International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 5
Number 3
September 2011
291
1 INTRODUCTION
The ship arrival distribution test is a vital piece basic
research for port planning and for the choice of dis-
tribution pattern in the simulation approach. The test
implements the ship arrival distribution approach.
The test result of the ship arrival distribution will in-
fluence the choice of port queuing system ,which
subsequently influences relevant variables measured
from such model .The purpose of this paper is to
find the ship arrival distribution and their proba-
bilites in the spread sheet simulation systems. After
many ship arrivals are merged and verification are
required to define the statistical pattern of the ship
arrival time distribution. Base on ship dynamic data
of international port in Yangshan and using AIS data
for this study. This study also investigated the evolu-
tion of the ship arrival distribution pattern and theirs
probabilities by observation system .It was focused
on the probability distribution pattern of the arrival
distribution for vessels with the poission distribu-
tion.
2 OPERATION BACKGROUNG
Vessel Traffic studies are necessary in harbour con-
struction. In planning and design of harbours and use
both real vessel and scale model to do experiment
and collect data. Also depends on statistical studies
and synthesize domestic marine traffic data. Ships
routeing system is at the sea area Yangshan port.
The Yangshan deep-water port is a new port in
Hangzhou Bay south of Shanghai. 27.5 kilometres
from Shanghai's southern coast, and under the juris
diction of the neighbouring Province Zhejiang, was
chosen as the site of the deepwater port of Shanghai.
The average water depth in the area of the islands is
over 15 meters. Yangshan deep water port has five
container berths, each around 15 meters deep.
AIS is excepted to play a major role in ship re-
porting system .The systems is typically included in
the static voyage related and dynamic data automati-
cally provided by the AIS system .The use of the
AIS long range feature, where information is ex-
changed via communications satellite ,may be im-
plemented to satisfy the requirements of ship report-
ing systems . AIS will play a role in overall
international maritime information system, support-
ing voyage planning and monitoring. This will assist
Studying Probability of Ship Arrival of
Yangshan Port with AIS (Automatic
Identification System)
Ni Ni HlaingYin
Myanmar Maritime University, Yangon, Myanmar
Shanghai Maritime University, Shanghai, China
Hu Qinyou & Shi Chaojian
Shanghai Maritime University, Shanghai, China
ABSTRACT: The distribution pattern is considered to be a poission distribution for periodical schedule. The
evolution of the ship arrival distribution patterns and the χ
2
fit test for observation are based on the ship dy-
namic data of international harbour in Yangshan. AIS (Automatic Identification System) is used the frequen-
cy of ship arrivals in this study .This study aims to implement the test for performance of ship arrival distribu-
tions and theirs probabilities. The ship arrival distribution in the spread sheet simulation systems was found to
follow poission distribution; its frequency distribution is changed by observation system, tends to change the
system’s of the probabilities.
292
administrations to monitor all the vessels in their ar-
eas of concern and tracks.
Figure 1 Yangshan Deepwater Port in China
3 MODEL DEVELOPMENT
The scope of present study considers the effect of
harbour allocation on arriving times.Therefore, nec-
essary to model the system starting from the ship ar-
rivals and theirs probabilities to the berth opera-
tions.This simulation model was developed spread
sheet Excel software.
3.1 Ship’s arrival model
The ships arrive at a datum line randomly, the num-
ber of ships arriving at the datum line in a given in-
terval of times is a random variable and its distribu-
tion fits the poission distribution (k.Hara, 1966), and
the probability is:
(
=
)
=
!
k = 0,1,2,3,… (1)
where P (X=k) = Probability that k ship will arrived
at the daum line in a given interval of time t;
λ
= av-
erage number of ships arriving at the datum line in
unit time ; e = base of Naperian logarithm, e= 2.718;
t = given interval of time.
If no ship will arrive in the time interval t, that is
k=0, then
(
= 0
)
=
!
=
λ
(2)
The distribution of the number of ships arriving
enterend into a harbour in a week Figure.2 and The
data of the daily number of ships entered into a har-
bour in a week are fits the Poission Distribution in
Figure.3.
Figure 2 The distribution of the number of ships arriving
distribution of the ships arriving times
frequency ( number of ships )
293
Figure 3 Number of ships entered in a harbour and theris arrival times
3.2 Discussion of test approch
First, a base model is developed and AIS data of
ship arrivals are used the frequency of ships arrivals.
The data consists distribution of 164 ships arrivals a
period of a week .The generated data is used to run
actually arrived at the port in a week.The empirical
frequency distribution of daily number of ship is
sorted out and fitted the Poission Distribution in Ta-
ble 1.
=
the total number of ships in a week
the number of days in a week
=
41
7
= 5.85 /
Table 1 The Empirical frequency distribution of Daily Number
of ships
_______________________________
n f
j
Frequency (f
j
/ N)
_______________________________
1 1 0.143
2 1 0.143
3 0 -
4 1 0.143
5 0 -
6 1 0.143
7 0 -
8 1 0.143
9 1 0.143
10 0 -
11 1 0.143
_______________________________
Total 7 1.001
_______________________________
3.3
χ
2
fit test
The most appropriate approaches are the χ
2
fit test.
χ
2
fit test is to be applied .Hypothesis, the empirical
frequency distribution of the daily number of ships
fits the Poission Distribution.
=
(3)
where f
j
= the frequency of group j for empirical dis-
tribution; F
j
= the frequency of group j for Poission
Distribution, F
j
=NP
j
; N = the volume of a week; P
j
= the probability of Poisson Distribution; g= the
number of groups
Test the sample in this study should be divided
into group before applying this approach to the ship
arrival distribution. Grouping (selecting the number
of groups and group arrival) is critical factor for the
χ
2
fit test in this study. The χ
2
fit test of statistical
analysis is applied for the ship arrival distribution
test in this study.
3.4 Simulation
After simulating the base model, a replication was
performed for each of the ships arriving times rang-
ing for a week before any data is recorded to sure
state has been achieved .The model is then run for
another year to obtain the annual throughput.
4 RESULT
The purpose of the present study is to understand the
various ships arrival on the times within a week and
their probabilities. Table.2 shows the process of cal-
culation for χ
2
and figure.4 shows the arriving
groups and their probabilities percentage.
The result of the calculation is χ
2
= 10.637. DF
=g-γ-1= 7-1-1=5 (γ is the number of parameter of the
poission Distribution), α =0.05. The Table of χ
2
Distribution (Table.3) is referenced.
χ
2
α
= 11.070. Owing to the fact that χ
2
< χ
2
α
,
the hypothesis cannnot be rejected. That is to say,
theirs arrival times
number of ships entered in a harbour
294
there is no real evidence to doubt that the empirical
frequency distribution of the daily number of ships
fits the Poission Distribution.
Table 2 χ
2
Calucation
___________________________________________________
n f
j
P
j
F
j
χ
2
___________________________________________________
1 1 0.016 0.112 7.040
2 1 0.049 0.343 1.258
3 0 - - -
4 1 0.140 0.98 0.001
5 0 - - -
6 1 1.160 1.12 0.012
7 and more 3 0.035 0.245 2.326
___________________________________________________
Total 7 10.637
___________________________________________________
Table 3 χ
2
Distribution Table
___________________________________________________
DF α
0.10 0.05 0.025 0.01 0.001
___________________________________________________
1 2.706 3.814 5.024 6.635 10.828
2 4.605 5.991 7.378 9.210 13.816
3 6.251 7.815 9.348 11.345 16.266
4 7.779 9.488 11.143 13.277 18.467
5 9.236 11.070 12.833 15.086 20.515
6 10.645 12.592 14.449 16.812 22.458
7 12.017 14.067 16.013 18.475 24.322
___________________________________________________
5 CONCLUSION
The ship arrival distribution varies depending on the
test approaches of the number of group interval. The
χ
2
fit test is hard to pass with larger samples, the
study suggested that the threadhold limit value
should be modified appropriately for larger samples
in order to conform to realistic needs .The result
provides the statistical analysis of ships’ arrival
times and their probabilities at Yangshan terminal
in China .
Figure 4 The arriving groups and their probabilities percentage
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