Comprehensive Evaluation and Optimizing for Boarding Strategies
Da-wei Sun1, Xia-yang Zheng1, Zi-jun Chen1, Hong-min Wang1
1
Department of Electric and Electronic, North China Electricity Power University, Beijing, China
([email protected])
Abstract - In this paper, we focus on the need for
reducing boarding time for airlines. Therefore existing
researches devoted to designing boarding routines and
studying boarding strategies in existence. A model based on
cellular automata is developed for calculating the integrated
boarding time and testifies that the Reverse-Pyramid way is
one of the most effective strategies. Aiming at giving an
optimal boarding strategy, this paper combines a new
evaluating criterion with some further analysis of
Reverse-Pyramid
and
finally
concludes
that
Reverse-Pyramid strategy which is divided into 5 groups
and has more groups with a particular proportion is the best.
Somehow the present paper solves the neglect of passengers’
satisfaction and time spent on organizing before boarding in
existing researches and gives some recommendations to
airlines at last.
Keywords- aircraft boarding, aisle interference, cellular
automata, evaluating criterion
I.
INTRODUCTION
How much time is usually demanded for different
necessary tasks when the airplane is landed, which are
departure, fuel, baggage loading and unloading, catering,
and passengers’ boarding? According to reports from
Boeing, the passengers’ boarding is the most
time-consuming task, around 60% of the total. [1]
Because the plane makes money for airline only
when it is in motion, reducing the boarding time is helpful
to not only arrange more scheduled flight but also be
beneficial to finance and customer’s satisfaction. So in
order to reduce the boarding time, many researches and
the present paper build the boarding strategy, which is a
group of rules that aim at boarding all passengers as
quickly as possible.
For the former researches, in 2002, Van Landeghem
and Beuselinck compared the random strategy and
back-to-front strategy. And results showed that the random
strategy performed better [2]. Then in 2005, Pieric and Kai
modeled the aisle interference by grid simulation [3]. The
same year, Menkes and Briel firstly came out the reverse
pyramid strategy [4].
For the present paper, a model based cellular
automata is presented to study the different strategies. An
integrated standard is given to estimate the strategies
including the total boarding time, interference waiting
time per passenger and time spent on organizing before
boarding. Finally the paper optimizes the reverse pyramid
strategy and gives some recommendations.
II. COMPARING BOARDING STRATEGIES
A. 2.2 Model
2.2.1 Assumptions:
(1) Interferences are the major reasons lead to wait.
There are two main kinds of interferences which are aisle
interference and seat interference. The aisle interference
shows that the process of placing baggage will delay the
passengers who followed by them. And for the second
kind, when a passenger wants to settle in the window seat,
he may block other passengers of the same line. We call
this ‘seat interference’. But in the model, we ignore the
seat interference, because many researches made clear that
Outside-In strategy is better than Back-To-Front and
random strategy mainly because Outside-In strategy
avoiding the seat interference. The paper mainly studies
the strategies which avoid seat interference themselves on
the basis of predecessors, so the seat interference doesn’t
influence the results.
(2) Assumptions for the passengers: they will not
happen to have other’s seat or miss his seat. And they will
obey our arrangement of boarding. Also the paper doesn’t
consider the passengers’ coming late.
(3) Assumptions for the planes: the boarding gate is
in the top of the cabin. And the business class seats and
the first class seats are far less than economy class seats.
That allows us to only consider the boarding of passenger
in economy class.
2.2.2 Introduction of three strategies
Table 1 Introduction of three strategies
Name: Back-to-Front
Advantages
Somehow avoid the conflict
of gangway because the back
passenger will not be
obstructed by the front
passenger.
Name: Outside-In
Advantages
Totally avoid the conflict of
seat and fully make use of the
space of gangway to place the
luggage.
Name: Reverse-Pyramid
Advantages
Have the advantages of the
former two strategies.
Picture
2.2.3 Describe the cabin
Because we want to describe the individual behavior,
we decompose the cabin into many units. Just like the
following figure. The figure follows these assumptions:(1)
All the seats are treated as the same size and each seat is
considered as one unit which is arranged very closely.(2)
The gangway has the same width of a seat and it only
allows passengers to stand as single line.(3) The only
entrance is at the top of the economy class.
gangway
Figure 1 Cabin
This figure is the small size of plane that can have a
capacity of 100 passengers.
2.2.4 Describe the behavior of passengers
All the passengers fit the following three rules.
(1) There are 100 passengers and everyone’s target
seat is his own seat and will not have a wrong seat. (2) If
no one arranges the passengers, they will board randomly.
(3) Passengers board continuously.
The individual behavior fits the following five rules.
(1) If no one stops a passenger, he will walk directly to the
‘gangway unit’ that is the nearest one to his target seat. (2)
Once the passenger arrive the nearest gangway unit, he
will spend some time placing the luggage. (3) After
placing the luggage, he will move to the target seat. (4) It
is a discrete model, so when the timer adds a unit of time,
every passenger can move to the empty unit near his
present unit. (5) If timer adds a unit of time and the next
unit that the passenger wants to move in is busy, the
passenger will stay at his present unit until the next unit is
empty.
2.2.5 Describe time spending on placing luggage for every
passenger
Most researches consider the aisle interference as a
probability event, without considering the influence of
increasing and decreasing of the luggage. Although some
considered it that the time grew linear with the quantity of
luggage existed in the trunk. But these researches didn’t
account for the luggage capacity of the plane.
For these reasons, we draw support from literature [5].

Tbag 
(c  1)  (nbin  nlug )
s.t. : 0  (n bin + n lug )  c
nlug



In the formula,Tbag means the time using for placing
the luggage. nbin means the present amount of baggage
that already be placed in the luggage trunk. Nlug means
the number of bags that will be put in the luggage trunk. c
means the number of capacity of luggage rack for one row
of seat.  is correction coefficient. According to [5], c=4,
=20 [7-8].
Figure 3
In this hyperbolic model, set ΔT to stand for the unit
time of placing luggage. ntotal stands for the total number
of capacity of luggage rack for one row of seat.
So
is a hyperbola (see figure 3). We
can find that when the spare of suitcases become smaller,
the time of placing luggage is longer. When ntotal>4, the
time of placing luggage approaches infinite [9].
But not everyone will bring luggage and they have
different number of bags. The paper refers to the report
from ‘Data 100 Market Research’ and gets the probability
for every passenger as the following table [10].
Table 2
Number of bags
zero
One
two
A passenger
20%
70%
10%
B. 2.3 Results
No.
How to divide the group
1
5
7
1
3
8
6
4
2
gangway
2
3
4
2
6
1
5
8
4
7
3
gangway
3
7
1
4
8
5
6
2
gangway
1
2
gangway
Steps of
boarding
Waiting
steps
196.5
42.5
190
39
185
36
199
38.5
201
45
194
42
189
37
2
1
5
6
7
3
4
1
2
4
3
2
1
gangway
2
4
1
3
4
2
3
1
3
4
1
3
4
2
2
1
gangway
gangway
Figure 4
For each result, we simulate 200 times and average the
results to become the finally result. And we calculate the
root-mean-square deviation of every result and find that all
the root-mean-square deviations are smaller than the 5%
of the corresponding results. So we can say the results are
credible.
Compare the results of strategy 1, 2, 3. We can see
the strategy 3 is best because its boarding steps and
waiting steps are the least. Strategy 1 is similar to the
strategy of Back-To-Front. Strategy 2 is similar to the
strategy of Outside-in. And strategy 3 is similar to the
strategy of Reverse-Pyramid. Therefore, we can see the
advantage of Reverse-Pyramid. For the same reason, when
we compare the strategy 4, 5, 6, 7, we can get the same
laws. So we can conclude that Reverse-Pyramid is the best
one on the hand of total steps and waiting steps. So we
concentrate on the strategy of Reverse-Pyramid.
III.
OPTIMAL NUMBER OF GROUPS
IV.
Compare with the four strategies in figure 5, we find
the strategy 13 is the best. These four strategies are all
Reverse-Pyramid. The difference between the four
strategies is shape of the second, the third and the fourth
group. The second group has some window seats and
some aisle seats. If we change the proportion of the two
kinds of seats, the results will change. For the same
reason, changing the third and the fourth groups’
proportion of two kinds of seats will change the final
results. Comparing these four strategies, we infer that it is
better to arrange more groups that have the proportion of
7/3 approximately (7 is window seat and 3 is aisle seat).
The higher the number of groups of seats in the
airship, the longer it takes to organize a line before
boarding. Most researches didn’t explain how they chose
the number of groups. The present paper calculates the
financial lose because of the time spent on organizing a
line and waiting time. So using the economic indicator, we
find the optimal number.
First we assume that all the 100 passengers sit in
waiting hall by a line. Finally, different strategies require
different orders of queues. For example, if one strategy
requires every one boarding in a certain order, that’s to
say, the number of groups is 100, the queue must be
formed in order one by one. But, if one strategy makes the
passengers’ boarding randomly, all passengers will stand
the position closest to his seat in waiting hall. Finally, we
get the total average steps using for organizing a line for
different number groups. Some results are showed as
follow.
Table 3
Number of groups
0
Organizing steps
0
5
105
100
2514
We treat the steps using for organizing a line the
same as the average waiting steps, because the two kinds
of steps reflects the satisfaction of passengers. And
according to the literature [6] and The Civil Aviation Act,
Air China’s flying hours is 736770 in 2007 and retained
profits are 3773 million RMB. Also airline pays every
passenger 200 RMB for 4 hours aircraft delay. So
according to the ratio of money, we get the ratio of waiting
step and boarding step which is 1/25.605. With all the
data, we can calculate the optimal number of groups. The
result is that 5 is the most optimal number and there are
some results as follow.
Table 4
Number of groups
0
Total steps
226
5
211
Figure5
No.
How to divide the group
4
3
2
4
5
11
5
3
4
12
4
2
3
2
2
4
3
4
3
2
2
2
2
4
4
2
3
2
3
2
3
2
4
4
V.
205.5
44.2
209.5
45.4
1
5
5
2
44.7
1
3
2
3
2
gangway
3
207.5
1
5
5
3
44.9
1
gangway
4
209
1
5
3
Waiting
steps
1
5
3
4
13
14
2
3
gangway
4
Steps of
boarding
1
3
gangway
4
1
CONCLUSION
The present paper simulates a model to calculate the
total boarding steps, waiting steps and organizing steps.
First the model compares the three boarding strategies.
Finding that the best one is Reverse-Pyramid, the model’s
results are the same as the other researches and that
somehow proves the reliability of the model. Then a new
way of evaluating boarding strategies comes out and
shows that dividing into 5 groups is the best choice.
Finally an optimal Reverse-Pyramid is given. And the
paper recommends airline that for the similar structure as
figure 1, it’s better to use Reverse-Pyramid strategy which
is divided into 5 groups and arranges more groups that
have the proportion of 7/3 approximately. For the other
type of planes, one method is to divide the bigger plane
into the structures as figure 1 shows. Another way is to
change the parameter in figure 1 to fit the special type
plane. Both methods are easy to achieve.
100
217
All the results in section 3 are for Reverse-Pyramid
strategy.
OPTIMAL REVERSE-PYRAMID STRATEGY
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