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A Holistic Approach to Crowd Congestion Management in Singapore’s
Mass Rapid Transit System
Mithila Harish
Student Category
NUS Graduate School for Integrative Sciences and Engineering (NGS), NUS
Contact number: 90178530, Email address: [email protected]
Published and used with permission by Temasek Defence Systems Institute and
Department of Industrial and Systems Engineering, Faculty of Engineering, NUS
Abstract: As the population in Singapore continues to increase, it is extremely
important that an increased focus is given to crowd control and management. In
this regard, this paper gives an overview of traditional crowd modelling strategies
and proposes some new techniques to potentially improve upon existing models,
as well as examining the ease with which they can be implemented. It is hoped
that these models will provide a better realization of crowd behavior and how
these systems can help in building a smart city.
The algorithm suggested is targeted at the Mass Rapid Transit System but it is
hoped that it can be applied to crowded environments in general, with suitable
modifications.
1 Introduction
The population of cities and urban areas is increasing. As world bank data
shows, there has been a upward trend in the increase of urban population [1].
This is a result of both migration and natural increase.
Cities have a limited space. The Global Health Observatory data from the World
Health Organization says that [2]: “The urban population in 2014 accounted for
54% of the total global population, up from 34% in 1960, and continues to grow.
The urban population growth, in absolute numbers, is concentrated in the less
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developed regions of the world. It is estimated that by 2017, even in less
developed countries, a majority of people will be living in urban areas”
As a result of so much population increase in urban areas, there will undoubtedly
be a need to improve existing crowd control technologies.
As Hugo Winter [3] from Lancaster University says in his paper ‘Modelling Crowd
Dynamics During Evacuation Situations Using Simulation: “Public spaces will
naturally become busier, which increases the possibility of crowd related
disasters. There seems to be no eminent reduction in population densities in the
near future which makes modelling in this area especially important.”
1.1 Crowd Behavior Analysis
Crowd behavior is complex. Humans are not governed by a set of rigid,
deterministic laws. We cannot say that, for example, one week hence, exactly at
10 am, something momentous or equally mundane will occur.
Lorenz in his popular work ‘Predictability: Does the Flap of a Butterfly's Wings in
Brazil set off a tornado in Texas?’ [4] mentioned the extreme sensitivity in initial
conditions for a system like the weather predictive system to work. Even a very
small change can cause very different effects to appear. He goes on to say that
an event as minute as a butterfly flapping its wings could affect a system’s
dynamics! This has even been appropriated in popular culture, albeit to an
extreme degree. Ashton Kutcher’s movie ‘The Butterfly Effect’ [5] is an example.
This may have caused misunderstandings of the term but it seems to have
evolved in the public’s imagination nevertheless.
Such an example illustrates how hard it is to model and predict crowd behavior.
The author will not elaborate much on this point- as there have been exhaustive
studies done on psychology and decision-making process of crowds. Some
important issues relating to crowd management along with some algorithms that
have used various strategies spanning different fields are discussed in the
subsequent sections that may help in yielding an effective solution for tackling
crowd congestion in systems like the SMRT.
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2 MRT in Singapore
Singapore’s population continues to increase. Due to its being a world class city
with excellent facilities and governance, it is natural to expect that people across
the world will be attracted to live in or tour Singapore. A significant portion of
Singapore’s workforce is accustomed to travelling in busy trains and buses to go
to work. The long queues at 8 am in the morning at MRT stations are a familiar
sight.
Figure 1 Crowds in MRT Stations [6]
It is interesting to note that Singapore has the lowest fares among the countries
analyzed. This could be a reason why an increasing number of people are using
public transport in Singapore.
Figure 2 shows an interesting comparison between Singapore and some other
countries in terms of average daily transport trips per person and average MRT
and bus fares taken from statistics from Singapore’s Land Transport Authority [7]
[8].
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Figure 2 Taken from Ref [7][21]
2.1 Public’s Perception of the MRT Service
It is interesting to note how members of the public express their opinions on the
aspect of congestion in public transport.
From ‘Singapore Hardware Zone’, an online forum, a group of users were
expressing their opinions that prices should be increased, especially at crowded
areas like Raffles City [9]. However by increasing MRT costs, members of the
populace who are not very well-off will have problems.
Some
other
suggestions
were
brought
forth
by
the
website
stomp.singaporeseen.com where a member suggested offices could tweak their
working times [10]. This may be a good solution, but businesses generally have
inflexible working hours [11]. The public sector has been very cooperative- by
offering its staff work starts at 7 am to avoid crowd congestion.
It may be very difficult to persuade businesses to incorporate flexibility in their
working hours. It is unreasonable that all companies will change their working
hours just to make a portion of its workforce escape crowded MRTs.
2.2 Singapore LTA Efforts to Combat Congestion
Traffic lights were rolled out at certain stations to display the amount of crowds
present. Thus, if there is a lot of crowding, a red light will be displayed, such as
displayed in Figure 3. This is a very good step. However, a problem arises when
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no good transport alternatives are present for the commuters. In that case, they
may ignore the warning and join the crowds [12].
Figure 3 Traffic Lights at Ang Mo Kio MRT, 2014. Photo: Oi Boon Keong
The Singapore LTA website mentions plans to add two new rail lines- the Cross
Island Line (CRL) and the Jurong Region Line (JRL) as well as doubling the rail
line to about 360 km by 2030. In 2012, the LTA had increased capacity of trains
by 15% as a result of a 4 year investment [13].
These plans are undoubtedly very helpful, but it is hoped that a holistic solution
to manage crowds will aid the LTA in managing crowds more easily.
3 Feedback in Crowds
Let us analyze a crowd- for instance, a large number of people waiting for the
MRT. In crowded situations, it is very important to understand why crowds could
react in an unruly manner. This can be a simple case of analyzing crowd
feedback.
In a crowded scenario, when the crowd stops moving, people are inclined to think
that the person in front of them isn’t moving and may be prompted to push. This
is due to a lack of feedback. A pictorial representation of this in the MRT System
framework is shown in Figure 4.
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Figure 4 Feedback in Crowds
In severe scenarios, as described by Helbing et al [14] or Ivancevic and Reid
[15], this could manifest itself in crowd turbulence and shock waves.
Individual’s decision making process:
In brief, the following steps illustrate an individual’s decision making process as
described by Pan et al [16].
1. Following instinct: This could be the cause of pushing others, trampling
etc. as instinct takes over in cases of panic.
2. Following Experience: Individuals may rely upon past experiences. This is
important to note as it suggests that absolute instinct doesn’t take over in
these scenarios- people are still able to draw from their experiences.
3. Bounded Rationality: Not all information is known, and not all
consequences are considered. This may result in irrational behavior.
The Inverted U Hypothesis, as illustrated in Figure 5, supports the hypothesis
that when an individual is under increasing stress, there is an increase in
disruptive and decrease in productive thoughts which may hamper the individual
especially during such situations [17].
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Figure 5 Inverted U Hypothesis [18]
3.1 An approach to holistic crowd management
Based on the above description of feedback system among crowds and the
taking the example of MRT of Singapore, a wholistic approach to managing
crowd might include the following tasks

Analysing crowd collectiveness

Crowd counting

Resource allocation to crowd
Each of these is described below
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4 Analysing crowd collectiveness – a Topological
Approach
Zhuo et al in a recent 2014 paper [19] had suggested a method to calculate the
‘Crowd Collectiveness’ using manifold analysis. This is a useful technique that
could aid in observing interactions between people.
They say: “Collectiveness, which indicates the degree of individuals acting as a
union in collective motion, is a fundamental and universal measurement for
various crowd systems.”
They mention that some spatially coherent structures may emerge from such
movements of crowd. They refer to this as the Collective Manifold.
An important point to note is that they observe behavioral consistency between
individuals and their neighbours. For a collected crowd, this is high locally but
may be lower at greater distances- i.e. it need not be high globally. Measurement
of this collectiveness could help in gauging when ordered crowds become
disorderly.
Zhou et al say that most surveillance technologies do not possess universal
descriptors to model crowd dynamics. They propose an important point: …
empirical studies of collective motion, which have shown that animals maintain
local interaction among neighbors with a fixed number of neighbors on
topological distance, rather than with all neighbors within a fixed spatial distance
Excessive crowding would violate these rules. In such cases, people are pushed
and shoved in the direction the crowd as a unit moves. This system could be
used as an alert for when these rules are violated. Even in cases of infighting and
unruly crowds, this system could be of help too- as disorder would lead to global
interactions with people fleeing or fighting amongst themselves.
Zhuo et al use techniques such as analyzing velocity correlations for k-nearest
neighbours, using an example of k=20 in their paper. They use a weighted
adjacency matrix and calculate the spectral radius of the matrix. Finally, using a
method of thresholding, they propose a convergence criterion which analyzes
crowd stability. This method could be useful in conjunction with the crowd density
calculation proposed by Baryshnikov and Ghrist [20] to analyze crowd stability.
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Barnett et al [21] in their work had also used topological concepts to model crowd
behavior. Though their emphasis is on their model being a potential aid for crowd
simulation for animators, the ideas that they mention in their paper- specifically
that of global instead of merely local interactions- are indeed very interesting.
Applying methods like that of [21] are important. It would be better that, instead of
immersing the system in the observation of local phenomena, to use it in
conjugation with a global outlook to yield better results.
Barnett et al describe placing sinks at the start and exit points in a given area.
They suggest the usage of Reeb Graphs and Harmonic Fields to find the
topology of the environment. The Reeb Graphs are derived from the Harmonic
Fields and in this way, global pathways to the exit are found taking into
consideration the possible obstacles in the path. Some figures from their work
are displayed in Table 1.
Table 1 Some figures from Barnett et al's work [21] illustrating their results
2(a) Reeb Graph computed by the
help of Harmonic Field
2(b) Resultant route set provided for
agents
Interestingly they mention: “Our method produces control at a higher level which,
while still compatible with previous methods, also automatically distributes the
crowd to avoid the formation of congestion”.
Use of Barnett et al’s method in situations of high crowd density with the
possibility of providing a set of clear routes for passengers to board the different
entry doors of the MRT will be useful as it reduces the burden of the SMRT staff
to manually gauge which routes should be used for best distribution.
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5 Topological approach to Crowd Counting
A popular paper by Baryshnikov and Ghrist [20] discussed ways to enumerate
targets using multiple sensors. In the MRT framework, cameras could be
installed at the escalators and the entry points to the MRT so that crowd density
at each station and for each train can be calculated.
They describe a field of infinitesimally small sensors, one at each point x
h( x)  N in a planar domain. It is assumed that finite set of points act as targets
and that the sensor at each target returns a quantized count h( x)  N that equals
the number of targets which are close by. They describe that this method can be
sensed by various modalities, but the author assumes the use of camera or
optical sensor.
They go on to say:
The sensors have no information about target location or identity. How can
sensors merge their local counts into a global count of the number of targets? If
the targets are sufficiently separated, then this becomes a simple problem of
counting the number of connected ‘on’ clusters in the network….. Assume that
each target Oa impacts its environment in such a way that Oa is detected
precisely on those sensors within Euclidean distance R of Oa . This is a
reasonable assumption if all targets are identical on a homogeneous domain.
Then the total number of targets may be computed as an integral:
# O 
1
M
 h( x)dx
R
(1)
2
Where M   R2 is the ‘mass’ of the support set on which the target Oa is
detected.
M  M #
 h( x)dx  

R
(2)
2
This is a simplistic situation for targets having supports with identical mass. In
their paper, they generalize this to target supports with different and unequal
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supports. A pictorial representation of sensor fields and target supports is
displayed in Figure 6.
Figure 6 Sensor Fields and Target Supports. Figure taken from [16]
They describe a method to do so using the Euler characteristic. The equation (2)
is modified as:
 (U )
 hd   

X
(3)
Where  (U ) is the nonzero Euler characteristic of the target support U  . The
advantage of using their method is that the target supports need not be assumed
to be round or convex, thus providing flexibility, and the formula is simple.
Table 2 illustrates four situations, after analyzing the crowd density.
1. Image 2(a) depicts a low density crowd with high patience parameter,
especially near the entry point of the escalator. Here, the p is high as there
are two queues, one on the left and one on the right on the escalator.
There is no pushing or shoving or crowding.
2. Image 2(b) depicts a number of escalator systems with orderly crowds in
all of them. The patience parameter p is high in this case as well.
3. Image 2(c) depicts a three escalator systems but the difference between
(b) and (c) is that here, one escalator has more crowds than the other two
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4. Image 2(d) depicts a very high density crowd with low patience p. This is
because there are no orderly queues and people are clustered at a single
exit. It is unclear whether more exits are available, but even if this is the
only exit available, the faster-is-slower effect must be used to bring the
crowd to order.
Table 2 Patience Parameter Determination for Different Cases. Images are taken
from [22]
2(a) Medium Crowd Density with 2(b) High Crowd Density with
High Density Parameter
High Patience Parameter
2(c) Low Crowd Density with High 2(d) Very High Crowd Density
Patience Parameter
Crowd with Low Patience
Parameter
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5.1 A practical application in the MRT context
As noted earlier, use of “Traffic lights” in MRT stations is a good move. Going
further, the author suggests that once the crowd density at every station has
been determined – on a near real time basis – the same can be used to reflect in
the MRT route map. This is shown pictorially in below
Normal MRT Route Map
Crowd density based Route Map
To be put to practical use, the route maps will have to be projected on to a
display screen from a centrally maintained crowd density database. The benefits
of such a system for both the residents of Singapore and for the visitors to
Singapore cannot be overemphasized.
6 Crowd Dynamics and Resource Allocation- A
Stochastic Approach Using Sandpile Model
It is common for systems which exhibit some critical phenomena, to require that
some adjustable parameters to be carefully tuned in order for the system to
reach the critical point. However, in 1987, Bak, Tang, and Wiesenfeld introduced
the sandpile model, in which the system was such that it spontaneously moved
towards the critical point and because of this, the critical behavior exhibited by
this model was termed as self-organized criticality [SOC].
Crowd behaviour in an MRT locale might be deemed to have characteristics of
SOC.
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Paragraph 6.1 describes the sandpile model in general and Paragraph 6.2
describes how the model can be applied to MRT system with suitable
modifications.
6.1 Sandpile model in General
An interesting paper by Ghosh et al [23] describes an experiment modelled on
the Kolkata Paise Restaurant Problem [KPR] [24] - which is in turn similar to the
El Farol Bar Problem proposed by Arthur [25] to analyze whether the system
moves to an absorbing from an active state, i.e. from multiple to single
occupancy which illustrates Self Organized Criticality.
The KPR Problem analyzes the case when gN agents wish to go to N
restaurants wish the assumption that agents will not prefer to go to crowded
restaurants. The result of this analysis is to observe how efficiently resources are
utilized, given such constraints.
They used two models- model A- based on the usual KPR problem, and model
B- which had an element ‘patience’, represented by p.
v(n)  (1  p) (n 1)
(1)
Here v(n) represents the inclination of particles to move and  (n  1) is a function
representing how v(n) is updated with every addition of a ‘grain’ into the local
system. They say:
Given the nature of the problem, we will consider models with v(1)  0 , i.e.
costumers are happy while alone, and v(n  1)  v(n) , i.e. repelling particles.
They found that if crowds had a larger value of p, the critical time or relaxation
time was lowered. This proves the faster-is-slower effect, which says that an
ordered exit will result in faster evacuation time than a chaotic exit. This may be
intuitive, but it is very important to bring this problem to light and use this in
developing an efficient algorithm.
They also note a critical density g c where a phase transition occurs from a frozen
phase with satisfied agents to an active phase with unsatisfied agents. This
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parameter could be useful to calculate at which point crowds will cross the frozen
or satisfied phase to an unsatisfied phase with the potential to turn unruly.
Ghosh et al [23] noted that their model was similar to that of Manna’s FES model
[26]. Simply put, Manna’s model is a modified version of the Bak-TangWeisenfeld sandpile model [27], which is a famous model of Self Organized
Criticality (SOC).
The BTW model assumed a lattice with open borders with ‘sand grains’ being
added to the model continuously. It is seen to reach a self-organized state.
Manna’s model was different- it assumed closed borders but with the grains
added in the initial stage with no addition of grains in subsequent stages. With
some conditions, the grains were observed to attain SOC stochastically.
The similarity of Ghosh et al’s model with that of Manna’s model could be
because, like Manna, they conserve mass in the system and allow the system to
approach criticality. They observe an interesting faster-is-slower effect related to
the relaxation time of the frozen phase.
6.2 Sandpile Model for the MRT Framework
One could start with a total of N seats, which gN commuters compete for. Of
course, some commuters would prefer to stand, and seats are exchanged
dynamically, i.e. seats may not be occupied for the whole journey- people would
get off, people would get in and some seats would even be offered to people who
may need it more- like pregnant women, disabled people or the elderly.
However, allowing a certain percentage of these situations- which could be
treated as ‘outlier’ cases, we have g1 N commuters competing for the fixed
number of N seats. Here g1 is the adjusted parameter removing the outliers
from the total population at any given time. This parameter can be found out
through observing video footage to determine the mean number of people who
might stand instead of compete for a seat even if they are available. It could even
be thought of as ‘noise’ in the system and could be modelled using Normal or
Gaussian Curve with values of mean and variance fixed using data from the
footage. It would appear that the number of such people willing to give up their
seats is fairly constant, and small compared to the large number of commuters
travelling in the MRT. Thus, the calculation of this parameter would perhaps not
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be very difficult.
After this analysis:
1. The term g1c could be calculated assuming a given value of p which is
reasonably high, i.e. at the start, the crowd is assumed to be behaving
rationally in an orderly manner with a fixed p value which reflects the
patience parameter. g1c is the critical density beyond which a frozen or
absorbing to active phase transition is observed.
2. This could be corroborated with real-time video footage of the crowd. If
the p value is found to be low then a revised value of g1c is
calculated. This could suggest the possibility of overcrowding.
3. An alert could be sent to the SMRT staff and required authorities.
4. This could be done at every station and even near the escalators.
5. Thus getting off from crowded trains could be made less strenuous if
alerts are given if the value of p gets too low- suggesting impatience and
possible pushing and shoving of commuters.
Figure 7 illustrates a flowchart of using a modified version of their model to be
possibly used in the MRT Crowd Control Framework.
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Figure 7 Using Sandpiles to Manage Crowds in MRT
6.3 Suggested Way to Incorporate Patience Parameter
A topological approach could be used to analyze crowd density and
collectiveness. Here an approach to calculate crowd density from sensors is
described, and a method to analyze crowd collectiveness will also be discussed
in the later sections.
7 Proposed Method
Congestion
and
Algorithm
to
Control
The author suggests the implementation of a system for crowd control
management in MRT and other areas as well. The proposed solution uses the
ideas suggested above, but in a holistic way so that benefits will be enhanced.
The ideas proposed by Ghosh et al [23] cannot be used as they are- this is
because they assume a sandpile model that has its mass conserved. Obviously,
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this is not applicable to systems like MRT that involves people leaving and
coming in.
1. Use a Modified Sandpile Model: The MRT can be regarded as a closed
system with a given number of fixed exits. Additionally, there are an
unequal number of people who get in and off at different stations. A
modified sandpile mode is suggested as follows: Use partially open
borders and addition and removal of sandgrains at predetermined
intervals- which refers to the MRT stations. For instance if the time taken
to travel from Bishan to Ang Mo Kio is k minutes, then this information can
be incorporated into the sandpile model. Figure 8 displays a suggested
sandpile model.
Figure 1 As MRT doesn’t have open exits, or a fixed number of sand grains
added regularly, it needs to be modified to fit the layout in the figure
2. After using modified sandpile, use Model B from [11] which incorporates
the patience parameter. The value p is derived using the data from the
camera sensors as described before. The critical density of the MRT
crowds g1c that has been corrected keeping in mind outlier cases is
calculated.
3. After this, the relaxation time could be computed keeping g1c and p in
mind. Accordingly, if p is low, the system could alert the SMRT staff to try
to intervene and regulate people entering an already crowded MRT
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This process must be repeated at every station, as there will be an influx of
people entering and leaving the MRT System.
Next, this could be corroborated with Zhuo et al’s Collective Manifold theory [17]
for calculating crowd collectiveness. This could be performed in the MRT as well
as be used near the escalators for observing crowding there. Excessive crowding
at escalators decreases commuters’ enjoyment.
Such a formation- which can be thought of as many ‘streams’ of people coming
together could be analyzed. This is important as a large crowd, especially at rush
hour, congregates at escalators to leave the station. Using Barnett’s research for
global crowd control, paths could be found that represent maximum flows for
commuters and instead of taking one path which could cause congestion at the
exits- different paths could be suggested so that commuters are spread out
across the region to avoid congestion. This is the ‘Global Analysis’ part. Figure 9
displays the flowchart of the process.
Figure 2 Flowchart of the Process
8
Conclusion
To summarize, the author proposes using a holistic algorithm to monitor crowd
behavior. This uses a combination of Self Organizing Criticality involving
Sandpile analysis, Topological Methods and Collective Manifold Analysis. It has
also taken into account various phenomena such as the faster-is-slower effect,
the Inverted U hypothesis and Bounded Rationality.
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Clearly the model needs much fine-tuning. A modified sandpile which takes into
account the MRT system must be developed fully. Crowd turbulence analysis to
analyze crowd ‘streams’ seems to be promising, but further studies may need to
be performed to gauge its efficiency.
A takeaway of this study is that a many-pronged algorithm might work better than
an algorithm with a limited focus. At the end of the day, such systems should be
able to work in harmony to make the commuter enjoyment more enjoyable. By
extension, it is hoped that they can find use in security situations as well – for
instance, in tracking abnormal behavior and even riot management and control.
Such warning systems that can send timely alerts to the authorities will indeed be
very helpful.
9 Bibliography
[1]
http://data.worldbank.org/indicator/SP.URB.TOTL.IN.ZS
[2]
http://www.who.int/gho/urban_health/situation_trends/urban_population_growth_te
xt/en/
[3]
Winter, H. (2012). Modelling Crowd Dynamics During Evacuation Situations Using
Simulation.
[4]
Lorenz, E. (1972). Predictability: does the flap of a butterfly's wing in Brazil set off
a tornado in Texas?
[5]
https://en.wikipedia.org/wiki/The_Butterfly_Effect
[6]
https://amylamsg.files.wordpress.com/2013/04/mrt-commuters-crowd-squeeze533623.jpg
[7]
https://www.lta.gov.sg/content/dam/ltaweb/corp/PublicationsResearch/files/Factsa
ndFigures/Stats_in_Brief_2013.pdf
[8]
https://www.lta.gov.sg/content/dam/ltaweb/corp/PublicationsResearch/files/Factsa
ndFigures/Statistics%20in%20Brief%202014.pdf
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[9]
http://forums.hardwarezone.com.sg/eat-drink-man-woman-16/only-way-reducecongestion-mrt-trains-issue-coe-usage-4983671.html
[10] http://singaporeseen.stomp.com.sg/singaporeseen/this-urban-jungle/could-crowdcongestion-in-mrt-trains-be-solved-if-companies
[11] http://www.straitstimes.com/news/opinion/more-opinion-stories/story/spreadingout-peak-mrt-crowds-20140520
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Temasek Defence Systems Institute
Department of Industrial and Systems Engineering, Faculty of Engineering, NUS
Systems Engineering Essay Competition 2015
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Jointly organised by
Temasek Defence Systems Institute
Department of Industrial and Systems Engineering, Faculty of Engineering, NUS
Systems Engineering Essay Competition 2015
Page 23 of 23
Biography
Mithila Harish is a PhD Research Scholar from the NUS Graduate School of
Integrative Sciences and Engineering (NGS), NUS. She is keenly interested in
crowd dynamics and incorporation of improved evacuation dynamics in Smart
Cities. She also possesses an avid interest in Signal Processing, particularly
relating to Speech and Audio Processing. She completed her B.Tech in
Electronics and Instrumentation from the Vellore Institute of Technology (VIT),
India.
_____________________________________________________________________________
Jointly organised by
Temasek Defence Systems Institute
Department of Industrial and Systems Engineering, Faculty of Engineering, NUS