International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 3 - September 2015
Empirical Study On Passenger Facilities Layout In An Airport
Using Centre Point And Median Point Graph Theory
Concepts - Study Of The Indira Gandhi Domestic Airport,
New Delhi.
Shrinkhala Singhania, Shivam Shashikant
BTECH, Computer Science Department, VIT University
Vellore, India
Abstract - In the given paper, we apply centre point
and median point concepts to effectively study
passenger facilities layout at the Indira Gandhi
Domestic Airport, New Delhi. We identify key
passenger facilities at the departure terminal and look
at the volume of passengers travelling between these
facilities. On the basis of this study, we look at a
better restructuring of the passenger facilities to
improve passenger flow between the identified
stations. This can be better used in future planning of
airports and hence determine the optimum passenger
flow between major junctions in an airport.
Keywords — airport, traffic management,
passengers, median point.
B. DEFINITION OF CENTER POINT
It is defined as the vertex (or vertex set) with the
minimum eccentricity. Suppose we have M(i) be
the maximum of the distances from vertex i to all
vertices in Graph G,
M(i) = maxj{dij}
Then let M (x) be the one which makes M(i) to
reach minimum in all i , where i=1,2,3,…,n, so we call
M(x) the centre point of Graph G,
M(x) = mini maxj {dij}
C. DEFINITION OF MEDIAN POINT
I. INTRODUCTION
The number of people using airline services has
increased manifold in the recent times thanks to the
developing economies, cheap air fares and the need to
travel faster and more comfortably. This pressures the
airports to effectively position their passenger
facilities such that the large number of people can be
easily managed and transported form one place to
another. Thus, passenger facilities management
becomes a major task while planning the airport
layout. We look at two key concepts, the centre point
and the median point concepts to reduce the distance
between those facilities where passenger volume is the
maximum. We also heavily apply the principles of
rationalization while theoretically interchanging any
two facilities.
II. GRAPH THEORY CONCEPTS
The graph theory concepts used are described
below:
A. DISTANCE
Consider a graph G with the vertex set V(G) =
{v1 ,v2,…., vp} and the edge set E(G)={e1 ,e2,…..,
eq}. Let us consider the vertices vi and vj. The
coordinate of vi is (xi,yi), that of vj are (xj,yj). The
distance between the two vertices is defined as:
Median point is utilised in making the sum of
distances to a minimum. Suppose the sum of the
distances from vertex i to all vertices of Graph G
be written as S(i). Now,
S(i) = ∑ dij
Then let S(x) be the one which makes S(i) to reach
minimum in all i , where i=1,2,3,..,n, so we call S(x)
the median point of Graph G,
S(x) = min {∑ d(i,j)}
III. PASSENGER LAYOUT FACILITIES
The passenger flow is analyzed at the “Departure”
terminal. The five key facilities are identified as:
Baggage counter, boarding pass center, commercial
area, utility area and restaurants. They are labeled as A,
B, C, D and E. The center point is chosen as the point
where the inflow of passenger volume is the
maximum. Median point is chosen as that node where
the sum of distances is a minimum. The five facilities
are now mapped in the Indira Gandhi Domestic
Airport Departure Terminal MapAll paragraphs must
be indented. All paragraphs must be justified, i.e. both
left-justified and right-justified.
dij={(xi- xj)2 + (yi-yj)2}1/2
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 3 - September 2015
IV. APPROACH
To make passenger transportation volume
minimum we use the New Method wherein the
passenger volume data V is written in descending
order and the distance between various facilities D is
written in ascending order. We then calculate V x D to
get a threshold value for passenger transportation
volume. Let us call this value T.
Our main objective is to distribute the core
passenger facilities such that we can obtain a V x D
value which is less than or closest to T.
For this we apply the principle of large logistic
volume-short distance.
In this principle we try to assign the area with the
largest passenger volume to the minimum distance by
replacing the location of the core facilities A, B, C, D
and E amongst themselves. This is done based on
priority (Highest passenger volume first).
After interchanging locations amongst the core
facilities, we again calculate the V x D value and
compare it with the threshold value T. Let the value
obtained at this stage be T1.
If T1 > T, then we interchange the locations pair
wise and again calculate V x D.
If our value exceeds T1 then we utilize the previous
locations as the best possible passenger facility layout.
Else we repeat the process iteratively till the results
of the new process decrease and move closer to the
final data or till it increases over the previous data.
This process can be used to design the passenger
layout of upcoming airports to reduce the passenger
volume transportation.
V. MAP OF IG DOMESTIC AIRPORT, NEW
DELHI
FIGURE II
FIGURE III
VI. CALCULATIONS
TAB I
FIGURE I
Statistics state that on an average approximately
9500 people are present per day at the Delhi Indira
Gandhi Domestic Airport. We assume that there are
100 people per day on an average at the airport.
In figure 1, the minimum distance between the
baggage counter (A) and the boarding pass area
(B) The map [4] is scaled and hence we consider
distances in the smaller unit (cm)
The height and width of the distance is 1.1 and 4.3
inches. The distance is then calculated using
Pythagoras theorem which comes out to be 11.4cm.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 3 - September 2015
An important approach in the determination of
distances between the identified passenger facilities is
that in case of a passenger facility present at more than
one point (such as the utilities facility), we consider
the nearest facility for calculation of distance. Also
Similarly we calculate the distance between the
other points.
First, we use the data from V, and make these data
ordered from large to small and then from small to
large, respectively. So we get:
(VAB,VAC,VBC,VAE,VBE,VDE,VAD,VBD,VCD)
=(100, 100,100,60,60,60,40,30,30,20)
(dAD, dCD, dDE, dBC, dAB, dBD, dCE, dBE, dAC,
dAE) = (5.1, 5.5, 7.2, 7.6, 11.4, 11.9, 13.2, 18.8, 19,
30. 2)
Now,
V x D = (100,100,100,60,60,60,40,30,30,20) x
(5.1,5.5,7.2,7.6,11.4,11.9,13.2,18.8,19,30.2) = 5900
This value is a minimum threshold, used to measure
the degree of optimization of the model. According to
the principle of large logistics volume-short distance,
these data are be reordered in Tab. II
For example, the largest passenger volume is =100,
and the minimum distance between A and D is =5.5.
That is, between the site 1 and 4, A can be assigned 1
or 4 then B is assigned to the remaining one; similarly,
we check for other volumes. Based on above
constraints, we list the following table that shows the
location of available assigned points of these five
regions, which also considers the priority, as showed
in Tab. II.
A. THE LOCATION OF AVAILABLE ASSIGNED
POINTS OF THESE FIVE REGIONS
VEB x d12 + VEC x d13 + VEA x d14 + + VED x
d15 + VBC x d23 + VBA x d24 + VBD x d25 + VCA
x d34 + VCD x d35 + VAD x d45 = 6882
Since this value is greater than the minimum
threshold value, so it is not the optimal solution. Since
the objective function value of initial layout program
is 6,882, larger than 5900(the minimum threshold), so
it is not the optimal solution. Therefore, we use
Modification Method to optimize the initial program.
The concept of Modification Method is to interchange
the location of these five regions on the basis of
original program, re-calculating their objective
function, as shown in Tab. IV.
TAB IV
In Tab. IV 6678, this is the smallest of all objective
function values. Therefore exchange C and E as the
first improved program, as showed in Tab. V.
B.
FIRST IMPROVED PROGRAMME:
SITE
1
2
3
4
5
REGION
C
B
E
A
D
TAB V
From the TAB V, the transportation volume of the
first improved program is calculated out to be 6,678.
Available assigned
sites(considering the
Regions
priority)
A,B
A,C
B,C
A,E
B,E
P1: 1 or 4
P2: 3 or 4
P3: 4 or 5
P4: 2 or 3
P5: 1 or 2
TAB II
TAB VI
We now get a minimum when we successfully
interchange the nodes A and B. Rationally, this is not
feasible. Therefore, our first improvement is the final
possible program under our analysis.
INITIAL PLANNING PROGRAM
SITE
REGION
1
E
2
B
3
C
4
A
5
D
TAB III
From TAB IV the passenger volume can be calculated
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ISSN: 2231-5381
VII.
CONCLUSIONS
Thus, we see that after each step, the optimized
value keeps getting closer towards the threshold value.
This means that there is certainly room for
improvement in the current passenger facilities layout.
This method, which is used for designing the airport
facilities, can also be extended to the passenger
facilities layout in an airport terminal.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 3 - September 2015
ACKNOWLEDGMENT
We would like to thank Prof. Selvakumar R Senior
Professor & Controller of Examinations Professor,
School of Advanced Sciences, VIT University for
mentoring us in the research done on this paper.
REFERENCES
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“Research on Layout of Airport Logistics Park Based on
Graph Theory: An Empirical Study of Ningbo Airport
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2010
International
Conference on Intelligent Computation Technology and
Automation By Changbing Jiang, Lijun Bai, Wenwen
Zheng of Contemporary Business and Trade Research
Center Zhejiang Gongshang University.
“A review of models and model usage scenarios for an
airport complex system” By Paul Pao-Yen Wu, Kerrie
Mengersen of Queensland University of Technology,
Mathematical Sciences School, 2 George Street, Brisbane,
Australia.
“Graph Based Model To Transport Network Analysis
through GIS” By Paulo Morgado and Nuno Costa of
University of Lisbon, Portugal.
Map of the New Delhi, India airpot [Online]. [Available]: [4]
http://www.newdelhiairport.in/interactive- maps.aspx
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