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Vulnerability and resilience of transportation systems: A
recent literature review
Shouzheng Pana, Hai Yana, Jia Hea,∗, Zhengbing Hea
aBeijing Key Laboratory of Traffic Engineering, Beijing University of Technology, Beijing, China
Abstract
With the development of integrated and intelligent transportation systems, the sta-
bility and security of system performance are highly emphasized. Resilience and
vulnerability are representative indicators in the performance analysis of trans-
portation systems. A large number of related studies have emerged in recent years.
Therefore, this paper reviews the recent progress in the study of vulnerability and
resilience. Specific definitions of resilience and vulnerability are first given from
the perspective of transportation system’s supply and demand. Other related con-
cepts of transportation system performance(TSP) are also discussed including reli-
ability, robustness, survivability and risk. The existing studies can be divided into
two aspects, i.e., the traditional topological structure and system structure analy-
sis. The study of topology structure mainly revolves around graph theory, which
is also the cornerstone of TSP research. In recent years, advances in data analy-
sis and model simulation technology have led to an increasing number of studies
considering the overall transportation system structure. The related metrics and
research methods are carefully analyzed and summarized from qualitative and
quantitative perspectives. Research challenges are discussed, and future directions
are presented.
Keywords: Resilience, vulnerability, transportation system, network performance
∗Corresponding author
Email address: hejia@bjut.edu.cn (Jia He)
Preprint submitted to Physica A: Statistical Mechanics and its Applications June 22, 2021
1. Introduction1
The transportation system, which is closely related to the social economy and2
people’s lives, is a large and complex networked system. A large number of par-3
ticipants are involved and encountered in the system, making it unprecedentedly4
complicated in structure and spatiotemporal evolution. As with most social sys-5
tems, the transportation system faces all kinds of risks and disturbances, and losses6
are considerable when system breakdown occurs. For example, the four-month-7
old bushfire in Australia caused countless traffic disruptions and flight cancella-8
tions. The most affected is the transportation infrastructure, which directly leads9
to network nonfunctionality and accessibility loss. Other emergencies, such as10
signal failures and power outages, result in high operating costs and increase the11
difficulty and inconvenience of traveling. A global COVID-19 outbreak in 2020 sig-12
nificantly reduced travel demand and increased the requirement for in-trip health13
protection, posing a considerable challenge in providing safe and reliable travel14
services. Therefore, it is particularly important to analyze both the internal com-15
position and the external dynamics of the transportation system and find the key16
components that play critical roles in guaranteeing the long-term stability of the17
transportation system and reliable performance at critical moments.18
For a long time, the most important concepts in the transportation system per-19
formance evaluation have included resilience, vulnerability, robustness, reliability,20
and survivability. These are all technical terms for assessing the security of system21
operation but differ in their main concerns and angles of view. Among them, the22
most relevant and representative concepts are vulnerability and resilience, which23
can cover almost the entire scope of transportation system performance (TSP).24
Therefore, this paper mainly summarizes the research progress of vulnerability25
and resilience in the field of transportation in recent years and proposes sugges-26
tions as a reference for researchers. Through a systematic review, we hope to pro-27
vide a comprehensive and easy understanding of the field for newcomers and of-28
fer reliable background information to professional researchers. In addition, the29
summary of research methods and discussion of research challenges will provide30
2
a stage for researchers and managers to think about key issues.31
Ten review articles are found in the existing literature. Among them, some32
mainly focus on the field of resilience. Beˇ
sinovi´
c(2020) reviewed research progress33
on the resilience of rail transit in the past 11 years, focusing on quantitative meth-34
ods and indicators. Leobons et al. (2019) summarized the resilience metrics of35
urban transportation systems and proposed a framework for the use of these indi-36
cators, while Hosseini et al. (2016) analyzed the resilience of the whole engineering37
system by dividing approaches into qualitative and quantitative assessments. In38
addition, the concepts and methods of research on the resilience of transportation39
systems in recent years have been discussed (Zhou et al.,2019b;Wan et al.,2018).40
Others consider more aspects, such as resilience and vulnerability. Mattsson and41
Jenelius (2015) summarized recent research on the resilience and vulnerability of42
transportation systems by distinguishing different modes of transportation. In the43
same year, they also summarized the concept and application of the vulnerability44
of road networks (Jenelius and Mattsson,2015). In contrast, Reggiani et al. (2015)45
discussed the differences and connections between traffic resilience and vulner-46
ability with connectivity as a bridge. Through a specific case, Gu et al. (2019)47
analyzed the similarities and differences among the reliability, vulnerability and48
resilience of the transportation network.49
In the above research, some analyzed one aspect of TSP or transportation modes50
(Hosseini et al.,2016;Beˇ
sinovi´
c,2020;Zhou et al.,2019b), some described the two51
concepts separately (Mattsson and Jenelius,2015). In particular, there are few sum-52
maries of research methods on resilience and vulnerability in recent five years.53
Therefore, based on the description of various concepts of TSP, this paper defini-54
tively summarizes the relationships, metrics and research methods of resilience55
and vulnerability. Finally, we discuss research progress and development trends56
for the future. With this review, we hope to clearly answer the following questions:57
Which concepts can reflect the performance of transportation systems? How are58
these concepts defined, and what is the relationship between them? Why do we59
choose to review studies on vulnerability and resilience? What metrics are used to60
3
quantify resilience and vulnerability, and how are they analyzed?61
The remainder of the paper is structured as follows. Section 2 introduces the62
methodology for this review. The related concepts of TSP are defined, and their63
interrelations are explained in section 3. Sections 4 and 5 separately describe the64
main research methods of traffic resilience and vulnerability in recent years from65
a topological and systematic perspective. The conclusion and opinions for future66
research directions are provided in Section 6.67
2. Methodology of literature review68
To provide a systematic review, we conducted extensive and rigorous litera-69
ture collection, including database keyword searches, core literature citations and70
literature screening. The specific steps are summarized in Figure 1. A bibliometric71
evaluation was carried out in the preparation phase. First, we used the well-known72
Web of science and Google Scholar databases to collect literature in related fields73
by searching the important keywords from the title, keyword and abstract and re-74
stricted the journal papers and conference papers from 2010 to 2020. Due to the75
problem of the retrieval mechanism, many irrelevant articles were included in the76
retrieval results. Therefore, we further checked the title and abstract of each arti-77
cle to exclude some irrelevant papers, such as power systems, signal systems, and78
bridge structural materials and finally selected 44 papers. Second, we identified79
many relevant cited papers in the process of literature reading, including some80
highly cited papers in journals with low impact factors. Similar to the snowball81
principle, we further collected a large number of important articles, and the time82
span also extended from 1960 to 2020. Eventually, there were approximately 14083
papers overall, including 59 studies in the field of resilience, 80 papers related to84
vulnerability and some comprehensive articles.85
Those papers were from more than 40 journals. We selected the top 15 journals86
by volume of publication as shown in Table 1. Most papers were published in the87
field of systems security and physics. Two of the top journals with the highest88
volume of publications are Transportation Research Part A and Reliability Engi-89
4
Figure 1: Literature review steps
neering and System Safety.90
Table 1: The top 15 journals sorted by the number of related publications
Rank Journal title Papers
1 Transportation Research Part A: Policy and Practice 19
2 Reliability Engineering and System Safety 13
3 Physica A: Statistical Mechanics and its Applications 8
4 Transportation Research Part E 6
5 Journal of Transport Geography 6
6 Transportation Research Record 5
7 Transportmetrica A: Transport Science 4
8 Transportation Research Procedia 4
9 Networks and Spatial Economics 4
10 International Journal of Disaster Risk Reduction 4
11 Transportation Research Part C: Emerging Technologies 3
12 Transportation Research Part B: Methodological 3
13 Safety Science 3
14 Physical Review E 3
15 Journal of Transportation Engineering, Part A: Systems 3
The thematic scope of this review focuses on passenger systems (including air,91
rail, and mass transit, expressways) in the transportation field, without consider-92
ing the vulnerability and resilience of cargo transportation networks or the analy-93
sis of individual lines or tools. This paper mainly summarizes the concepts, basic94
principles and research methods of papers from major journals and conferences in95
the past 10 to 20 years and discusses the current research gaps and challenges, as96
well as future directions.97
5
2.1. Distribution by year of publication98
To visualize the research trend of traffic vulnerability and resilience in recent99
years, we sort the number of relevant papers published in core journals from 2010100
to October 2020, as shown in Figure 2. It can be seen that research on traffic re-101
silience and vulnerability is increasing, among which the study of traffic resilience102
is more popular than that of vulnerability. The two fields achieved the same vol-103
ume of publishing in 2019. Therefore, we notice that more researchers are focusing104
on the analysis of the overall level of performance change in the transportation105
system after interference.
Figure 2: Annual publications from 2010 to 2020
106
2.2. Distribution by application fields107
In addition, the articles collected are divided into the following five types ac-108
cording to the mode of transportation: road, rail transit, waterway, multimode109
6
transportation and aviation. As shown in Figure 3, among the studies on the re-110
silience of transportation networks, the number of studies on road networks is the111
largest. As the basic transportation network, the road network is still the crucial112
research subject with more risks and the widest influence range. In the field of113
traffic vulnerability, research on rail networks is also one of the most common,114
which also shows that the development of rail traffic has attracted increasing at-115
tention from all countries. Furthermore, research on the combination of different116
modes of transportation is beginning to interest researchers, including subways117
and buses, subways and expressways, airlines and high-speed rail networks.
Figure 3: Number of papers from different fields
118
2.3. Classification of research methods119
Research on transportation vulnerability and resilience is mainly analyzed from120
qualitative and quantitative perspectives. Quantitative research methods can be121
divided into the following four categories. Relevant literature can be seen in Table122
3. Qualitative analysis is mostly used with review articles, see Table 2.123
• Traditional topology analysis. The topological structure plays a fundamental124
7
role in the operation of transportation systems and has always been the fo-125
cus of research. The majority of articles are on network vulnerability based126
on complex network theory, and those analyses are usually carried out in127
combination with the simulation method.128
• Mathematical-model optimization. The mathematical model, which is de-129
veloped from static to dynamic in the evaluation index considering traffic130
capacity to travel demand changes, and in the network model from a single131
transportation network to a multilevel combination, is currently the domi-132
nant research direction.133
• Simulation. Many researchers refer to simulation as a means of verification,134
such as simulating different interrupt scenarios, identifying vulnerable trans-135
portation system components and testing the effectiveness of various esti-136
mate indicators. Some papers used more than one method (e.g. Testa et al.,137
2015;Guidotti et al.,2017;Liao et al.,2018;Gauthier et al.,2018).138
• Approaches based on traffic data. The development of traffic datalization in139
recent years has become a new research trend for analyzing and verifying140
models by analyzing historical GPS data and passenger flow data. How-141
ever, the data-driven method is still in the exploration stage, and it mainly142
performs further analysis on the traditional topological method and mathe-143
matical model without a special evaluation index.144
8
Table 2: Qualitative analysis of transportation system performance
Reference Vulnerability Resilience Reliability Robustness
Husdal (2004)! !
Snelder et al. (2012)!
Reggiani et al. (2015)! !
Mattsson and Jenelius (2015)! !
de Oliveira et al. (2016)! !
Zhang and Zhang (2019)!
Berdica (2002)!
Tamvakis and Xenidis (2012)!
Reggiani (2013)!
Hosseini et al. (2016)!
Wan et al. (2018)!
Gu et al. (2019)! ! !
Leobons et al. (2019)!
Zhou et al. (2019b)!
Beˇ
sinovi´
c(2020)!
9
Table 3: Classification of research methods in transportation resilience and vulnerability
Quantitative method Resilience Vulnerability
Topological analysis
24%
Zhang et al. (2015), Testa et al. (2015),
Dunn and Wilkinson (2016), Wang et al. (2017),
Guidotti et al. (2017), Aydin et al. (2018),
Zhang et al. (2018)Chopra et al. (2016)
Holme et al. (2002), Angeloudis and Fisk (2006), Gao et al. (2019),
Wang and Rong (2009), Su et al. (2014), Ouyang et al. (2014),
Lordan et al. (2014), Deng et al. (2015), Yang et al. (2015),
Ma et al. (2020), Sun et al. (2015), Duan and Lu (2015),
B´
ıl et al. (2015), Zhang et al. (2016), Yin et al. (2016),
Candelieri et al. (2019), Sun and Guan (2016),
Lordan and Klophaus (2017), L´
opez et al. (2017),
Furno et al. (2018), Sun et al. (2018), Zhang and Yao (2019)
Model optimization
48%
Faturechi and Miller-Hooks (2014b), Li et al. (2019b)
Bhavathrathan and Patil (2015b), Liao et al. (2018),
D’Lima and Medda (2015), Jani´
c(2015), Jani´
c(2018),
Bhavathrathan and Patil (2015a), Lu (2018),
Soltani-Sobh et al. (2016), Chan and Schofer (2016),
Kim et al. (2015), Nogal et al. (2016), Cats et al. (2017),
Kaviani et al. (2017), Adjetey-Bahun et al. (2016),
Gauthier et al. (2018), Adjetey-bahun et al. (2016),
Calvert and Snelder (2018), Tang and Huang (2019),
Nabian and Meidani (2018), Guidotti et al. (2017),
Twumasi-Boakye and Sobanjo (2018)
Bell (2000), Bell (2003), D’Este and Taylor (2003), Hong et al. (2020),
Berdica and Mattsson (2007), Jenelius (2009), Chen and Li (2017),
Dinh and Thai (2011), Taylor and Susilawati (2012), Rose (2013),
Jenelius and Mattsson (2012), Knoop et al. (2012), Dinh et al. (2012),
Rodr´
ıguez-N ´
u˜
nez and Garc´
ıa-Palomares (2014)), Bell et al. (2017),
Cats and Jenelius (2014), Rupi et al. (2014), Ouyang et al. (2015),
Dinh and Thai (2015)), Jenelius and Mattsson (2015),
Version (2016), Fiondella et al. (2016), Ouyang et al. (2019),
Muriel-Villegas et al. (2016), Hong et al. (2017), Gecchele et al. (2019),
Chen and Li (2017), Starita and Scaparra (2020)
Bababeik et al. (2017), Xu et al. (2017), Bagloee et al. (2017),
Ye and Kim (2018), Xiao et al. (2018), Ye and Kim (2019),
Hong et al. (2019), Nogal et al. (2019), Lu et al. (2019),
Zhao et al. (2019), Zhang and Wang (2019), Li et al. (2019a)
Simulation
18%
Testa et al. (2015), Adjetey-Bahun et al. (2016),
Chen and Rose (2016), Voltes-Dorta et al. (2017),
Gauthier et al. (2018), Do and Jung (2018),
Liao et al. (2018), Gu et al. (2019), Aydin et al. (2018),
Ganin et al. (2019), Li and Rong (2019)
Jenelius et al. (2006), Lu and Peng (2011), Nian et al. (2019),
Knoop et al. (2012), Yang et al. (2015), Hong et al. (2015),
Kim and Yeo (2016), Kermanshah and Derrible (2016),
Singh et al. (2018), Cats and Jenelius (2016),
Data-based
10%
Zhu et al. (2016), Zhu et al. (2017), Zhang et al. (2019a)
Donovan and Work (2017), Mudigonda et al. (2018),
Chandramouleeswaran and Tran (2018),
Diab and Shalaby (2019), Ilbeigi (2019)
Kermanshah and Derrible (2016), Woodard et al. (2017),
Furno et al. (2018), Zhou et al. (2019a), Chen and Wang (2019)
10
3. Summary of related concepts145
Reliability, vulnerability, resilience and robustness are all important concepts in146
the evaluation of TSP. Therefore, this section summarizes the definitions of these147
categories and discusses the relationships between these concepts.148
3.1. Definition of vulnerability149
The concept of vulnerability first appeared in the disaster literature in the early150
1970s, and then it was introduced into other fields and the definition was con-151
stantly extended. In the late 1990s, vulnerability first emerged in the study of road152
networks, following the Kobe earthquake in 1995 (Lu and Peng,2011). Abrahams-153
son (1997) believed that the vulnerability of road networks is induced by minor154
accidents but causes large damage. For example, if the event is small, but it hap-155
pens at an important time or place, the damage will be magnified, which will af-156
fect the surrounding area and even eventually cause the entire network to crash.157
Later, Berdica (2002) and D’Este and Taylor (2003) further studied the vulnerabil-158
ity of road networks and proposed a widely accepted definition: susceptibility to159
unusual incidents that can result in considerable reductions in system serviceabil-160
ity. These events are difficult to predict and can be triggered passively or actively.161
Once this occurs, the system’s service capacity, which refers to the ability of net-162
work elements to operate normally within a certain period of time, will be greatly163
reduced.164
Then, D’Este and Taylor (2003) defined vulnerability from the perspective of165
network accessibility. When a small number of links to a network node are dam-166
aged, the accessibility of that node is greatly reduced, indicating that this point is167
relatively fragile. If extended to the whole network, the failure of a few lines leads168
to a decrease in the accessibility of a large number of nodes and the corresponding169
system function, which indicates that the network or system has a large connec-170
tive vulnerability. Snelder et al. (2012) linked vulnerability to the cost of loss and171
proposed that vulnerability refers to the increase in consequential costs caused by172
specific circumstances. Jenelius and Mattsson (2012) found that the impact of sys-173
11
tem disruption largely depends on the travel demand in the relevant area. Over-174
all, there has been no uniform definition of traffic vulnerability. We identified some175
representative definitions of traffic vulnerability in related papers, as shown in Ap-176
pendix 1. These definitions can roughly include three aspects: dangerous events,177
the system, and the influence of users. Hence, the essence of vulnerability is actu-178
ally the uncertainty of consequences for the system and users due to the occurrence179
of dangerous events. Therefore, we specifically provide a definition of transporta-180
tion system vulnerability from the perspective of supply and demand considering181
the impact of the system itself and its users:182
Definition 1: Abnormal sensitivity of transportation systems to internal or ex-183
ternal risk scenarios, which can result in a considerable reduction in system ca-184
pacity; The service quality of the transportation system is obviously decreased (in-185
cluding reduced accessibility and increased travel costs).186
3.2. The concept of resilience187
Resilience stems from the Latin resilire, which means to spring back or rebound188
to the original state after being compressed or disturbed. Holling (1973) later in-189
troduced resilience into the description of ecosystems to distinguish the concept of190
stability in ecological evolution, indicating the ability of the system to withstand191
shocks and maintain balance in the face of environmental changes. This term has192
since been applied to other fields, such as psychology, economics and engineering,193
and its concepts have been expanded and supplemented. Notably, resilience in194
ecology and engineering is a different concept. In ecology, the equilibrium state195
of the elastic system can be changed from one equilibrium state to another state196
after being disturbed. However, in the engineering field, the elastic system is197
concentrated in the vicinity of a certain equilibrium steady state (Holling,1996).198
Transportation resilience also belongs to the engineering field. The resilience of199
transportation systems was first defined by Murray-Tuite (2006), which can be di-200
vided into ten dimensions: adaptability, mobility, safety, and the ability to recover201
quickly etc. Then, a number of traffic-related concepts of resilience were devel-202
12
oped. The National Academy of Sciences (Ganin et al.,2019) defines resilience as203
”the ability to prepare for, absorb, recover from, and adapt to disturbances”. The De-204
partment of Transport in the UK (Diab and Shalaby,2019) defines traffic resilience205
from the perspective of transport capacity: ”the transport network is capable of bear-206
ing the impact of extreme weather, operating in such weather and quickly recovering from207
the impact”. From different angles, we can obtain different definitions of resilience.208
More definitions of traffic-related resilience are shown in Appendix 2. In summary,209
resilience means that the transportation system has the ability to resist external dis-210
turbances and threats, absorb the loss of internal turbulence, and finally, return to211
the original state.212
In addition, we find that most of those definitions are universal in the field213
of engineering, while few are proposed specifically for the field of transportation.214
Traffic resilience is mainly divided into static resilience (Rose,2007;Wang et al.,215
2014) and dynamic resilience (Jani´
c,2018;D’Lima and Medda,2015). Dynamic216
represents the speed of the system returning to a normal state after severe distur-217
bance, which is closely related to the change in users’ travel demand and system218
supply capacity. Static resilience emphasizes the ability of the system to maintain219
function and do not consider reconstruction activities and recovery. It focuses on220
meeting the users’ demand, which is often referred to as static economic resilience221
(Rose,2007). Therefore, combined with the actual dynamic characteristics, a spe-222
cial definition about TSP from the perspective of supply and demand is suggested:223
Definition 2: The abilities of the transportation system to resist and adapt to224
external disturbance and then quickly return to a normal service level to meet the225
original travel demand after being disturbed by internal or external factors.226
3.3. The relationship of related concepts227
In recent years, the research focus of transportation safety has expanded from228
traditional risk research to safety research, and developed towards resilience and229
sustainability (Wan et al.,2018). The development of the TSP assessment starts230
with considering a single line or station in the network and analyzing from the231
13
perspective of risk, including interference scenarios, occurrence probability and232
impact consequences. After that, it starts from the perspective of network security,233
including reliability, vulnerability and robustness. Now, the resilience, survivabil-234
ity and flexibility of the transportation system are studied from the perspective235
of system integrity. There are great similarities between these concepts, but the236
emphasis is different. Their common definitions are shown in Table 4.237
Table 4: Common definitions of related concepts
Concept General definition References
Reliability
Reliability can be defined as the probability that
the transportation network performs an accepted
level of service adequately in a confined time
interval, which can be divided into three
subconcepts: connectivity reliability, travel time
reliability, and capacity reliability.
Gu et al. (2019)
Soltani-Sobh et al. (2016)
de Oliveira et al. (2016)
Robustness
Robustness is the network’s capacity to maintain
its original service level in the presence of
incidents.
Snelder et al. (2012)
de Oliveira et al. (2016)
Survivability
Survivability is the ability to withstand sudden
disturbances to functionality while meeting
original demand and continue to perform its
intended function.
Faturechi and Miller-
Hooks (2014a)
Recoverability
Recoverability is related to understanding the
ability and speed of systems to recover after
a disruptive event.
Baroud et al. (2014)
Flexibility
or Adaptability
Flexibility is the ability of a system to respond
to shocks and adjust to changes through
contingency planning after disruptions.
Wan et al. (2018)
As the most widely used concepts, resilience and vulnerability are not simply238
opposite relations (Seeliger and Turok,2013), nor are they purely complementary239
relationships. It is more accurate to say that there are both intersections and dif-240
ferences. Traffic vulnerability represents the network’s sensitivity to emergencies,241
and it mainly analyzes the severity of incidents, generally from the perspective of242
network structure. Traffic resilience analysis includes two aspects: the system’s243
ability to absorb interference and to recover after being disturbed. It emphasizes244
the overall performance of systems from being damaged to returning to a normal245
state over a period of time, and the recovery time is one of the important indi-246
cators. This is generally considered from a systematic perspective. In terms of247
analysis difficulty, traffic resilience is more difficult to analyze than vulnerability248
14
(Reggiani et al.,2015). Combined with previous studies, we give some key words249
to describe the four concepts, which can help us better understand the categories250
contained in these concepts and their relations, as shown in Table 5.251
Table 5: Some keywords that describe related terms
Term Keywords
Resilience redundancy, resourcefulness, rapidity, strength and stability
Vulnerability riskiness, rareness, susceptibility, severity, accessibility and serviceability
Robustness tolerance, persistence, stability and resistance
Reliability probability, satisfaction, stability, certainty and predictability of travel conditions
Risk interference scenarios, probability and consequences
In addation, we present the dynamic relationship between these concepts(see252
Figure 4). Simple probabilities and consequences may not be very precise but they253
show the general trend. As shown in Figure 4, the abscissa represents the severity254
of the interference event (increasing gradually from left to right), and the ordinate255
represents the probability of the event (increasing gradually from bottom to top).256
For example, when the probability of system failure is high and the damage caused257
by the event is large, the system has low survivability and high risk of paralysis.258
In summary, there are differences and overlaps between the various concepts259
of TSP assessment. Vulnerability and resilience are the research hotspots in recent260
years and also the representative concepts of TSP. Therefore, we mainly review261
the research method and metrics on resilience and vulnerability in the following262
sections. According to different research methods, relevant papers in recent five263
years can be summarized in Table 6.264
15
Table 6: Remarks based on different research methods
Research methed Topic concerned References Remarks
Topological
structure Specific components Deng et al. (2015), Yang et al. (2015),
Sun et al. (2015), Yin et al. (2016)
Special components in transportation networks,
such as transfer stations and hubs, have
different effects on performance
Collection of elements
Sun and Guan (2016), L´
opez et al. (2017),
Gao et al. (2019), Duan and Lu (2015),
Lordan and Klophaus (2017)
The collection of different elements or research
objects in the network can reflect different
system performance
Redundancy and
recoverability
Aydin et al. (2018), Zhang et al. (2018),
Zhang et al. (2015), Testa et al. (2015),
Chopra et al. (2016)
The study of traffic elasticity includes not only
the network’s ability to absorb interference but
also its ability to recover after interruption
Topology intervention Zhang et al. (2016), Guidotti et al. (2017),
Dunn and Wilkinson (2016)
Optimization of network topology can effectively
improve the performance of the system
Accessibility
Taylor and Susilawati (2012),
Yang et al. (2016), Jiang et al. (2018),
Reggiani et al. (2015)
Accessibility is mainly from the user’s perspective,
such as the influence of path selection
behavior
Mathematical
model
Computational
efficiency
Ouyang et al. (2015), Muriel-Villegas et al. (2016),
Starita and Scaparra (2020), Bababeik et al. (2017)
Dinh and Thai (2015), Soltani-Sobh et al. (2016),
Version (2016), Xu et al. (2017)
Reducing computing costs is important for
modeling large networks, new models are
thus proposed
Game theory Bhavathrathan and Patil (2015a), Fiondella et al. (2016)A minimax optimization problem
16
Research methed Topic concerned References Remarks
Local network
Jenelius and Mattsson (2015), Ouyang et al. (2019)
Twumasi-Boakye and Sobanjo (2018),
Kaviani et al. (2017), Li et al. (2019b)
The impact of regional interruption on network
performance
Spatial-temporal
variation
Bagloee et al. (2017), Bababeik et al. (2017),
Ye and Kim (2018), Xiao et al. (2018), Hong et al. (2019)
The performance and index of the network are
spatiotemporal difference
Multilevel
transportation network
Adjetey-bahun et al. (2016), Zhao et al. (2019),
Adjetey-bahun et al. (2016), Ouyang et al. (2015),
Zhang and Wang (2019), Hong et al. (2020),
Jani´
c(2015), Li et al. (2019c), Hong et al. (2017)
Different traffic networks are interconnected,
which will lead to the propagation of faults
and, therefore, have different effects on the
overall performance of the network
Resilience index Mudigonda et al. (2018), D’Lima and Medda (2015),
Liao et al. (2018)
An elastic curve and elastic triangle are used
to analyze the resilience of traffic from the
geometrical angle
Connectivity Liao et al. (2018), Tang and Huang (2019),
Nabian and Meidani (2018)Bayesian network model, shortest path model
Simulation Basic map Kim and Yeo (2016), Kermanshah and Derrible (2016) Macroscopic fundamental diagram, intensity maps
Degree of interference Cats and Jenelius (2016), Chen and Rose (2016),
Gu et al. (2019)
Different degrees of interference will cause
different levels of line capacity reduction
Interrupted scenario
Hong et al. (2015), Kermanshah and Derrible (2016),
Hong et al. (2015), Singh et al. (2018),
Comes et al. (2020)
Different interruption scenarios and interference
types, such as natural disasters and deliberate
attacks
Historical data Voltes-Dorta et al. (2017), Ganin et al. (2019),
Do and Jung (2018), Singh et al. (2018), Nian et al. (2019)
Simulation of future scenarios based on historical
data
17
Research methed Topic concerned References Remarks
Date-driven Weighted network
Yang et al. (2015), Sun et al. (2015), Ma et al. (2020),
Yin et al. (2016), Zhou et al. (2019b),
Sun and Guan (2016)
Different travel data were used to construct
the weighted network
Natural disaster
Kermanshah and Derrible (2016), Zhu et al. (2016),
Mudigonda et al. (2018), Hong et al. (2015),
Singh et al. (2018), Chen and Wang (2019)
Effects of natural disasters such as earthquake,
hurricane and flood on traffic performance
Daily interruption
event
Khaghani et al. (2019), Erhardt et al. (2019),
Zhang et al. (2019a)
Daily events such as traffic congestion have
spatiotemporal characteristics and can cause
changes in network performance
Real-time monitoring Donovan and Work (2017), Ilbeigi (2019),
Chandramouleeswaran and Tran (2018)
Detection methods for different interference
events
18
Figure 4: Dynamic geometric relationship from the perspective of network interference
4. Topological structure: the cornerstone265
Early research on traffic resilience and vulnerability is mainly based on network266
topology. As a typical networked system, the basic performance of the transporta-267
tion system is determined by the topological characteristics of the network. There-268
fore, for a long time, research on network performance based on network topology269
has been developing continuously. Traffic vulnerability is the focus of the study,270
while resilience is more focused on the research of operational performance. Graph271
theory and complex network theory are the main methods for topology research.272
The steps include three elements of risk analysis: interrupted scenario, probability273
and event consequence. Specifically, the corresponding topology model is first es-274
tablished for a given transportation network, and then some specific attack modes275
are set to destroy the network. Finally, the vulnerability or resilience of the net-276
work is analyzed according to specific metrics and research methods, and the key277
components are identified . Therefore, this section summarizes the research on278
traffic resilience and vulnerability in recent years from three aspects: attack mode,279
metrics and research method.280
19
4.1. Description of interrupted scenarios281
In the real world, transportation systems face many unstable factors, and the282
degree of system breakdown induced by different factors is also different. Re-283
searchers usually study transportation systems as a network structure to facili-284
tate processing and maximize the approach to reality. Therefore,the possible in-285
terrupted scenarios are also simplified when modeling and analyzing, which are286
mainly divided into random attacks and malicious attacks. Random attacks mainly287
analyze the damage caused by natural disasters to the transportation network (B´
ıl288
et al.,2015). Malicious attacks are mainly man-made events such as terrorist at-289
tacks. In topological performance analysis, targeted disruptions are usually sim-290
ulated according to the importance in the network structure such as the node de-291
gree and betweenness (Zhang et al.,2016;Duan and Lu,2015;Sun et al.,2015).292
As shown in Table 7, researchers often use a combination of random and delib-293
erate attacks to conduct comparative studies, and a general conclusion is that the294
transportation network has good robustness in the face of random attacks but vul-295
nerability to malicious attacks based on certain principles, such as subway systems296
(Angeloudis and Fisk,2006), public transportation (Candelieri et al.,2019) and the297
urban road network (Duan and Lu,2015). In addition, some researchers intro-298
duced scenarios from other fields, such as the cascading failure mode (Zhao et al.,299
2004;Jenelius,2009;Candelieri et al.,2019;Ma et al.,2020). Due to the fixed ca-300
pacity of the network, traffic flow from surrounding components is redistributed301
when a point of interference failure results in more capacity overload causing a302
cascading failure. Candelieri et al. (2019) analyzed the changes in connectivity vul-303
nerability in cascaded failure scenarios, and found that different cascaded failure304
starting points affect the failure propagation speed. Due to numerous constraints305
and the large number of computations required for this scenario, it has not received306
much attention. How to establish a real and efficient cascade failure model is also307
an important topic for future research.308
20
Table 7: Disruption scenarios and topological metrics for transportation network
Performance Disruption scenarios Metrics References
Vulnerability
Components fully or
partially lose its
functions
Network efficiency Deng et al. (2015)
Random failures and
malicious attacks
Combination of degree and
betweenness Yang et al. (2015)
Exit of member
airlines
Normalized average edge
betweenness
Lordan and
Klophaus (2017)
Random node
disruption Network autocorrelation L´
opez et al. (2017)
Malicious attacks Cascading failure proportion Sun et al. (2018)
cascading failure
The average shortest path,
congestion degree, and
average passenger flow
intensity
Ma et al. (2020)
Resilience Capacity drop Average degree, diameter,
and cyclicity Zhang et al. (2015)
Monte Carlo simulation Giant Connected Component Aydin et al. (2018)
Targeted versus
random disruptions
Redundancy and fracture
coefficient Chopra et al. (2016)
Central attack and
proportion failure
The largest connected
component and the
shortest average path length
Dunn and
Wilkinson (2016)
4.2. Topological metrics for transportation network309
Metrics based on the topological structure can represent the size and change in310
the resilience or vulnerability of the transportation network before and after the in-311
terruption. Some representative indicators of recent years are summarized in Table312
7. Researchers tend to use a variety of different topological indicators for combina-313
tion or comparative analysis to reflect the performance of transportation systems314
more comprehensively. Dunn and Wilkinson (2016) used two topological indexes315
of the largest connected component and the shortest average path length to quan-316
tify the network resilience from the perspective of connectivity and performance.317
It is found that simply using the shortest average path length causes a large error.318
Wang et al. (2017) analyzed the relationships among various topological metrics319
and described the embodiment of different aspects of network robustness in the320
form of a radar map. Yang et al. (2015) proposed a combination index of degree321
and betweenness that can evaluate the system performance from the global and322
local scope. Ma et al. (2020) used three indicators, the average shortest path, con-323
21
gestion degree and average passenger flow intensity, to reflect the structural and324
functional vulnerability of the transportation network.325
In addition, most studies on traffic resilience focus on redundancy (Testa et al.,326
2015;Chopra et al.,2016) and recovery (Aydin et al.,2018). In addition to the above327
static indicators, researchers have been interested in analyzing the dynamic indi-328
cators related to the system operation level based on the topological structure in329
recent years. From the perspective of line operation, Sun and Guan (2016) pro-330
posed a comprehensive metrics of weighted mediation degree, weighted network331
efficiency and number of passengers considering the changes in passenger flow.332
They found that the circular topological form of lines has a great impact on pas-333
senger flows, which reflects the basic role of topology structure in the analysis of334
network performance. Sun et al. (2018) also considered the impact of traffic allo-335
cation and evaluated network vulnerability by cascading failure rates. Zhang and336
Yao (2019) proposed a comprehensive structure-state evaluation index by combin-337
ing network efficiency and betweenness considering the status of traffic flow. In338
addition, there are studies that consider changes in demand and supply, such as339
the role of travel demand in topology performance analysis (B´
ıl et al.,2015) and340
the impact of changes in traffic capacity (Zhang et al.,2015).341
4.3. Measurement approaches for topological performance342
Approaches to the topological structure are mainly based on graph theory or343
complex network theory. Through the analysis of topology characteristics (includ-344
ing degree, betweenness, shortest path, clustering coefficient and network effi-345
ciency), some failure strategies of traffic networks are simulated (random or delib-346
erate attacks) to determine the weak points of the system according to the change347
of metrics. This method is mainly applied to the analysis of traffic reliability and348
vulnerability, while the study of traffic resilience is limited. This article will present349
a specific summary from the following directions (see Table 6).350
Traditional studies of network vulnerability are mainly analyzed from the per-351
spective of nodes and edges. In recent years, more attention has been on the spe-352
22
cific characteristics of these components (Deng et al.,2015;Yang et al.,2015;Sun353
et al.,2015). Yang et al. (2015) proposed a method for calculating the failure prob-354
ability of transfer stations based on distance. They proposed that transfer stations355
in the subway network have different robustness levels from other stations. When356
a station fails, the failure conditions of the connected transfer stations are different.357
Considering the function of diversion and channeling of transfer stations, Sun et al.358
(2015) found that the nodes with the greatest influence on network connectivity are359
not necessarily the stations with the greatest passenger flow. Some metro trans-360
fer stations with high betweenness and centrality are equally important. How-361
ever, different calculation methods of betweenness (such as betweenness-based on362
shortest paths, k-shortest paths and passenger flow) result in different rankings of363
importance (Yin et al.,2016;Sun and Guan,2016). Their differences need further364
study.365
Of course, considering only a single component is not comprehensive. Some366
researchers have analyzed the interaction of components and traffic vulnerability367
under the aggregation of elements. Sun and Guan (2016) analyzed the vulnerabil-368
ity of a weighted network from different line operation levels. L´
opez et al. (2017)369
considered the autocorrelation of network flows by using Moran’s I and found370
that the vulnerability of nodes increases with the global autocorrelation. Unlike371
physical networks, topology shape also has an effect. Gao et al. (2019) considered372
the geometric characteristics of regions to analyze the vulnerability of the network373
using a discrete Ricci curvature. Combined with the actual situation, Lordan and374
Klophaus (2017) analyzed the vulnerability caused by alliance interruptions in the375
aviation network from the perspective of group nature. Duan and Lu (2015) further376
established three different types of segment-based, stroke-based and community-377
based topology models and analyzed the robustness of networks with different378
granularity in the case of traffic interruption. The results also demonstrate the im-379
portance of topology in affecting network performance.380
The study of traffic resilience should not only consider the network’s ability to381
absorb interference but also analyze its ability to recover(Aydin et al.,2018;Zhang382
23
et al.,2019b;Clark et al.,2018). Zhang et al. (2015) analyzed the impact of two pre-383
paredness and three recovery actions on network resilience. They found that the384
higher the redundancy of the network is, the better the resilience of the network,385
while recovery actions are more effective than improving redundancy. The change386
in the node redundancy rate under network interruption was also analyzed (Testa387
et al.,2015). Chopra et al. (2016) considered the changes in the edge redundancy by388
calculating the number of connected node pairs before and after an edge failure.389
In addition, there are studies on changing the network topology to improve the390
system’s performance. To improve the connectivity and reliability of the network,391
Zhang et al. (2016) used the nearest-link method to carry out topological interven-392
tion on the transportation network and simulate the addition of lines to improve393
the redundancy of the system. Dunn and Wilkinson (2016) adopted ‘adaptive’394
and ‘permanent’ strategies to increase network resilience by changing topological395
structures. It may also involve a trade-off between the cost of construction and the396
resilience of recovery (Renne et al.,2020). Other ways to add nodes can not only397
increase the accuracy of the measurement, but also increase the computational cost398
(Guidotti et al.,2017).399
Furthermore, many scholars applied network vulnerability to other areas, such400
as accessibility (Taylor and Susilawati,2012), and understanding the concept of401
network resilience and vulnerability from the perspective of accessibility (Reggiani402
et al.,2015;Yang et al.,2016;Jiang et al.,2018). These methods focus on the analysis403
of travel costs and influences of the user’s choice behavior after the network is dis-404
turbed. It can also be used to analyze the vulnerability of the evacuation network405
in the case of disaster, which is very effective for the site selection of emergency406
facilities and service facilities under fragile conditions (Zhang and Zhang,2019;407
Sriram et al.,2019).408
5. Model and data: a leading role409
Compared with traditional topology analysis, the methods based on mathe-410
matical models and data-driven models can more truly reflect the changes in sys-411
24
tem performance, which has attracted the attention of an increasing number of412
researchers. Another important approach, the simulation method, also uses his-413
torical data to simulate different failure scenarios to analyze the change in TSP.414
The mathematical model, simulation and data-driven method are collectively re-415
ferred to as system structure-based performance analysis. They mainly consider416
the impact of dynamic travel demand and supply on traffic vulnerability and re-417
silience. Next, we summarize the metrics and three main research methods based418
on the system structure.419
5.1. Metrics based on system performance420
The metrics based on system structure are different from the pure topological421
indicators, and the results of the evaluation of important nodes are also different422
(Gauthier et al.,2018). In general, its metrics mainly include changes in travel423
costs (Nian et al.,2019;Gauthier et al.,2018;de Oliveira et al.,2016), accessibility424
(Lu and Peng,2011;Kermanshah and Derrible,2016), travel delays (Knoop et al.,425
2012;Ganin et al.,2019;Gauthier et al.,2018;Adjetey-bahun et al.,2016) and per-426
formance index.427
The metrics based on travel costs mainly include travel time, distance and loss428
cost. From the perspective of game theory, Fiondella et al. (2016) used the net-429
work’s expected cost as the vulnerability assessment indicator. Soltani-Sobh et al.430
(2016) proposed a generalized line cost as a performance indicator, considering431
factors such as network topology, demand balance and travel cost. Gauthier et al.432
(2018) defined a travel cost by combining travel time and distance to evaluate the433
importance of a route.434
In addition, metrics based on accessibility are usually considered from the per-435
spective of users. For example, Ouyang et al. (2015) used daily accessibility to an-436
alyze the vulnerability of a comprehensive transportation system, indicating the437
ratio of travelers from a given node to other nodes using multiple transportation438
modes on a typical day. However, these metrics do not consider the impact of439
dynamic changes in passenger flow. This affects the accuracy of the accessibil-440
25
ity analysis. Then, Hong et al. (2017) calculated the topology-based accessibility,441
travel range-based accessibility and time-based accessibility on the basis of pas-442
senger transfer preference .443
Travel delay is also an important index in the TSP evaluation. Adjetey-bahun444
et al. (2016) used the changes in passenger delay and passenger volume as met-445
rics. Voltes-Dorta et al. (2017) adopted the total travel delay after node failure446
as the importance basis and combined the actual demand data with the simula-447
tion model to reflect the change in system performance more truly. Ganin et al.448
(2019) evaluated the system’s delay in different regions and scenarios. Hong et al.449
(2019) further refined the interrupted scenario and proposed a time-related dam-450
age scenario considering the occurrence time and duration in the interruption. In451
addition, Knoop et al. (2012) used total travel time as the TSP evaluation standard452
and proposed comprehensive metrics by linear fitting of multiple vulnerability in-453
dexes. D’Lima and Medda (2015) used the rate at which the number of passengers454
returned to normal as metrics to study the diffusion effect brought by disturbance455
on a subway system.456
At present, there are only a few metrics based on the vulnerability index that457
mainly focus on central nodes and hub nodes (Ye and Kim,2018;Yang et al.,2015).458
Although quantitative analysis of traffic vulnerability can be realized, more inputs459
need to be considered, and the model is complicated and costly to calculate. Ye460
and Kim (2018) used a degree of nodal connection (DNC) index to assess the con-461
nectivity vulnerability of the central node effectively. Yang et al. (2015) proposed462
a weighted composite index, which can reflect the system’s performance changes463
more comprehensively and is easy to calculate. In addition, Kim and Yeo (2016)464
proposed an MFD-based vulnerability index based on the macro basic graph and465
analyzed the vulnerability of urban road systems from the perspective of operating466
speed. These indicators are currently scattered and reflect different performance.467
A comprehensive indicator may enable researchers to better evaluate the perfor-468
mance of the resilience and vulnerability of the transportation system (Sun et al.,469
2020)470
26
5.2. Optimization of mathematical model471
The method based on a mathematical model mainly calculates the change in472
network cost by considering the dynamic travel demand and changes in passenger473
flow. It can more accurately assess the vulnerability and resilience of the network474
but requires many simulations and functional calculations, which cannot currently475
be applied to large-scale networks. See Table 6for specific classification.476
Therefore, many studies focus on improving the computational efficiency of477
models. Traditionally, the enumeration method has been used to establish a math-478
ematical model for the retrieval of important parts of transportation networks in479
the study of traffic vulnerability. Ouyang et al. (2015) used a genetic algorithm480
to retrieve important parts of the transportation network, which is more accurate481
and cheaper than the traditional enumeration method (Muriel-Villegas et al.,2016).482
Bababeik et al. (2017) and Xu et al. (2017) transformed the bilevel model into a483
single-layer mixed-integer linear programming model for solving, which improves484
the computational efficiency. In the analysis of travel costs, Starita and Scaparra485
(2020) adopted a customized version of the customer-randomised adaptive search486
procedure and proposed a user equilibrium-based interdiction model considering487
the impact of congestion. Soltani-Sobh et al. (2016) established a generalized travel488
cost model based on the Bureau of Public Roads (BPR) function considering the489
uncertainty of travel demand and supply after disasters. The results showed that490
the variation in travel time can greatly affect the reliability of transportation sys-491
tems. Dinh and Thai (2015) combined simulated annealing, variable neighborhood492
search, and spectral clustering to obtain the minimum network loss cost.493
The ideas of game theory are often used in mathematical models of transporta-494
tion systems. Considering the change in traffic capacity, Bhavathrathan and Patil495
(2015a) established a system interruption as a minimum-maximum optimization496
problem and used a two-space genetic algorithm to quantify the traffic resilience.497
System resources are limited, and it is impractical to comprehensively protect the498
transportation system. Only by selectively protecting some important components499
can we effectively reduce system vulnerability. Fiondella et al. (2016) combined500
27
game theory with a genetic algorithm to allocate limited resources, which effec-501
tively reduced the system’s vulnerability. Lu et al. (2019) also used game theory502
to analyze the vulnerability of evacuation networks under natural disasters. A503
heuristic-based algorithm using the method of successive averages was proposed504
by considering link risk and route choice, as in Equation 1. However, the author505
did not consider the influence of time-based dynamic evacuation behavior on path506
selection, which needs further discussion.507
minpmaxqTC(p,q) = ∑
j∈E
∑
i∈E
qj·pi·ti,j(1)
where pand qare link choice probabilities and failure probabilities, respectively. t508
is the travel cost. In the analysis of large transportation networks, researchers usu-509
ally analyze only regional networks due to the high computing cost. Jenelius and510
Mattsson (2015) analyzed the impact of regional interruptions on network vulnera-511
bility by means of grid division. However, the size of the actual interrupted area is512
irregular and closely related to the surrounding population and geographical fac-513
tors. Ouyang et al. (2019) further analyzed network vulnerability under regional514
failure and proposed three regional failure models. Twumasi-Boakye and Sobanjo515
(2018) evaluated the resilience of regional networks and proposed a method for516
identifying high-impact zones according to the mean link speed. In addition, to517
improve the computational efficiency, Kaviani et al. (2017) proposed a bilevel opti-518
mization model that is solved through both a relaxation optimization method and519
a heuristic method. To solve this kind of model, Li et al. (2019b) also designed a520
new algorithm that combines a genetic algorithm and the Frank-Wolfe algorithm.521
The change of transportation system resilience is dynamic. It is a good choice522
to study from the perspective of space-time difference, including separate spatial523
differences (Bagloee et al.,2017;Ye and Kim,2018) and analysis of temporal dif-524
ferences (Xiao et al.,2018), as well as a combination of the two. Spatial differences525
include interruption area, interruption level, etc. The influence of dynamic pas-526
senger flow was the main factor for time difference. In order to analyze the link527
28
vulnerability under different disruption scenarios, a time-space flow model was528
used to simulate flow changes (Bababeik et al.,2017). Hong et al. (2019) analyzed529
the variation in the importance of stations due to the temporal and spatial differ-530
ences in passenger flow. Lu (2018) analyzed the network resilience under different531
delay times. The results all show that the time-related attributes have an important532
impact on traffic vulnerability.533
As a complex transportation system, the analysis of only one kind of trans-534
portation modes is often incomplete. Adjetey-bahun et al. (2016) considered the535
interdependence of multiple subsystems (transportation, power, telecommunica-536
tion and organization subsystems). In addition, some studies divided the same537
network into multiple layers to analyze the influence of fault propagation among538
different networks. Jani´
c(2015) proposed a framework for analyzing the vulner-539
ability and resilience of a multilayer aviation network. By dividing the airline540
network into three layers, Zhao et al. (2019) analyzed the impact of fault transmis-541
sion between different networks. Hong et al. (2020) also analyzed the vulnerability542
of two-layer networks from the time-varied accessibility angle. Furthermore, dif-543
ferent transportation systems are found to be complementary to each other, and544
they are usually more robust than a single system. Ouyang et al. (2015) proposed545
an analysis method of the complementary relationship between different trans-546
portation networks. The study found that the complementary relationship be-547
tween different transportation systems could improve the strength of the whole548
system, and there were the same key nodes among different networks. Hong549
et al. (2017) established a vulnerability assessment model of urban complementary550
public transportation system considering passengers’ intermodal transfer distance551
preferences. Cats et al. (2017) provided a metric for performance analysis of differ-552
ent network combinations, the level of capacity decline. Li et al. (2019c) proposed553
a method of key region identification, and found that the vulnerability changes554
of different subsystems and important regions are different. At the same time,555
the importance of components is related to the economy and population density556
of the region. In addition, there are comprehensive performance studies between557
29
transportation networks and other systems such as power grids (Ulak et al.,2021).558
The study of the resilience index is also an important method that uses elastic559
change curve, such as the elastic triangle method (Mudigonda et al.,2018). D’Lima560
and Medda (2015) adopted a mean regress random model to conduct quantitative561
analysis on the recovery speed of system performance. According to the elasticity562
curve, Liao et al. (2018) proposed a resilience index (RI) considering a variety of563
properties (such as redundancy and recovery), as shown in Equation 2). It repre-564
sents the expected mean of the ratio of the area between actual performance curve565
and timeline to the area between the target performance curve and timeline over a566
given period of time. AP(t)and TP(t)are the actual performance and target per-567
formance function curves, respectively, and Trefers to a given time interval from568
the disaster occurrence to the complete restoration of the TSP.569
RI =E
T
Z
0
AP(t)
TP(t)dt
(2)
Twumasi-Boakye and Sobanjo (2018) then improved the algorithm according570
to the recovery time and state (Equation 3).571
Rk=1−1
¯
TZTmod
0h1−φp(h)
k(t)idt +ZText
Tmod h1−φp(h)
k(t)idt +ZTcomp
Text h1−φp(h)
k(t)idt(3)
Tmod is the time for restoring moderately damaged infrastructure in days, Text is572
the time for restoring extensively damaged infrastructure in days, Tcom p is the time573
for restoring completely damaged infrastructure in days, ¯
Tis the mean time for574
network recovery in days, and φrepresents the performance measure for indicator575
kfor each damage state h.576
In addition, there are also suggestions that TSP be analyzed from the perspec-577
tive of connectivity (Liao et al.,2018;Tang and Huang,2019;Nabian and Meidani,578
2018) and accessibility (Lu,2018;Nogal et al.,2019;Ye and Kim,2019). The main579
methods include the Bayesian network model (Tang and Huang,2019), shortest580
path model (Ye and Kim,2019), impedance model (Lu,2018) and deep learning581
(Nabian and Meidani,2018;Sriram et al.,2019).582
30
5.3. Method based on simulation583
Generally, this method is mainly to simulate different interrupt scenarios. It can584
be divided into several research directions, as shown in Table 6. Methods based on585
network topology structure often combine simulation methods to carry out the586
analysis of simulation scenes by simulating the transportation system affected by587
random failures and malicious attacks(Li and Rong,2019). Finally, the changes588
in topological indicators are measured to identify the important components of589
the transportation network (Yang et al.,2015). In addition, simulation analysis is590
usually used to study the effectiveness of evaluation models or metrics. Based on591
Monte Carlo simulation, Hong et al. (2015) analyzed and verified the proposed592
vulnerability metrics in different interrupted scenarios. This method is also often593
used in the analysis of natural disasters (Kermanshah and Derrible,2016;Hong594
et al.,2015;Singh et al.,2018), which is characterized by low occurrence probabil-595
ity and high consequences, and there’s not enough real-world data. In this regard,596
Zhang et al. (2013) established a micro simulation model of a highway network,597
which can carry out quantitative analyses on evacuation performance of large re-598
gional network under different conditions.599
Traditional evaluation methods of TSP are based on changes in travel time and600
distance, which are complex to build models. Kim and Yeo (2016) proposed an601
effective real-time monitoring method of road network status by using the concept602
of the macro basic map, and eight different simulation scenarios are set to observe603
the MFDs in different cases. Kermanshah and Derrible (2016) then simulated the604
impact of earthquakes based on intensity maps and provided a vulnerability as-605
sessment method with multiple , including travel demand and accessibility. All606
of these methods can analyze the complex changes of system performance simply607
and efficiently.608
In practice, different degrees of interference have different effects on transporta-609
tion systems. Some components will not be completely interrupted after being610
damaged. Therefore, Cats and Jenelius (2016) simulate different decline levels of611
line capacity and use a nonequilibrium dynamic assignment model to analyze the612
31
degree of their influence. Computable general equilibrium (CGE) analysis is usu-613
ally used for macroeconomic simulation modeling. Chen and Rose (2016) devel-614
oped a multimodal CGE framework to investigate traffic resilience from an eco-615
nomic perspective. Gu et al. (2019) used normal and uniform distributions to616
simulate the decline in line capacity at different rates and performed a compar-617
ative analysis of the reliability, vulnerability and resilience of the transportation618
network. At each capacity ratio, the analyses were conducted in 100 random fluc-619
tuation scenarios. The differences of recovery levels in different regions have also620
been studied under the same destruction scenario. After disasters, metropolitan621
areas with high socioeconomic level have stronger coping capacity and faster re-622
covery speed (Yabe et al.,2020).623
Simulation of TSP based on historical data can identify vulnerable points of624
the network and provide guidance for practical management. Voltes-Dorta et al.625
(2017) simulated the impact of airports closure on transportation networks based626
on historical passenger flow data and analyzed the traffic vulnerability from the627
perspective of passenger delay. Do and Jung (2018) used GIS data and OD data to628
carry out a macro and micro simulation of the differences in interruption scenarios629
and recovery levels. Research showed that recovery efficiency and maintenance630
costs are not linearly related. In addition, the simulation analysis is of great signif-631
icance for the planning and construction of routes in the transportation network632
(Nian et al.,2019). Some simulation tools have been used, as shown in Table 8, to633
evaluate traffic resilience or vulnerability.634
Table 8: Simulation analysis tools based on system performance
Metrics References Tools
Vulnerability Hong et al. (2015) GIS technology
Kim and Yeo (2016)The 7.0 version of the AIMSUN
program (TSS, 2012)
Kermanshah and
Derrible (2016)
Geographic Information
Systems (GIS)
Singh et al. (2018) ArcGIS and The MIKE 21
Nian et al. (2019) GIS package
Cats and Jenelius (2016) C++
Resilience Do and Jung (2018) TransCAD 5.0 and GIS
32
5.4. Data-driven methods635
A typical application of data-driven approaches is to construct a weighted net-636
work with travel data based on the network topology structure and conduct a dy-637
namic evaluation of TSP based on new metrics (Yang et al.,2015;Sun et al.,2015;638
Sun and Guan,2016;Yin et al.,2016;Zhou et al.,2019a;Ma et al.,2020). Table 6639
shows the main research directions of the method. Compared with the traditional640
statical analysis of topology that cannot reflect the real operation status and charac-641
teristics, data-driven methods can solve this problem well. Among them, passen-642
ger flow is the key factor of traffic vulnerability (Sun and Guan,2016). Chopra et al.643
(2016) found that the intensity of passenger transport follows a power-law distri-644
bution, thus showing the robustness characteristics of a similar topology. Here,645
some representative data-driven studies are categorized and summarized in Table646
9.647
Typical data types are mainly derived from transportation systems affected by648
natural disasters, including earthquakes (Kermanshah and Derrible,2016), hurri-649
canes (Zhu et al.,2016;Mudigonda et al.,2018), floods (Hong et al.,2015;Singh650
et al.,2018) and extreme weather (Chen and Wang,2019). Kermanshah and Der-651
rible (2016) used USGS ShakeMaps to determine the interrupted areas caused by652
earthquakes. Among them, researchers mostly use floating vehicle data for anal-653
ysis. Zhu et al. (2016) analyzed the spatiotemporal variation in posthurricane re-654
covery performance with the help of historical traffic data and the recovery curve.655
Mudigonda et al. (2018) used multisource data to analyze the resilience of public656
transportation systems. Resilience triangles were also used to analyze the network657
recovery efficiency, which shows that the recovery of road infrastructure is much658
faster than that of rail transit. Combining the operation data and weather data of659
aviation and high-speed railways, Chen and Wang (2019) found that the opera-660
tion delay caused by severe weather differs in time and space between different661
transportation systems.662
In addition to natural disasters, data-driven approaches can be used to analyze663
daily interruption events. Khaghani et al. (2019) analyzed the impact of traffic con-664
33
gestion during rush hours on the resilience of road networks using GPS data of665
large taxis. In addition, the diversity of regional transportation systems will in-666
crease the resilience of corresponding travel networks. However, this may lead667
to a decrease in the travel time reliability of the road network, and residents need668
to reserve more time to arrive at their destinations on time (Erhardt et al.,2019).669
Starting from the spatial-temporal characteristics of traffic congestion, Zhang et al.670
(2019a) quantified resilience into the size of the congestion cluster. They found that671
the resilience and recovery time of the transportation systems of different cities672
both follow a scale-free distribution, which is related to the spatial-temporal distri-673
bution and duration of congestion. This is helpful for understanding the impact of674
changes in demand and supply, such as traffic congestion and system failure, and675
provides a new perspective for the study of the resilience of urban road networks.676
Data-driven methods are also used for the detection of daily interference events.677
Donovan and Work (2017) proposed a method to identify interrupting events in678
transportation systems only with coarse-grained GPS data. Chandramouleeswaran679
and Tran (2018) also proposed a detection method of extreme anomaly events, the680
Mahalanobis distance, and analyzed its impact from the perspective of system re-681
silience. Ilbeigi (2019) proposed a real-time quantitative monitoring network based682
on the trajectory data of the abnormal state method, the CUSUM statistical process683
control chart. The resilience and recoverability of the system were also evaluated684
at different scales through the analysis of real-time changes in closeness centrality.685
However, there are many interference factors that can cause performance changes.686
How to distinguish different types of interference according to various traffic data,687
as well as the triggering factors that cause system failure is a topic for future re-688
search. And whether these factors will cause changes in other evaluation indexes689
is also an important direction for future research.690
6. Discussion and future directions691
The research on the resilience and vulnerability of transportation systems in re-692
cent years is reviewed from the theoretical level. They also have important guiding693
34
Table 9: Typical datasource
References Network Type Datasource Performance
Kermanshah and
Derrible (2016)Road networks
ShakeMaps and Longitudinal
Employment Household
Dynamics (LEHD) data
Vulnerability
Woodard et al. (2017) Road network Mobile phone GPS data Reliability
Zhou et al. (2019a)Air transport
networks
The data of routes being
operated by all the
airlines
Robustness
Chen and Wang (2019)High-speed rail and
aviation network
On-time performance records
of HSR and air services,
weather conditions
Vulnerability
Zhu et al. (2016)Road and subway
network
Taxi trips and subway
turnstile ridership
Resilience and
recoverability
Donovan and Work (2017) Road network Taxi GPS data Resilience
Mudigonda et al. (2018)Public transit
networks
Various infrastructure,
traffic and transit data
Vulnerability
and resilience
Chandramouleeswaran
and Tran (2018)
Air Transportation
Network Flight data Resilience
Zhang et al. (2019a) City road networks Traffic GPS data Resilience
Diab and Shalaby
(2019)Rail transit system Metro system
interruption data Resilience
Ilbeigi (2019)Transportation
network Taxi GPS traces Resilience and
recoverability
Wu et al. (2019)Maritime transport
network
Official website of each con-
tainer shipping company Vulnerability
significance for relevant organizations and practitioners in practice. These results694
can provide reference for decision makers to study the relationship between pa-695
rameters in the system and the rationality of operation (Li and Rong,2019), which696
is conducive to resource allocation and supervision by managers. Therefore, some697
of the issues and specific recommendations identified in the relevant studies are698
summarized from three perspectives. Future research directions are discussed.699
6.1. The management perspective700
To improve the TSP, the main tasks of the transportation department are system701
performance evaluation, emergency strategy formulation, daily supervision and702
coordination organization. Relevant agencies should pay attention to potential703
threats and shift from passive repair to proactive protection and risk assessment,704
which can greatly save resources and manpower and identify vulnerabilities in a705
timely manner. In addition, multiple modes of transportation can be integrated706
into the unified management of departments, which is conducive to resource allo-707
35
cation and emergency management (Renne et al.,2020). Unlike the operating com-708
pany, the government’s primary concern should be the safe and effective operation709
of the system, rather than the cost of maintenance and recovery. Strictly control the710
construction quality of transportation infrastructure and strengthen market super-711
vision of system operation. On the one hand, transportation departments should712
formulate unified management standards and emergency response mechanisms,713
focusing not only on short-term flexibility, but also on long-term flexibility (Renne714
et al.,2020). On the other hand, It is also necessary to develop appropriate man-715
agement and recovery strategies for different levels of disasters. Appropriate mea-716
sures should be taken for different types of interruption events, taking into account717
economic and social conditions. When the system is disrupted by interference, the718
responsibility for repair and diversion should be shared by the transportation de-719
partment, law enforcement agencies and operators (Chopra et al.,2016). In addi-720
tion, the transportation system is inseparable from other urban systems, such as721
power system, communication system and so on. Effective integration between722
different systems should be ensured (Sriram et al.,2019).723
6.2. The operational department’s perspective724
Different transportation systems have different actualities and operation modes,725
and thus appropriate management methods and coping mechanisms should be726
adopted accordingly. For example, for a rail transit, we should not only pay atten-727
tion to the hub stations with large passenger flow, but also pay attention to some728
non-hub stations in branch lines, since the failure of few non-hub stations may lead729
to the delay of the whole line. Moreover, the repair ability of the system should be730
improved to avoid the long-term failure of sites, especially the continuous failure731
of multiple sites (Lu,2018). This requires not only important protection of key732
sites, but also vigilance against changes in the status of their surrounding sites or733
facilities (Ma et al.,2020). If necessary, other modes of transportation can be used734
to mitigate the severe effects of system disruptions. The operation department735
should strengthen the impact analysis of different levels of accident risk and pre-736
36
vent early, with the help of big data analysis, machine learning and other advanced737
technologies. It is also necessary to develop a detailed risk management mecha-738
nism to improve the recovery rate of system resilience. Especially for the passenger739
flow system, the front-line departments should focus on improving the rapid and740
effective dissemination of information in case of interference, so that passengers741
can know the situation in time. To establish an effective passenger guidance mech-742
anism to ensure the safety of passengers in the limited resources. For the aviation743
system, more attention should be paid to those airports with few routes but high744
connection intensity. Community-based airport construction can better improve745
the robustness of the system (Zhou et al.,2019a). In addition, as a transportation746
system greatly affected by weather, a single airline network is easy to collapse. Air747
alliance can effectively reduce vulnerability and cooperate with other transporta-748
tion systems, such as multimodal transportation (Voltes-Dorta et al.,2017). For749
road network, regional collapse is easy to occur. When confronted with distur-750
bances such as natural disasters (Jenelius and Mattsson,2012). At this time, we751
should not only pay attention to a certain node or the state of the edge, but also752
consider the regional location and economic conditions, etc. Accidents are easy to753
happen in areas with dense population density and road network.754
6.3. The participant’s point of view755
The main players in the transportation system are the passengers. They are756
important factors considered in most metrics in the analysis of resilience and vul-757
nerability. We hope participants to be sensitive to changes in their perceptions of758
information and systems. At present, most studies assume that passengers are759
familiar with the system conditions and can make a rational choice (Jenelius and760
Mattsson,2012). Regardless of whether this is reasonable or not, the users should761
try their best to have a wide understanding of the travel information and make762
a more reasonable transfer. In a system incident, reasonable transfer can greatly763
reduce the impact on travelers. In addition, it is necessary to travel sensibly after764
the system is restored. We believe that researchers in the field of transportation are765
37
also an important group of participants. Their theoretical research on the perfor-766
mance of transportation systems with advanced technologies, such as simulation767
experiments, can provide practitioners with a scientific basis to restore rare inci-768
dent scenarios and discover the vulnerable positions of the system at a minimum769
cost. However, many current theoretical models lack data for calibration and veri-770
fication (Gecchele et al.,2019), which requires the support of operating companies771
and government agencies.772
6.4. Future directions773
Through the above detailed review, we further propose some future research774
directions for reference.775
• Considering from the user’s perspective776
Most of the existing research is usually considered from the perspective of777
the transportation system or management, ignoring the study of the choice778
behavior of travelers. For example, travelers’ responses to early warning in-779
formation before the disaster occurs, their perception of the consequences,780
and what choices travelers will make based on cost and risk after interfer-781
ence (including travel mode and path planning). Furthermore, what impact782
will these behaviors have on system performance recovery and vulnerabil-783
ity reduction? With the development of smart transportation and big data,784
quantitative analysis of these factors will be more easily realized.785
• Research on large-scale transportation systems786
At present, the main problems in the performance analysis of large-scale787
transportation networks are high calculation cost and complex models. Mean-788
while, the study of regional transportation networks has limitations, so it is789
worth considering how to analyze the performance of large-scale transporta-790
tion networks effectively. Some approaches, such as network compression,791
simplified models and data analysis, may be better choices.792
• Consideration of multilayer transportation systems793
Many studies on resilience and vulnerability are usually focused on a sin-794
gle type of transportation system or network, so the dynamic analysis of795
38
the number of users in the network and travel demand only considers the796
changes within the system. However, the connection between different trans-797
portation systems has become very close to the diversification of travel meth-798
ods and the improvement of transfer efficiency. It is worth considering the799
changes brought by the combination of various transportation modes to the800
system performance. In the future, the modeling of multilayer transportation801
systems and even the comprehensive analysis between different systems will802
be increased.803
• Increasing consideration of the impact of geographic information804
The transportation network is closely related to social production activi-805
ties, and the operational state of the network is spatiotemporally different.806
The population density, land types and production activities (such as schools807
and hospitals) in different regions can create changes in the resilience and808
vulnerability of the transportation network. Therefore, the analysis of TSP809
will be more accurate when combined with geographic information technol-810
ogy.811
• Data-driven approach812
As an emerging method, the data-driven approach still has considerable813
challenges. Facing diverse data types and extensive data sources, how to ob-814
tain and extract effective information, and what metrics to use to evaluate the815
vulnerability or resilience of dynamic transportation networks are all worthy816
of our consideration. In addition, with the aid of advanced data analysis tech-817
nology and concepts, we can transfer traffic vulnerability research from the818
macro to the microlevel, such as considering residents’ travel choice behavior819
after transportation interruption (changing the destination or travel mode),820
influence of heterogeneity of drivers on network operation, cost-effectiveness821
of travel and weather factors. In addition, the prediction of travel time and822
performance changes are also worth exploring by combining historical data823
with machine learning and other model algorithms.824
39
7. Conclusions825
Starting from the field of transportation systems, this paper provides a sys-826
tematic review of recent studies on resilience and vulnerability, including road,827
rail, aviation and water transportation systems. First, we classified and counted828
the important literature of the past 10 years through rigorous literature retrieval829
methods. At present, research on the resilience and vulnerability of transporta-830
tion systems is relatively mature, but there is still a great imbalance between the831
development of various transportation modes. Additionally, with the rapid de-832
velopment of traffic intelligence and integration, the assessment of resilience and833
vulnerability is also faced with new challenges. Second, many of the current defi-834
nitions of traffic resilience and vulnerability are loosely drawn from other systems,835
which is unspecific. Therefore, we define the two concepts from the perspective836
of transportation supply and demand. In addition, we systematically illustrate837
the interrelationships between various concepts in the TSP evaluation, which ef-838
fectively avoids the confusion of different terms in the use of researchers. Finally,839
we summarize the research on traffic resilience and vulnerability from the per-840
spective of metrics and research methods and propose some opinions. We find841
that the topological analysis usually focuses on the change of traffic vulnerability,842
while simulation and model optimization methods are usually used to study the843
change of system resilience. At the same time, the optimization and simulation844
method using a mathematical model is more rigorous and reliable and can evalu-845
ate the TSP more comprehensively. In addition, the original data-driven method is846
more real and simple and has a realistic guiding role for operators. Finally, com-847
bined with literature review, the present situation and future research direction of848
management operation are discussed from different perspectives. Although this849
paper has made a comprehensive review of the research on various transportation850
modes, it does not have an in-depth analysis of the resilience and vulnerability of851
a particular system including specific research methods and development context,852
which is limited by space. In the future, in-depth summaries can be made on a853
particular topic.854
40
Acknowledgment855
The research is funded by National Natural Science Foundation of China (71871010).856
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