al., 2021). Since the outbreak of the COVID-19 pandemic, there has been a renewed focus on studying public psychological resilience, with a particular emphasis on examining people’s resilience (Olsson et al., 2015).
Ecological studies have extensively discussed resilience, with a particular focus on ecosystem theories and states of equilibrium. Holling (1973) proposed that the resilience of an ecosystem determines its systematic persistence, defining resilience as the system’s ability to absorb change, accommodate disturbances, and maintain its functions. Building on this foundation, Perrings (2006) introduced a broader definition of resilience as the system’s capacity to withstand unexpected disturbances. From the perspective of research subjects, fields such as ecology and environmental science have concentrated on the resilience of natural ecosystems, gradually developing ecological and engineering resilience theories (Olsson et al., 2015).
As critical geographical units where human and natural ecosystems interact, cities confront uncertainties in ecological environments and socioeconomic development, underscoring the imperative to enhance urban resilience capabilities. The concept of the resilient city encompasses a comprehensive theoretical framework comprising infrastructure, institutional, economic, and social resilience perspectives (Cai et al., 2012; Jha et al., 2013). Research on resilient cities primarily focuses on enhancing a city’s capacity to restore its normal functions and structures in the face of environmental changes or unpredicted events while evaluating and optimizing its integrated resilience against risks (Li et al., 2014). In the post-pandemic era, resilient city research has primarily investigated the capacity of urban resilience to revert to a preimpact state or adapt to stable conditions after public health events or significant societal disruptions (Chester et al., 2021).
In the study of resilience, whether at the individual or city level, the key issue revolves around measuring and enhancing the subject’s capacity to adapt positively and adjust in response to negative disturbance. From an analytical perspective, resilience can be categorized into the recovery capacities of the supply and demand sides. For instance, social resilience reflects the ability of social policies and governance to help individuals overcome crises during major disasters or public health events, thereby representing supply-side resilience. In contrast, behavioral resilience reflects the reciprocal influence of individual recovery capabilities on social policies, governance, and the community environment. Based on the interplay between supply and demand, research on transportation resilience can also be divided into the supply and demand sides. However, existing studies have focused predominantly on the recovery capacity of transportation supply following significant disturbances, neglecting the resilience of the demand side (Bešinović, 2020). Previous research has identified three distinct phases in the resilience of transportation systems: a dramatic reduction, maintenance at a low level, and linear recovery (Persson et al., 2021). Conversely, the recovery process of transportation system demand exhibits more intricate variations when interacting with the supply side (Zhang, 2021), which is broadly related to the “travel behavior resilience” proposed here.

2.2 Conceptual theoretical framework

As a derivative demand stemming from residential life and socioeconomic activities, travel closely correlates with the level of socioeconomic development and has been steadily escalating in tandem with the rapid and interconnected advancement of transportation systems (Mokhtarian et al., 2015). Without any external influences, transportation supply and demand reach a stable equilibrium, as postulated by the theory of transportation supply and demand equilibrium (Holling, 1973; Hayes et al., 2019; Schwanen, 2021). If external stimuli, such as the construction of new transportation facilities or the closure of transportation systems due to faults, occur, this state of equilibrium will be disrupted. After adjustments on both the supply and demand sides, the system either returns to its previous state of equilibrium or establishes a new equilibrium. The recovery process on the supply side exhibits stepwise and incrementally increasing characteristics, akin to the resilience triangle in civil engineering. Consequently, resilience measurements on the transportation supply side often adopt a phased resilience triangle approach (Davoudi et al., 2013). However, the recovery process of residential travel demand is characterized by continuous fluctuations and intricate interplay with factors such as individual psychological adaptation, gradual relaxation of travel restrictions, restoration of social activities, and recovery or improvement of the transportation supply. Therefore, the concept of travel behavior resilience should include variations in travel intensity, the process of dynamic interaction with transportation supply, and the restoration to the initial equilibrium state or attainment of a new state.
From the perspective of externalities, these disturbances can be categorized as positive or negative (Table 1). Positive disturbances, such as major events or holidays, lead to an immediate surge in residential travel, which quickly reverts to the original equilibrium state after the disturbance ends, followed by a gradual increase. The influence of positive disturbances on travel willingness is generally flexible and promotes spontaneous growth in residential travel during such disturbances. In contrast, during negative disturbances, residential travel tends to show a significant downward trend, the duration of which varies in response to changes in the intensity of the negative disturbance. Following the cessation of such disturbances, residential travel gradually returns to its original equilibrium state or establishes a new equilibrium. Therefore, the recovery process following negative disturbances is more intricate than that following positive disturbances, necessitating a comprehensive examination of the equilibrium state between the transportation supply and demand sides. Moreover, the resilience of the travel demand side to adverse disruptions more accurately reflects the rebound capacity of residential travel.
Table 1 Categories and examples of disturbance and its influence on travel willingness
Disturbance feature Examples Travel willingness
Direction Duration Attributes
Negative Long Hard Private car restriction measures, Lottery systems for private vehicle license plates Passive restriction
Soft Advocacy for travel reduction during pandemic periods Spontaneous reduction
Short Hard Earthquakes, mudslides, and other natural disasters;
Lockdowns and home quarantine among pandemic
prevention measures		 Passive restriction
Soft Advocacy for travel reduction during severe weather
warnings		 Spontaneous reduction
Positive Long Soft Summer and winter vacations Spontaneous increase
Short Soft Major sporting and entertainment events Fluctuation
Periodic Soft Weekends and public holidays Spontaneous increase

Note: Negative disturbances are typically sporadic, with infrequent occurrences of periodic and regular negative disruptions; positive disturbances often serve as inducing stimuli, rarely resulting in significant impacts.

The characteristics of negative disturbances (Table 1) can be categorized into physical impacts (hard) and policy adjustments (soft). Hard disturbances include natural disasters, such as earthquakes and landslides, which result in disruptions to facilities and sudden halts in transportation operations. Soft disturbances include storm weather warnings and travel restrictions during pandemics. Based on the duration of impact, disturbances can be categorized as long-term, short-term, or periodic. Because negative disturbances are sporadic, they are typically nonperiodic or irregular in occurrence. For instance, while advisories urging urban residents to limit travel during a surge in COVID-19 cases can be regarded as long-term disturbances, travel restrictions imposed in locked-down areas and home quarantine measures are time-sensitive and therefore considered short-term disturbances. The former constitutes a soft disturbance, encouraging residents to voluntarily reduce their willingness to travel; the latter represents a hard disturbance, passively restricting their willingness to travel. Moreover, disturbances during the pandemic represent a combination of long- and short-term, hard and soft impacts, triggering passive travel restrictions and leading to a subjective reduction in residents’ willingness to travel to minimize exposure risk. The impact varies depending on the urgency of the event, weekdays/weekend, psychological willingness, travel purpose, and other factors. This complexity adds spatial heterogeneity and group differences to the recovery process of travel demand (Figure 1).
Figure 1 A theoretical framework of travel behavior resilience
Inspired by resilience studies in ecology, psychology, urban science, and transportation engineering (Holling, 1973; Bešinović, 2020; Zhang, 2021), we introduce the concept of travel behavior resilience based on the temporal characteristics of negative disturbances and the intricacy involved in recovering from residential travel. Travel behavior resilience is determined by travel demand (residential travel) preferences before a negative disturbance, experiences during the disturbance, and the real-time interactive recovery process with urban systems and transportation supplies after the disturbance. This refers to how residential travel returns to its original supply-demand equilibrium state or establishes a new equilibrium state following negative disturbances. In this context, travel behavior resilience research focuses on the travelers (individuals or groups), with particular emphasis on measuring their ability to recover travel demand levels prior to the disturbance or their capacity to attain stability during long-term coupling with such disturbances. The measurement principles of travel behavior resilience are as follows: (1) Measurement of travel behavior resilience should commence once the supply disturbance has stabilized, capturing the process and capacity of travel recovery after the transportation supply disturbance if there is a resource input. (2) The relative demand comparison entails measuring travel behavior resilience by comparing travel demand to the baseline level before the disturbance. In this context, the baseline level primarily represents travelers’ travel (demand) volume and spatiotemporal characteristics (groups) under normal circumstances. Assessing travel behavior resilience requires including both the extent of impairment and the duration required for recovery; specifically, given an equivalent degree of impairment, a longer recovery time indicates less travel behavior resilience. In summary, travel behavior resilience can be used to describe how residential travel interacts with disturbances, urban spaces, and transportation systems with a processual, continuous, and dynamic analytical framework.

3 Measurement methodology

3.1 Transportation system resilience measurement: from a single indicator to a
resilience triangle

The measurement of transportation system resilience can be classified into two streams. The first is “engineering resilience”, which focuses on the system’s ability to withstand and absorb disturbances and is characterized by metrics such as robustness (the capacity to maintain service level), bouncebackability (the capability to recover to predisturbance functionality), adaptability (the ability to transition to different states), and vulnerability (the extent to which it can withstand maximum disturbance). The second is socioecological resilience, which primarily focuses on the system’s flexibility and agility throughout the continuous adaptation process (Schwanen, 2021; Hayes et al., 2019). Flexibility refers to anticipated changes in response to disturbances, while agility represents the unexpected changes that occur. For any transportation system, the service level on the supply side can be denoted by S(x), where S0 represents the normal service level prior to negative disturbances and $\bar{S}$ represents the service level exhibited after negative disturbances. The meaning and criteria for these indicators are illustrated in Table 2. Furthermore, these indicators can also be applied to assess the level of travel demand. For instance, vulnerability refers to the maximum extent of disturbances that travel can endure, while travel behavior resilience focuses on the feedback mechanisms and recovery capabilities exhibited by individual (group) travel activities in response to disturbances.
Table 2 Indicators in the study of transport network resilience
Indicators Meaning Judgment criteria
Robustness Resisting negative disturbances to preserve the fundamental service levels of transportation systems Smin. $\bar{S}={{S}_{\text{min}}}$
Bouncebackability Bouncing back to a stable state prior to the negative disturbance, that is, the normal service level of the transportation system before the disturbance. $\bar{S}={{S}_{0}}$
Adaptability Resisting negative disturbances and adjusting to the maximum level of service that can be provided ${{\bar{S}}_{\text{max}}}$. $\bar{S}={{\bar{S}}_{\max }}$
Flexibility Responding to negative disturbances, exhibiting the anticipated level of service Sexp. $\bar{S}={{S}_{\text{exp}}}$
Agility Responding to negative disturbances, demonstrating unanticipated changes in service. $\bar{S}\ne {{S}_{\text{exp}}}$
Vulnerability The maximum degree of disturbance that can be resisted, and the level of disturbance when the service level is at its lowest. $\bar{S}=0$

Source: Compiled by the author. Herein, the normal service level of the transportation system prior to experiencing a negative disturbance is represented by S0, while the service level exhibited after the negative disturbance is denoted by $\bar{S}$.

The primary aim of measuring transportation system resilience is to quantify the level of threat posed by disturbances to the transportation system, assuming that the studied subject is typically in a state of equilibrium where the internal cycle is stable (Schwanen, 2021). The interaction between transportation supply and demand, following significant disturbances, transformations, and adaptations, typically reaches a new state of equilibrium. During the transition from a normal state to a new equilibrium, assessing flexibility and agility in transportation systems has emerged as a focal research question. Evaluating these attributes necessitates understanding the magnitude and impact of disturbances or their potential probabilities (Chester et al., 2021), employing measurement methodologies grounded in statistical testing and probability theory. Many studies have started from the perspective of transportation supply, using indicators such as the disturbance resistance capacity of transportation systems and the duration of recovery after emergency closures to measure transportation system resilience (Hayes et al., 2019; Chester et al., 2021). This research draws upon measurements from engineering resilience, applying theories from disaster management, operations research, civil engineering, and other fields, focusing on measuring the capacity of the transportation system’s supply side to maintain a certain level of service during disturbances and its ability to return to normal service levels. Transportation system resilience is gradually transitioning from relying on single, one-dimensional indicators to incorporating multiple indicators and comprehensive quantitative measurements. This shift reflects a processual and continuous trend in observing its performance.
By identifying critical inflection points in the transportation supply capacity (disturbance points, low capacity values, and recovery points), Bevilacqua et al. (2017) proposed a method to measure the resilience triangle of transportation systems. This approach simplifies intricate measurements into pivotal assessments, showcasing robust generalizability. Its primary application is in quantifying the resilience of supply chains. However, there remains a dearth of theoretical research on the dynamic interactive process between transportation supply and demand following disturbances. In contrast to disturbances from a supply-side perspective, which are typically distinct and quantifiable changes, the challenge in resilience research on the demand side lies in devising continuous measurement methods that focus on the dynamic interactive process of the supply and demand sides while also analyzing the characteristics of demand that frequently exist in a dynamic nonequilibrium state. Therefore, this paper presents a socioecological resilience measurement approach utilizing quantitative methods to crystallize the theory of travel behavior resilience, specifically focusing on demand-side resilience, and establishes a corresponding methodological framework.

3.2 Travel behavior resilience measurement

Travel behavior resilience is determined by the process of transportation supply change during disturbances S(st), the duration of the travel demand recovery process Δt, and the magnitude of travel demand change D(t). Therefore, the function of travel behavior resilience can be expressed as FR(S(st), Δt, D(t)), where R denotes the level of travel behavior resilience, and both S(t) and D(t) are time-varying functions.
When facing negative disturbances, changes in transportation supply due to differences in infrastructure conditions, operational and management models, and supply entities lead to various response mechanisms, which are mainly categorized into two types. (1) The first is restoration of transportation facilities until the level of supply is reinstated. When transportation infrastructure sustains damage, the transportation system undertakes repair and maintenance of the infrastructure’s physical network. For instance, road transportation systems exhibit spontaneous and self-organizing characteristics, and in areas affected by adverse disturbances, measures such as regional restrictions and temporary road closures are implemented until roads are restored. The supply changing S(st) in category (1) is often a phased function. (2) The adjustment of transportation organization and travel policies relies on the supply entity. For instance, government-led transportation systems, such as railways and public transportation, ensure the provision of essential services by adjusting transportation timetables to meet the minimum level of supply ($\bar{S}={{S}_{\min }}$), as shown in Table 2. In contrast, market-oriented supply entities, such as civil aviation, ride-sharing, and bike- sharing entities, adhere to this principle $\bar{S}={{\bar{S}}_{\text{max}}}$ (Table 2) when adjusting their flight schedules and resource inputs. This approach effectively balances service and demand while simultaneously reducing operational costs during negative disturbances. The schematic in Figure 2a presents a more intricate phased function. Overall, the period of change in transportation supply from the start of decline st1 to the moment the supply level returns to normal st3 is the cycle of transportation supply change. The moment when the supply level drops to the lowest value Smin is st2, and the change in transportation supply is $\Delta S={{S}_{s{{t}_{1}}}}-{{S}_{s{{t}_{2}}}}$, where ${{S}_{s{{t}_{2}}}}={{S}_{\min }}$.
Figure 2 Illustration of the travel behavior resilience calculation and inflection points
According to the function of travel behavior resilience, evaluating travel behavior resilience requires identifying three inflection points in travel demand D(t) for (Figure 2b): (1) The inflection point where residential travel experiences a significant decline due to disturbances, referred to as the decline point ${{D}_{{{t}_{1}}}}$; (2) The lowest point reached during the disturbance, namely, the lowest point ${{D}_{{{t}_{2}}}}={{d}_{\min }}$; and (3) The point after the disturbance has stabilized or been eliminated, where no significant increase in residential travel occurs, namely, the stable point ${{D}_{{{t}_{3}}}}$. Additionally, it is imperative to ensure that the inflection points in transportation supply do not precede those in travel demand, thereby incorporating the interactive process of supply and demand into the assessment of travel behavior resilience. Therefore, the identification methods for the three inflection points in evaluating travel behavior resilience can be summarized as follows: (1) The determination of t1 is based on the change from dD / dt > 0 to dD / dt < 0 in the travel demand function D(t), satisfying t1 ≥ st1; (2) t2 represents the moment when dD / dt < 0 changes to dD / dt > 0, satisfying t2 ≥ st2; and (3) t3 represents the moment when$\text{ }\!\!~\!\!\text{ }{{D}_{1}}\approx {{D}_{3}}$, satisfying t3 ≥ st3, indicating that travel demand has essentially returned to normal levels, as shown in Figure 2c. (4) If the negative disturbance persists long-term, t3 indicates the change from dD / dt > 0 to dD / dt = 0, as shown in Figure 2d, suggesting that travel demand cannot return to normal levels or represents a phase in the recovery process of residential travel. (5) Figure 2e illustrates the changes in travel demand during positive disturbances. The measurement of travel behavior resilience is relative to the level of residential travel volume before the disturbance d0, primarily using the current travel volume d(t) compared to the average level of the same period before the disturbance, that is, D(t) = d(t) / d0. This indicator allows for the dimensionless expression of different travel behavior indicators’ recovery status.
The concept of travel behavior resilience refers to long-term, dynamic changes in residential travel, which is considered a process variable. Therefore, calculus methods can be employed for the calculations (Figure 2c). Following the identification method for travel demand inflection points, the theoretical value of travel behavior resilience TS can be defined from the moment t1 when the disturbance initiates and travel declines until t3 when the disturbance stabilizes and travel recovers:
$TS=\frac{1}{\left( {{D}_{1}}+{{D}_{3}} \right)\left( {{t}_{3}}-{{t}_{1}} \right)/2-\mathop{\int }_{{{t}_{3}}}^{{{t}_{1}}}D\left( t \right)dt}$
In many cases, the continuous curve of residential travel demand D(t) requires high data continuity, making it challenging to calculate the theoretical value of $\int_{{{t}_{3}}}^{{{t}_{1}}}{D\left( t \right)}$. Moreover, Formula (1) is applicable to scenarios where travel demand does not recover to predisturbance levels, as shown in Figure 2d. Based on the three key points of measurement, the travel behavior resilience triangle (Figure 2b) is calculated as follows:
$T{{S}_{tri}}=\left( {{D}_{1}}-{{D}_{2}} \right)\left( {{t}_{3}}-{{t}_{1}} \right)/2$
Travel behavior resilience can be derived from the resilience triangle measurement with the following simplified formula:
$TS=2/\left( {{D}_{1}}-{{D}_{2}} \right)\left( {{t}_{3}}-{{t}_{1}} \right)$
Formula (3) shows that the smaller the value of travel behavior resilience, the less ability of residential travel to recover, necessitating longer periods and experiencing greater magnitudes of impact; the converse is also true.
For positive disturbances (Figure 2e), the theoretical value of travel behavior resilience is calculated using the following formula:
$TS=\frac{1}{\mathop{\int }_{{{t}_{1}}}^{{{t}_{3}}}D\left( t \right)dt-\left( {{D}_{1}}+{{D}_{3}} \right)\left( {{t}_{3}}-{{t}_{1}} \right)/2}$
According to the varying levels of research granularity in the travel demand function Dt(x), the assessment units for evaluating travel behavior resilience range from individual to group scales. The data collection requirement aims to ensure spatial coverage, the duration of the disturbance and the recovery process, enabling the capture of the three inflection points in the travel demand function Dt(x). Data sources for researching individual travel behavior resilience can include long-term tracking of activities such as smart card data and mobile payment records. In contrast, measuring the travel behavior resilience of mobility groups requires data that encompass socioeconomic attributes, such as student transit cards and airline platinum cards. Classifying data lacking explicit socioeconomic attributes can be conducted with spatiotemporal travel characteristics, such as the concentration of commuter groups during peak hours (Huang et al., 2018).

4 Case studies

The COVID-19 pandemic has emerged as an extensive and intricate dynamic disturbance to urban transportation in recent years. Its recurrent nature impeded the restoration of prepandemic travel behaviors, establishing a novel substable state (Schwanen, 2021; Davoudi et al., 2013). The study of travel behavior resilience contributes to examining transportation systems’ capacity to recover from negative disturbances and return to a preimpact state or readjust to a stable condition. Aligned with the emerging trend of people-oriented transport planning and resilience city research, this paper reports the application of travel behavior resilience measurement methods through two case studies. (1) Utilizing mobile phone signaling data, we investigate the residential travel volume recovery process in Beijing following the ‘Xinfadi’ market pandemic while analyzing the spatial heterogeneity of travel behavior resilience. (2) Utilizing smart card data, this study examines the recovery process of metro travel in Kunming city after the first wave of the pandemic outbreak as an example, clarifying the resilience of travel behavior for mobility groups (Wang et al., 2020). These two empirical case studies demonstrate the adaptability of travel behavior resilience measurement methods to different data sources, research granularity and city scales.

4.1 Spatial differentiation of travel behavior resilience in Beijing

As the measurement of travel behavior resilience involves the real-time integration of transportation supply, an analysis of group-based travel behavior resilience should include the spatial geographic units where these groups are located and explore the impacts of supply-side factors such as land use and transportation location (Zhao and Wan, 2020). Existing research suggests that the demand for green and open spaces has increased due to the higher transmissibility rates of the COVID-19 pandemic in enclosed areas (Zhang, 2020). Areas closer to outbreak sites exhibit slower recovery in resident travel as a result of changes in travel willingness and heightened control measures, indicating lower travel behavior resilience (Wang et al., 2020). This study utilizes mobile phone signaling data from February to September 2020, employing a grid size of 250 m*250 m in Beijing’s Xinfadi market, to investigate the impact and dynamic changes of the COVID-19 pandemic. The analysis focuses on the monthly volume of the origin-destination (OD) pairs between grids. As shown in Figure 2b, the change in travel demand (ΔD) is defined as ΔD = D3 - D1, where D3 represents the total volume of OD pairs in September 2020 and D1 corresponds to the month with the lowest volume between February and September 2020. The duration of travel demand recovery (Δt) is calculated as Δt = t3 - t1, where t3 denotes the month when the volume of OD pairs reaches D3. Therefore, ΔD /Δt serves as an indicator for measuring the rate of travel demand recovery. Based on both the magnitude of change in travel demand and recovery speed, four distinct categories are identified: (a) the first category exhibits small changes in the volume of OD pairs and a slow recovery speed; (b) the second category shows small changes in the volume of OD pairs but a fast recovery speed; (c) the third category experiences large changes in the volume of OD pairs with a slow recovery speed; and (d) the fourth category encounters both large changes in the volume of OD pairs and a fast recovery speed. Using this categorization method, the spatial units within the study area are classified based on thresholds determined by changes in travel demand and recovery speed, followed by kernel density clustering (Figure 3).
Figure 3 Spatial differentiation of travel behavior resilience according to kernel density analysis in Beijing (a. small variation with slow recovery; b. small variation with fast recovery; c. large variation with slow recovery; d. large variation with fast recovery)
Following the COVID-19 outbreak at Xinfadi in Beijing, the spatial heterogeneity of travel behavior resilience in the city can be categorized as follows: The first category primarily comprises areas with low travel volumes, where land use is less important in residents’ lives and has a limited influence radius. These areas include small street parks and a few leisure and entertainment venues. The second category primarily encompasses residential areas, representing the city’s core functional zones and exhibiting strong resilience and recovery capabilities in terms of travel behavior. The third category includes areas with dense transportation networks and advantageous locations, serving as vital links to other parts of the city. As depicted in Figure 3c, the third-category areas are predominantly concentrated within Beijing’s Fourth Ring Road and expand outward along the transportation network. The fourth category encompasses employment centers that exhibit robust travel behavior resilience, reflecting the city’s resumption of work and production. Overall, the spatial heterogeneity of travel behavior resilience is influenced by factors such as the built environment, land use patterns, transportation infrastructure locations, prepandemic travel volumes, outbreak site distribution, and control measures.

4.2 Sequential variations in travel behavior resilience by mobility group in Kunming

Based on the theory of travel behavior resilience, the spatiotemporal characteristics of daily travel significantly influence travel behavior resilience in the face of disturbances. In the analysis of travel behavior, temporal characteristics are captured through metrics such as average travel duration, total travel time, and trip frequency, while spatial characteristics are assessed using factors such as total travel distance, activity space, and the number and loca-
tions of visited places. In addition, the RTR denotes the proportion of observed individuals who resumed their travel activities after experiencing the pandemic. Figure 4 illustrates the recovery process of metro travel groups in Kunming after the initial impact of the COVID-19 pandemic. The results indicate that temporal characteristics of travel exhibit a faster recovery rate than spatial characteristics, suggesting greater resilience in terms of time rather than space (Wang et al., 2020). Moreover, the recovery of public residential travel is a long-term process. By September 2020, indicators such as the overall weekly travel distance and frequency for metro commuters in Kunming had returned to prepandemic levels; however, the recovery of activity space reached only 94.72% (Wang et al., 2020). Previous studies have indicated that residential travel tends to involve revisiting familiar locations rather than exploring new sites (Chen et al., 2021; Ecoffet et al., 2021). This implies a discernible pattern in residential travel behavior, wherein individuals typically rely more on familiar geographical spaces and consciously limit their spatial range following negative disturbances.
Figure 4 Research samples and travel behavior variations of mobility groups during the COVID-19 pandemic (2020 vs. 2019 monthly average levels)
Because travel willingness is an inherent component of travel behavior, travel behavior resilience is intricately linked to post-disturbance travel willingness (Mokhtarian et al., 2015). The retravel ratio of metro passengers decreased to 3.34% of the predisturbance level during the pandemic, as depicted in Figure 4, representing a substantial decline. After the pandemic stabilized, its recovery accelerated significantly compared to other travel behavior indicators. Moreover, due to differences in the urgency, fixed timing, and personal needs of travel, the recovery of travel willingness demonstrates varying levels of travel behavior resilience based on the purpose of travel. For instance, commuting travel exhibits significantly greater travel behavior resilience than travel for leisure and entertainment (Zhao and Wan, 2020).
Temporal and spatial differences in group travel behavior resilience can be attributed to variations in travel preferences resulting from individuals’ socioeconomic backgrounds and differences in travel demand (Zhao and Wan, 2020). Based on the travel demand change \curve depicted in Figure 4 and employing the travel behavior resilience evaluation method described in Section 3.2, Table 3 presents the calculated values for travel behavior resilience across different groups. Generally, the larger the value of travel behavior resilience, the smaller the area of the resilience triangle, indicating greater travel behavior resilience. Previous studies have demonstrated that the commuting group exhibits the highest spatiotemporal regularity in travel patterns and urgency, particularly for occupations associated with social security. Consequently, this group displays strong travel behavior resilience, as evidenced by a greater number of travel indicators returning to prepandemic levels. According to longitudinal comparisons of travel groups, the commuting group is the most resilient in terms of trip frequency. The student group demonstrated remarkable travel behavior resilience in terms of total travel distance and activity space due to the predominant influence of school and home addresses on their travel patterns. Once the pandemic is under control, students will need to resume regular attendance at school, thereby exhibiting even stronger resilience in spatial travel behavior. From the perspective of returning to prepandemic travel levels, older people exhibit lower travel behavior resilience due to the importance of minimizing exposure and mitigating infection risks.
Table 3 Travel behavior resilience values by mobility group between February and September
Mobility groups Traveled days Trip distance Activity spaces Visited Stations
Commuters 0.067 0.062 -(93%) 0.060
Elderly -(97%) 0.061 -(97%) -(97%)
Students 0.062 0.069 0.059 -(95%)
Others 0.060 0.061 -(94%) -(89%)

5 Conclusions and discussion

This paper integrates resilience research from diverse disciplines, including ecology, psychology, and systems engineering, to develop a conceptual theoretical framework and evaluation methods for travel behavior resilience. The theory of travel behavior resilience is grounded in the dynamic interplay between transportation supply and demand, and innovative mathematical models and calculus methods are used to identify critical inflection points. The key metrics for assessing travel behavior resilience include variations in transportation supply, the duration required for travel demand recovery, and the magnitude of changes in travel demand. This measurement model is applicable to both continuous observations of intricate fluctuations and resilience triangle measurements using key inflection points. Research on travel behavior resilience can effectively use multisource big data to assess the spatiotemporal dynamics and patterns of changes in residential travel during the post-pandemic era resulting from the dynamic interplay between supply and demand. This approach applies to various quantitative studies and provides theoretical and technical support for multidisciplinary resilience research. The case studies presented in this paper demonstrate that residents’ travel behavior resilience has three distinct temporal phases characterized by fluctuations that vary by group socioeconomic attributes. Furthermore, it is observed that travel behavior resilience displays spatial heterogeneity within urban spaces, which is closely associated with the functional attributes of spatial units. Overall, the more significant a location in socioeconomic activities, the greater the travel behavior resilience exhibited by related residents.
Resilience research will offer scientific support across diverse fields as China progresses toward high-quality modernization. In the future, resilience research must be further integrated into the foundational theories of geography, providing a plethora of theoretical and methodological insights into multiscale and multiperspective resilience studies. With a specific focus on travel behavior resilience, novel research endeavors could consider: (1) employing retrospective methods and simulation models to compare the spatiotemporal heterogeneity between the post-disturbance equilibrium of transportation supply and demand with the predisturbance equilibrium, thus delving deeper into the response mechanisms of transportation systems toward the new equilibrium; (2) examining the relationships among the spatiotemporal characteristics of travel behavior resilience, fine-scale traffic congestion and carbon emissions; (3) examining the intercoupling mechanisms of travel behavior resilience across different modes of transportation, such as the mutual influence between the travel behavior resilience of public transit and private cars; (4) investigating the spatiotemporal constraints on travel behavior resilience at different locations or for different travel purposes; and (5) examining the impact of residents’ travel behavior resilience on changes in urban spatial structure.

Sincere appreciation is extended to the anonymous peer reviewers for the time and effort they invested in reviewing this manuscript. The reviewers provided constructive suggestions for improvements on the conceptual theoretical framework, methodological model, empirical studies, and conclusions, from which this paper has greatly benefited. Furthermore, gratitude is expressed to our PhD student FAN Wenying for conducting the data analysis for the case study in section 4.1. Also, we would like to thank our PhD student HE Wanqin for her careful assistance in translation.

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