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Weak nodes detection in urban transport systems:
Planning for resilience in Singapore
Michele Ferretti∗, Gianni Barlacchi†‡ , Luca Pappalardo§, Lorenzo Lucchini†‡, and Bruno Lepri‡
∗Department of Geography
King’s College London, London WC2B 4BG, United Kingdom
Email: michele.ferretti@kcl.ac.uk
†Department of information engineering and computer science,
University of Trento, Trento, Italy
‡Fondazione Bruno Kessler, Trento, Italy
Email: barlacchi@fbk.eu
Email: llucchini@fbk.eu
§ISTI-CNR, Pisa, Italy
Email:lucapappalardo@isti.cnr.it
Abstract—The availability of massive data-sets describing hu-
man mobility offers the possibility to design simulation tools
to monitor and improve the resilience of transport systems in
response to traumatic events such as natural and man-made
disasters (e.g., floods, terrorist attacks, etc. . .). In this perspective
we propose ACHILLES, an application to models people’s move-
ments in a given transport mode through a multiplex network
representation based on mobility data. ACHILLES is a web-based
application which provides an easy-to-use interface to explore the
mobility fluxes and the connectivity of every urban zone in a city,
as well as to visualize changes in the transport system resulting
from the addition or removal of transport modes, urban zones
and single stops. Notably, our application allows the user to assess
the overall resilience of the transport network by identifying
its weakest node, i.e. Urban Achilles Heel, with reference to
the ancient Greek mythology. To demonstrate the impact of
ACHILLES for humanitarian aid we consider its application to
a real-world scenario by exploring human mobility in Singapore
in response to flood prevention.
Index Terms—urban science, data science, human mobility,
complex systems, network science, multiplex networks, resilience,
social good
I. INTRODUCTION
Cities are a physical manifestation of continuous processes
of human interaction and of the weaving and knitting of social
relations unfolding through space and stratifying through time.
Cities are inherently “hard” to understand; their interlacing
facets and tangled assemblages render them difficult to frame
[9], [26], [27]. In particular, the nexus of human mobility
patterns, transport planning choices and urban policies pose
great difficulties for scientific modelling. It presents, in fact,
what Rittel et al. [36] call a “wicked problem”, that is, a
problem whose social nature and lack of objective truth makes
inherently hard to tackle with traditional analytic tools.
Despite being still far from adequately composing these
problems [9], nowadays the variability of massive data describ-
Luca Pappalardo has been partially funded by the European project So-
BigData RI (Grant Agreement 654024). Gianni Barlacchi has been partially
funded by the EIT project Cedus.
ing human movements allows planners and policy-makers to
face relevant urban challenges through computational methods
[1], [4]–[6], [12], [15], [32], [33], [37]. While the observation
of mobility flows offer for instance the possibility to investi-
gate the inner workings of urban transport systems, this is not
enough for efficient transport planning. As Ganin et al. [17]
note, traditional transport studies focus on efficiency measure
by observing a transport network under normal operating
conditions. This approach though fails to capture information
that really matters for real-world applications, i.e. how the
network reacts when is under stress conditions. Such is the
case of traumatic events that might cause disruption of service
or worse, like in the event of natural or man-made disasters
(e.g., floods, terrorist attacks, etc.). Thus, uncovering weak
points that affect a network’s resilience, a proven key metric
for transport policies [17], is not only a task of paramount
relevance for the design of proper intervention scenarios in
case of disasters, but also an actual requirement for managing
transport services in complex global cities like Singapore. We
refer to such weak points as Urban Achilles Heels.1
Starting from these considerations, we address the following
questions: (i) What and where are the weakest transport routes
in a city, i.e., its Urban Achilles Heels?(ii) Given some
changes in the transport system, what scenarios are likely to
occur and what is their impact on human mobility and on the
resilience of a transport system?
Here we propose ACHILLES, a web-based application which
provides an easy-to-use interface to explore the mobility fluxes
and the connectivity of urban zones in a city, as well as to
visualizes changes in the transport system resulting from the
addition or removal of transport modes, urban zones and single
stops. ACHILLES is based on a multiplex network representa-
tion of mobility data [14], where every layer describes people’s
movements with a given transport mode, e.g. buses, metros,
taxis. A node in a layer represents an urban zone of the city,
1https://en.wikipedia.org/wiki/Achilles%27 heel
arXiv:1809.07839v1 [cs.SI] 20 Sep 2018
edges indicate routes between zones and edge weights indicate
the amount of people moving between two nodes in a given
time window. ACHILLES exploits this network representation
and allows the user to visualize changes in the transport system
resulting from the addition or removal of transport modes,
urban zones and single stops. Notably, ACHILLES allows to
compute the Heel-ness of a zone, a measure introduced in this
paper which indicates the probability of a zone to disconnect
the network when edges adjacent to it are removed. The
computation of the Heel-ness allows ACHILLES to state that
the transport system has an Urban Achilles Heel if there is at
least one urban zone with a non-zero Heel-ness.
We show how ACHILLES can be used to explore human
mobility in Singapore and test the resilience of its network to
natural disaster, by using mobility data from several sources.
The application allows to point out weak routes among urban
areas in the city (i.e., routes where public transport does not
meet the needs of the citizens), and simulate changes in the
capacity of public transport to satisfy needs of citizens when
specific events occur in the city, e.g. closing/adding transport
modes or subway/bus stops. Additionally, it can be used by
supplement humanitarian agencies for resilience preparedness
and response, and in general fragile contexts where there is a
dire need of deploying fast, scalable and effective humanitarian
aid. Our approach is in fact highly flexible since it uses only
data about transport and mobility flows. Given that many open
datasets of such nature are nowadays publicly available2, our
approach can be potentially applied to any other urban area
to simulate traffic changes due to specific events, such as
the impact of adding or removing transport modes or stops,
the impact of closing the access to an urban area, or the
organization of city-wide public events.
II. RE LATE D WOR K
Understanding human mobility is a long-standing and
highly relevant challenge for today’s increasingly urbanized
world [40]. In their reconstruction of the discipline’s evolution
Barbosa-Filho et al. [3] highlight how through time different
scientific communities attempted to frame it using disparate
data sources; starting from geographers’ studies of spatial
interaction and regional migration [21], [42]. It is only recently
though that significant advancements having been made due
to novel data sources, such as Call Detail Records (CDRs)
and GPS location data collected through mobile phone devices
[19], [33] and analyzed through the lens of network science
[8], [39].
Using precisely methods from network science we can de-
sign powerful models and simulation tools for what-if analysis
of different urban planning scenarios [25], [30]. Singapore,
due to the complexity of its transport system, is precisely a
global city where such tools would be particularly valuable
[24]. Network science applied to the study of transport systems
has proved to be increasingly useful in recent years. Xu
and Gonz´
alez [41] have shown that a slight re-routing of a
2https://data.gov.sg/group/transport
fraction of daily car commutes produces significant reductions
in traffic, thus alleviating the congestion state of the overall
transport system. In this perspective the development of data-
driven analytic tools can help control the transport system
and improve both the customer’s travel experience and the
system’s overall efficiency. C¸ olak et al. [11] have investigated
the interplay of number of vehicles and road capacity to
determine the level of congestion in urban areas. In particular,
they show that the ratio of the road supply to the travel demand
can explain the percentage of time lost in congestion. De
Domenico et al. [14] show that the efficiency in exploring
the transport layers depends on the layers’ topology and the
interconnection strengths.
Although these works doubtlessly shed light on interesting
aspects about the structure of urban transport, they do not
provide easy-to-use tools for exploring a city’s demand for
mobility and the efficiency of the related transport system.
Giannotti et al. [18] partly overcome this problem by propos-
ing a querying and mining system (M-Atlas) for extracting
mobility patterns from GPS tracks. This system, still, does
not provide a method to assess weak points in cities, those
that will collapse first in case of traumatic events.
Wang et al. [22] highlight in fact many studies in resilience
engineering that try capture different facets of the problem
at stake, often tackling the most disparate domains (e.g.,
from spatial economics [35] to computer networks [38] and
socio-ecological systems [2]). However, as pointed out by
[17], since the majority of transport-oriented policies stress
efficiency aspects measured under optimal conditions, and
neglect to consider instead stress scenarios that happen in
the real word, there is still a need to provide policy-makers
with adequate tools to actually capture a transport network
resilience; here intended once again as the network’s capacity
to recover from a catastrophic event returning to its original
working state. Moreover, there is still a need to design tools to
test and prototype scenarios for rapid response under critical
conditions.
III. DATA SOU RC ES
In this work, we use different data sources from the city of
Singapore with information about (i) transport, (ii) adminis-
trative boundaries, (iii) mobility flows and (iv) floods.
a) Transport Data: The public transport data are pro-
vided by LTA Data Mall3, which published a wide variety of
land transport-related datasets both static and in real-time. In
this work we use data about bus lines4, which provide informa-
tion to build a transport network describing the displacements
of inhabitants between different urban zones of Singapore. In
particular, for every bus line, we retrieve information about its
stops and the GPS traces describing the bus route.
b) Administrative boundaries: The urban zones areas are
provided through the shape-files at different administrative
division levels of the city, and are available at the website
3https://www.mytransport.sg/content/mytransport/home/dataMall.html
4https://www.mytransport.sg/content/mytransport/home/dataMall.html
data.gov.sg5. We use the most fine-grained division and, by
applying a spatial join operation, assign every bus stop to the
corresponding urban zone. The resulting dataset contains 323
urban zones and 4856 bus stops.
c) Mobility flows: We use data indicating both the pres-
ence of people in every urban zone and the fluxes of people,
i.e. Origin-Destination (O-D) matrices [23] between urban
zones at a given date and time. Such data were obtained from
the data-as-a-service APIs provided by DataSparkAnalytics6.
In particular, the presence of people and the O-D matrix are
estimated starting from the mobile network data provided by
different Asian telco operators. It is worth mentioning that
location signals from the telcos are analysed in an anonymous
and aggregated way. We use these data to estimate the number
of people moving by bus between two urban zones in a given
time window, since official information about the number of
users traveling on the buses is not available. We aggregated
the flows by hour.
d) Flooding data: Flood prone areas forecasts, computed
by the Singapore’s Public Utilities Board (PUB), are provided
as an incentive to reduce the risk of recurring flood events and
to foster proactive measures among developers and the general
public. We used such areas, retrievable at www.pub.gov.sg7to
inform our use-case with substantiated data related to a real-
world problem related to a specific setting.
We hence obtain for every urban zone z: (i) the bus stops in
z, (ii) the bus lines passing through z, and (iii) all the urban
zones connected to z. We define two urban zones z1and z2
to be connected if there is at least one bus line connecting z1
and z2.
It is worth to mention that despite our experiment being
limited to the bus network system, due to limited data avail-
ability, further extensions to truly multimodal systems can be
integrated with ease. This will enhance the modelling of trans-
port planning scenarios with increased reliance and confidence.
Limitations standing, our proposed tool can already serve for
specific use-cases, such as precisely the considered instance
of Singapore’s bus network resilience to floods.
IV. METHODOLOGY
The use of complex networks to analyze complex systems
is a powerful way to simplify the description of a problem by
means of a process of abstraction. This process reduces the
complexity of the structure to two simple elements: nodes, i.e.
the objects of the system, and edges, i.e. the relations between
these objects. However, such a representation can lead to a
strong loss of information about the real system characteristics.
In this context, an interesting novel approach was proposed
by De Domenico et al. in their seminal work on multilayer
networks [13]. They have proposed a new framework in which
it is possible to encode information about the different possible
relations between the nodes of the system in different layers.
Each of these layers represents a specific kind of relation
5https://data.gov.sg/dataset/master-plan-2014-subzone-boundary-web
6https://www.datasparkanalytics.com/products/data-as-a-service
7https://www.pub.gov.sg/drainage/floodmanagement
between a set of nodes and can be considered as a partial
representation of the whole system without the loss of a
simple structure representation: for example, a sub-network
describing a specific kind of relation between the nodes of
the network, which again reflects some of the properties
or the characteristics of the complex system. In this work
we adopt a similar mathematical formulation to describe the
transport system of an urban environment. To better describe
the transport system of the city we are studying, in Section
VI we specifically model the network structure to best fit
the city characteristics following the more general formulation
discussed herein.
In an urban area, two zones can be connected through
several transport means (e.g., bus, taxi, subway, etc.).
As each transport mean differs from the other, also each
subway or bus line differs from the others. In fact, using
two different lines of the same mean require a transfer at
some stop. In turn, each of these transport modes may be
considered as a set of different lines following a specific
path; connecting specific zones of an area; and eventually,
can be considered as an additional layer of the system. To
express this kind of information we introduce the concept of
urban multiplex network by means of the following definition:
Definition: An Urban Multiplex Network (UMN) is
a network in which two nodes represent zones of an urban
area and can be connected, at the same time, by multiple
edges that belong to different layers. We model such structure
with an edge-labeled multi-graph denoted by G= (V, E , L)
where Vis a set of nodes, i.e. the zones in which the area
we are studying is divided; Lis a the set of layers which
encode the information about the different possible types
of connections between two nodes, e.g. the public transport
mean characterization and/or the line number; Eis a set of
labeled edges, i.e., a set of triples (u, v, l)where u, v ∈V
are two nodes, and l∈Lis a layer of the multiplex network.
The global connectivity of two zones, which is the
multidimensional connectivity (i.e., the connectivity
considering all the layers of the network) in an urban
area is a combination of two elements: (i) connection
intensity and (ii) connection redundancy. We define the
intensity of the connection between two zones on a single
layer as:
Definition: Connection intensity
hl(u, v) = wl(u, v)|Γl(u)∩Γl(v)|
min(|Γl(u)|,|Γl(v)|),(1)
where wl:V×V×L→Nis a weight function representing
the mobility flux between two zones on layer l, and Γl(u)
is the set of neighbours of the zone u. Connection intensity
consists hence of two factors: the first factor, wl, indicates
the percentage of people moving between the two zones
using a specific transport layer and line l. The second factor,
|Γl(u)∩Γl(v)|
min(|Γl(u)|,|Γl(v)|), is the percentage of common neighbours,
|Γl(u)∩ |Γl(v)|, with respect to the most selective zone,
min(|Γl(u)|,|Γl(v)|). The idea is that, on each layer,
the connection intensity is influenced by the number of
displacements between the two zones, weighted by the value
of selectiveness of the most selective zone, i.e. the ratio
between the neighbours shared by the two zones and the
number of neighbours of the zone with the smallest set of
neighbours.
The second element on which global connectivity depends
is connection redundancy, which takes into account the
relevance of a layer in the all-layers zone’s connectivity. This
quantity measures to what extent the removal of the links
belonging to a specific layer affects the capacity to reach a
neighbouring zone from the considered one. Redundancy in
general is a measure of the strength of node-node connections
considering the links connecting the two nodes over all
the layers of the network. Before defining the connection
redundancy, however, we need to introduce the layer l
relevance, LR(u, l), for the node u.LR(u, l)can be defined
as the ratio between the number of nodes that disconnect from
node uif all the links of layer lare removed (which is the
same as removing an entire layer to the multiplex network)
and the number of nodes reachable before the removal of the
layer [10]:
Definition: Layer Relevance
LR(u, l)=1−Nr(u, lc)
Nr(u, L)(2)
where Nr(u, L)is the number of reachable nodes from node
uusing all the multiplex network’s layers L, while Nr(u, lc)
is the number of reachable nodes from uafter the removal of
layer l, i.e. the reachable nodes from uconsidering only the
set of layers lc=L\l.
Definition: Connection Redundancy
rl(u, v) = (1 −LR(u, l)) ·(1 −LR(v, l)) ·
L
X
m=1
Au,v,m
L,(3)
where Au,v is a vector element of the adjacency tensor of the
multiplex that keeps track of the presence of edges between
node uand node vover the l∈Ldifferent layers. We give a
higher score to the edges that appear in several layers, so we
are interested in the complement of those values. If the two
areas are linked in more than one layer, the score raises until
a maximum of 1.
We combine connection intensity and connection
redundancy taking into account the multidimensionality
of multilayer network’s connectivity: a greater number of
connections on different layers is reflected in a greater chance
of having a strong connectivity.
Definition: (Global) Connectivity.
Let u, v ∈Vbe two nodes and Lbe the set of layers of an
urban multiplex network G= (V, E , L). The connectivity of
two urban areas u, v is defined as:
c(u, v) = X
l∈L
hl(u, v)(1 + rl(u, v)).(4)
It is worth noticing that the measure proposed can be used
to estimate the strength of the connectivity between nodes
also in single-layer networks, in which rlis one and the
overall sum is hl.
The aim of this work is to provide policy-makers, transport
planners and humanitarian agencies with a working tool that
has the versatility to adapt to different urban areas and the
capacity to quantify the level of susceptibility to disruptive
events related to a transport system own structure. More
specifically, we are interested in studying the weaker ties
as those potentially responsible for the disruption of the
multiplex network. In particular, to study the weaknesses of
a specific network, we introduce the notion of Heel-ness as
the relative importance of a node in the context of network
navigability.
Definition: Heel-ness.
Given a zone u∈V, the Heel-ness of uis defined as:
H(u) = max|V−Ru−(u,v,l)|
min[c(u, v)]v∈Nul∈L
,(5)
where Nuis the set of neighbors of u,Ruis the set of
reachable nodes from node uwhile Ru−(u,v,l)is the set of
reachable nodes from node uafter the removal of the edge
e= (u, v, l)∈E. As a consequence of these definitions
|V−Ru−(u,v,l)|is the number of non-reachable nodes after
the removal of the edge e.
This metric quantifies this importance in terms of optimal
disruptive events classified following the Granovetter’s theory
for single-layer networks [20]: the importance of a node in
preserving a network’s giant component depends on the con-
nectivity of the node. In particular, nodes which shares weak
connections tend to be those more important to be preserved.
Heel-ness measures the importance of a node considering the
weakest connection it has, and the number of unreachable
nodes after that edge disruption. The Granovetter’s theory
was proposed in 1973 in the context of social networks.
Since then it was studied and proposed in countless different
fields of application. Following a similar approach we adapt
the measures introduced in [31] to detect important ties in
transport networks. In particular we focus our attention on the
topological resilience of multilayer networks as proposed in
[14]. Topological resilience studies the robustness of a network
in resisting to topological failures, such as edge removal. Heel-
ness measures the single-event effects of the network and ranks
them depending on the greatest damage they can inflict to the
network structure if one particular edge is removed. Extending
then the idea from [20] to transport networks allows us to
refer to weak ties as those edges that make the network more
fragile and susceptible to targeted edge loss. We stress further
that topological resilience takes into account only the network
structure while edges can be weighted in such a way that more
important links, e.g. in a transport network those links that
sustain higher traffic flows, are naturally considered as more
crucial for the overall system connectivity.
Being able to classify nodes depending on the importance
of their connection in the network, we can classify networks
based on the presence or absence of fragile nodes. Using
the definition of Heel-ness we can state that an urban
multiplex network has an Urban Achilles Heel if there is
at least one node for which the Heel-ness has a non-zero value.
Definition: Urban Achilles Heel.
We define the Urban Achilles Heel of a multiplex network as
the node h∈Vfor which
H(h)>0and H(h)≥H(u)∀u∈V. (6)
This definition provides a classification based on a first-
order disruptive event, i.e. an event that only causes the loss
of a single edge. However, the extension of this definition
to further orders is straightforward and can be done by
sub-sequential removal of the nweakest ties of the network.
Applying this definition to real transport networks can help
in the identification of important edges and nodes that are
crucial for the stability and routing of all zones in an urban
area.
V. APPLICATION DESIGN
The application is freely available online at
http://achille.fbk.eu. For scientific dissemination and
to provide access for a larger external non-technical
audience it was also complemented by a video-tutorial
http://achille.fbk.eu/about. The application design follows
closely the analytical framework described in Section I,
while implementing a client-server architecture pattern. We
implemented a RESTful web service using Flask, a widely
used micro web framework written in Python. In the REST
architecture the server exposes the resources to a client
trough a set of defined URLs. For example, in order to get
the list of buses passing trough an area, the endpoint is
defined as http://achille.fbk.eu/area/hid areai/services. This
API is responsible not only for data provisioning, but also
acts as the communication layer between the user and the
network models. It is worth noting that, given its modularity,
our application can be re-purposed as an agnostic provider
of services to other consumers. In particular, the exposed
methods consist in:
•a query endpoint returning the network features’ geome-
tries for a given urban zone ID, and additional informa-
tion used to populate the geographic map application;
•a second query endpoint returning for each given urban
zone ID the computed network metrics, i.e., Connection
Fig. 1. Application User Interface (UI): Upon an area selection, the user
is presented with the 3D network metrics for the city of Singapore. The
interactive menu on the right allows then to select and deselect transport
routes.
intensity, Connection Redundancy, Connectivity (Section
IV).
The front-end application is thus the entry-point for quickly
interacting and prototyping future transport scenarios. The
User Interface (UI), visible in Figure 1, has been developed
with easiness of use and clarity of interpretation its standard
pillars. It allows a non-technical audience to inspect the
number of routes connecting an urban zone to the rest of
the city simply by clicking on an urban zone in the city
panel and control them via an interactive menu (Figure 1).
Upon addition/removal of one or more routes in the menu,
the user can trigger the calculation of the network metrics
(Figure 2), which are promptly displayed in three separate
windows. Every window shows a 3D map of the city, where
an urban zone’s height is proportional to its average networks
value computed over the connected urban zones (Figure 3).
The menu and the bottom windows allow the user to simulate
how the city’s connectivity changes after, for example, the
construction of a new route or the temporary closing of an
existing one. Further, the identification of sensitive areas, the
so-called Urban Achilles Heel, can be accessed through a
revealing button. The example in Figure 2 presents four areas
in the northern part of Singapore.
All of the geographic map components are fully interactive
and built with the latest web-mapping technologies taking
advantage of latest WebGL standards and 3D capabilities; as
such, they allow for a most fluid and seamless experience.
This is a crucial factor that allows the application to hide the
complexity of the models behind a fluid interface. It also let
the technological stack move out of the way, making room for
discussions and human elements that enhance decision-making
processes.
VI. CA SE S TU DY: FLOODS PREVENTION IN SINGAPORE
In the following section we discuss the specific modeling
adopted for the Singapore’s transport network and the results
obtained by studying the structure of the system and its
resilience to synthetic disruptive events.
Fig. 2. Metrics: The “Run” button allows to calculate the intensity, redundancy
and connectivity measures and to visualize them in the three bottom windows.
Further, every interaction with the bus lines menu will trigger the computation
of the Heel-ness metric. In the above image, four areas are identified as such
vulnerable sites.
Fig. 3. Zonal Focus (example): The 3D maps in the rightmost bottom window
inform the user with additional metrics. In the example, the height of the
extrude zone is proportional to the average value of its multidimensional
connectivity, computed across all the connected urban zones.
A. Network structure
When dealing with real-world problems a case-dependent
modelling usually ensures better performances and results in
terms of actionable solutions. In the advanced case study,
we deal with Singapore’s transport network with the aim to
specifically uncover possible solutions to disruptive events
(e.g. intense rainfall and consequent floods. . . ) which might
negatively impact the road network. We apply the methodol-
ogy presented in section IV considering the reduced transport
network composed by more than 300 different scheduled bus
lines. This operation enable us to scope down the issues and
focus solely on those related to the road network.
In our framework, each bus line represents a layer of the
network; each layer consists of all the Singapore’s administra-
tive areas (according to a government sanctioned classification
available at data.gov.sg8); each zone is a node of the multiplex.
Further, each bus line fully connects to every zone in which a
bus line has a stop with all the others zones in which the same
bus line has a stop. In this configuration, disruptive events
that involves only limited zones, which may not necessarily
disconnect the entire line if a reroute is prompted, are taken
8https://data.gov.sg/dataset/master-plan-2014-subzone-boundary-web
Fig. 4. Schematic of the structure of the multiplex network adopted to model
the road public transport services for Singapore. Each layer represents a
different bus line. Each of these fully connects different zones of the city.
This structure naturally takes into account possible rerouting strategies that
can maintain the layer partially connected.
into account. The model is indeed built in such a way that
edges can be removed gradually depending on the nature
of the disruptive event we want to simulate. In figure 4
we schematically represent the network structure used to
model and analyze the Singapore’s bus transport network. As
depicted, each layer share with the others the same nodes but
changes the connections between the zones depending on the
bus line it represents.
Even in this specific network configuration, the metrics
introduced in section IV maintain their significance. The rele-
vance of each layer depends, in fact, on the relative number of
neighbours in a layer with respect to the multiple degree of the
node. In particular, the shape of the connectivity, implemented
from the definition proposed in [10] ensures that the Heel-ness
of a node consistently depend on the node’s layer relevance
and the node’s connection redundancy instead that only on
the connection intensity. We stress that, if this would have
been the case, fully connected layers would have brought to
an initial connectivity measure that would have encoded only
operational information, i.e. information about the mobility
flow passing trough links, for all the nodes that share the same
bus lines independently on the possible different size of the
disconnected component they might cause after a disruptive
event involving one or all of their connections. This highlight
the importance of a combined approach that considers both
the structure of the multilayer network, i.e. relevance and
redundancy of the connections, and the network usage, i.e.
the information about mobility flows over different links.
B. Experiments
Moving from of the aforementioned considerations we
conducted an extensive connectivity assessment by observing
Singapore’s urban network resilience to the removal of high
and low connectivity links separately. We use this case study
to test the behavior of multilayer node connectivity, as defined
in IV, on a real transport network. To this extent we compute
the connectivity for every node in the network and we sort
them accordingly to the obtained score. In figure 5 we show
the connectivity for the network in its initial configuration. We
can see that there are two dominant behaviors.
The left side of the histogram consists of areas with a
low connectivity score. These are the areas dominated by
the contributions given by the number of layers who share
a connection showing different peaks. Each peak corresponds
to the different number of shared layers. The right side consists
of those urban zones that are geographically central and
functionally important urban nodes; the number of layers that
two such nodes share is no more dominating the contribution
to the connectivity score, while its increasing importance is
given by the length of the different bus lines and number of
nodes they are connected with.
As illustrated in Figure 5, connectivity can be used to clas-
sify and sort nodes depending on the strength and importance
of their ties. This allows us to test the weak ties theory for
transport networks.
We start by removing the weakest tie in the network, and
the subsequent in decreasing order of weakness, iterating the
computation after each removal. The expected outcome is a
faster network percolation than achieved adopting an opposite
strategy, i.e. removing the stronger ties of the network first.
The result of this experiment are presented in Figure 6. The
relative size of the largest network component changes with
the removal of a given percentage of links. The values are
sorted by increasing (red solid line) or decreasing (blue dashed
line) connectivity-score order. The red line shows the different
speed of percolation faced by the same system under targeted
attacks with different strategies.
Additionally, it is worth noting how the network faces a
first significant disruption after the removal of more than
50% of total number of edges. This finding holds even with
the adoption of a more effective disruptive strategy. Such
result highlights the high degree of resilience exhibited by
Singapore’s bus network, which is consistent with the city’s
highly efficient transport network [7]. Further studies might
benefit thus from replicating the above experiments in other
locales with different transport systems, to check whether a
similar pattern is present and how it behaves to disruptive
events.
VII. DISCUSSION AND IMPLICATIONS
Our simulated experiment has been conducted, due to data
availability, only on the bus transport layer. However, it is
Fig. 5. Connectivity value density within the network’s initial configuration
state. Connectivity is computed for each couple of nodes, which are then are
sorted depending on the computed score.
straightforward to extend our framework to multiple trans-
portation systems (e.g., metro and train). Testing the network
resilience to the aforementioned stress conditions in a truly
multimodal perspective represents thus an important tool at
disposal of transport planners to assess (i) the current state of
the transport network; (ii) to plan future operations; (iii) and
to keep running the system at its overall optimal capacity.
In particular, we found that Singapore has a resilient urban
network, as all the nodes are still reachable when removing
up to 30% of the links. Moreover, the deletion of links in
decreasing order of connectivity affect less the network’s
global connectivity, as more than 97% of the urban zones
are still reachable after the removal of 90% of the links
(Figure 6, blue dashed line). In contrast, when deleting the
links in increasing order of connectivity the network crumbles
faster, as almost 20% of urban zones become unreachable
after the removal of 90% of the links (Figure 6, red solid
line). These results suggest that the proposed connectivity
and risk metrics can profitably be deployed to discover those
urban connections whose existence is crucial for the network
resilience. Moreover, those metrics can also help to evaluate
the impact of changes and intervention in the city’s mobility
(e.g., the closure of a bus line). Figure 6 highlights the points
where the accelerated network disassembling commences, i.e.,
the Urban Achilles Heel: up to those values the transport
system exhibits a fair resilience, but surpassing such thresholds
provokes a rapid network fall-out.
Independently on the specific results obtained for the Sin-
gapore’s transport network, we believe that our approach and
our application can be used in several situations, both from a
geographical and structural point of view.
Application deployment: Considering for instance the level
of complexity and the structural organization of Singapore [7],
one of the most developed cities in the eastern hemisphere,
our model simulation showcases a relatively sound resilience
to potential catastrophic events. While this is an interesting
result in itself, another valuable aspect of our application is
its ease of reproducibility in urban contexts characterized by
more fragile infrastructural systems. In cities and urban areas
with newer or less developed transport systems the application
of the proposed methodology might in fact yield higher impact
results.
From from a data availability standpoint our application
can easily be deployed to other contexts. Out of the four
major sources of information presented in section III, namely
a) Transport Data, b) Administrative Boundaries, c) Mo-
bility Flows and d) Flooding Data only the very last one
is specifically tied to the Singapore’s context and the use-
case introduced. Other data sources, such as Administrative
Boundaries can in fact be commonly found either through
local authorities official data portals, or via open data al-
ternatives such as OpenStreetMap9. The pivotal source, i.e.
Transport Data, can additionally be found across different
urban settings also through open data standards such as the
General Transit Feed Specification (GTFS), which ”. . . allows
public transportation agencies to provide real-time updates
about their fleet to application developers”. GTFS is de facto
the standard for exposing and consuming public transit data;
can be globally found and integrated through ad hoc search
engines such as TransitLand10; and come with a robust track-
record of academic research and industry applications. [16],
[28], [29].
Lastly, in a final effort to extend the scalability of our
application to different contexts and use-cases, we devise
possible implications of our tool by distinguishing different
typologies of users, namely urban planners and policy makers,
and humanitarian agencies.
Urban planners and policy-makers: Current approaches in
transport network resilience focus on developing comprehen-
sive frameworks or policies that largely prioritize efficiency
and reducing delays, rather than considering the impact of
stressful events on the network [17]. While these approaches
are perfectly understandable from a policy’s stand-point, they
might often leave real-world transport systems vulnerable to
changing conditions. These conditions might also be exacer-
bated in complex urban environments such as Singapore. Thus,
the insights provided by testing such scenario might prove
extremely useful instead in preventing catastrophic events and
improving the overall resilience of the system.
Humanitarian Organizations: The possibility to prototype
scenarios and test the mutable conditions of a system has
direct implications for other cities; other kinds of disruptive
events; and other sectors, such as the humanitarian response.
The latter is in fact an area of application where the ability to
prevent damaging phenomena by containing negative impacts
and providing an adequate rapid response is absolutely crucial
[34]. By providing a clean interface and a tool able to scale
over a wide portfolio of settings, our application is suited to
address challenges where timing is the key factor, such as
9https://www.openstreetmap.org/
10https://transit.land/
Fig. 6. Stability of the urban network to links removal. The x axis shows
the percentage of removed links. The y axis shows the size of the greatest
network component.
pre-event preparedness prevention or post-event rescue team
deployment.
VIII. CONCLUSION
Transport planning is a difficult arena to operate in. This
is due to the inherently ”wicked nature” of the issues at
stake coupled with the complexity of urban environments
[9], [36]. Advancements in understanding human mobility
have recently been made through the use of computational
methodologies (see for instance [1], [4], [11], [33]). How-
ever, the need to operationalize and distill such methods
into actionable tools tailored to real-world problems is still
present. In particular, the humanitarian sector might benefit
from the application of models and methods coming from
the new science of data. Our proposed ACHILLES application
is a step forward in this direction, providing an easy-to-use
interface on top of complex models that allow non-expert
users, such as non-profit organizations, to rapidly prototype
different stress scenarios. It represents thus a tentative example
of how data science can be put to good use to tackle issues
of social relevance. In the presented experiments we tested
the case of Singapore, particularly suited due to its natural
geography and the frequent disruption thereby caused on the
bus transport network system by floods. Since the application
is built deploying data that are not site-specific (e.g. O-D
matrices), it is scalable to different environments, making
it suitable to be applied even in fragile contexts. Further,
due to its flexible architecture ACHILLES accommodates new
data sources with ease, adapting its modelling capacity to
meet local needs. As unpredictable stress events might present
themselves in the future, transport planners need to be vary of
mutable conditions. This requires not only a close monitoring
of transport networks under normal operational settings, but
the ability to quickly respond to new challenges [22]. The
solution we advance lies precisely in this direction.
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