Modeling the arrival process at dry
bulk terminals
Delft University of Technology
Faculty 3ME, Transport Engineering & Logistics
22-05-2012
T.A. van Vianen, J.A. Ottjes and G. Lodewijks
Delft
University of
Technology
Challenge the future
Modeling arrival process
1
Content
•
•
•
•
•
Arrival process
Average port time
Modeling arrival process
Continuous quay layout or multiple berths
Conclusions
Modeling arrival process
2
Arrival process (1)
• Typical performance indicator is the average ships’ waiting time
• Agreements between terminal operators and ship-owners are
made about the maximum ships’ port time
• Demurrage costs have to be paid if ships stay longer in the port
• How much capacity must be installed at the quay side?
Ship loading (Courtesy of Richards Bay Coal Terminal)
Ship unloading (Courtesy of J.Hiltermann)
Modeling arrival process
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Arrival process (2)
• How to prevent that ships are queuing before getting serviced?
Find the optimum
Costs
Ships waiting before servicing
Demurrage costs
Operational costs
Quay side capacity
Modeling arrival process
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Content
•
•
•
•
•
Arrival process
Average port time
Modeling arrival process
Continuous quay layout or multiple berths
Conclusions
Modeling arrival process
5
Average port time (1)
• Average port time is the average waiting time plus the average
service time
• Ships’ interarrival time predominately determines the average
waiting time
• Quay crane capacity and carriers’ tonnage determines the
average service time
Waiting
Anchorage position
Carrier tonnage distribution
Servicing
Nr. of berths
Arrival process
Nr. of cranes
Crane capacity
Modeling arrival process
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Average port time (2)
• Existing literature about ships’ arrivals:
• Ships do not generally arrive at their scheduled times because of bad
weather conditions, swells and other natural phenomena during the
sea journey as well as unexpected failures or stoppages (Jagerman
and Altiok, 2003)
• Uncontrolled ship arrivals results in ship delays (Asperen, 2004)
• Ships interarrival times best approximated by a Poisson or Erlang-2
arrival process (UNCTAD, 1985)
• An Erlang-2 distribution can be used to represent the service time
distribution (UNCTAD, 1985 and Jagerman and Altiok, 2003)
Modeling arrival process
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Average port time (3)
• But what is meant with Poisson or Erlang-2 distributed interarrival
times?
• In a Poisson and Erlang-2 arrival process, probability distributions
express the probability of a ship arrival in a fixed interval of time
0.1
0.08
Frequency [-]
Poisson
Erlang-2
0.06
0.04
0.02
0
0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Ships' interarrival time [h]
Poisson and Erlang-2 distributions for ships’ interarrival times with an average of 10 hours
Modeling arrival process
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Average port time (4)
• From 3 terminals, the arrival process was investigated to check
real-world data with existing literature
• T1: single-user, import terminal
T1 ~ Erlang-2
T2  Poisson
T3 ~ Normal
• T2: stevedore, import terminal
• T3: single-user, export terminal
Interarrival time distribution
depends on terminal type
0.18
0.16
T1 - 345 arrivals - 2.25 years
T2 - 898 arrivals - 3 years
T3 - 186 arrivals - 1 year
0.14
Frequency [-]
0.12
0.10
0.08
0.06
0.04
0.02
160
155
150
145
140
135
130
125
120
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0.00
Interarrival time [h]
Interarrival time distributions
Modeling arrival process
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Average port time (5)
• Service time relates directly to the carriers’ tonnage
Real-world data does not correspond with
the suggested Erlang-2 distribution
0.14
0.12
T1 - 345 arrivals - 2.25 years
T2 - 898 arrivals - 3 years
T3 - 186 arrivals - 1 year
Frequency [-]
0.10
0.08
0.06
0.04
0.02
315
305
295
285
275
265
255
245
235
225
215
205
195
185
175
165
155
145
135
125
115
105
95
85
75
65
55
45
35
25
15
5
0.00
Carriers' tonnage [kt]
Carriers’ tonnage distributions
Modeling arrival process
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Content
•
•
•
•
•
Arrival process
Average port time
Modeling arrival process
Continuous quay layout or multiple berths
Conclusions
Modeling arrival process
11
Modeling arrival process (1)
• Modeling of the arrival process based on Queuing Theory
Service times distribution
-/-/Queue
Service
facility
Number of servers
Interarrival times distribution
Queuing system
Basic of a queuing system
Labeling of queuing models
• M/E2/2:
• Interarrival times distributed according a Poisson (Markovian) arrival
process
• Service times distributed according Erlang-2 distribution
• 2 servers  2 berths where each berth is equipped with 1 quay crane
Modeling arrival process
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Modeling arrival process (2)
• For single berth queuing systems, the impact of the several
interarrival times distribution was investigated
4
M/E2/1
E2/E2/1
D/E2/1
3.5
3
Anchorage position
Wt [1/μ]
2.5
2
1.5
Single berth queuing system
1
0.5
M/E2/1:
  1
Wt  3 
4  1    
E2/E2/1:
  1
Wt  1 
2  1    
D/E2/1:
  1
Wt  1 
4  1    
0
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ρ (λ/μ) [-]
Average waiting time, expressed in average service time,
versus quay occupancy for single berths
Modeling arrival process
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Modeling arrival process (3)
• For multiple berths queuing systems, there are hardly
mathematical expressions
Graphs of UNCTAD can be used, but what if the service time cannot
be represented with an analytical distribution?
Research had shown that the unloading capacity is not constant
during the entire ship unloading
100
Anchorage position
Multiple berths queuing system
M/M/s:
1  C s,    1

Wt  
s  1    
unloading capacity per hour [%]
90
80
70
60
50
40
30
20
50% of load
10
15% of load
0
0
E2/E2/s: ……..
35% of load
10
20
30
40
50
60
70
80
90
100
unloading time [%]
Modeling arrival process
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Modeling arrival process (4)
• A discrete-event simulation model was developed
QC1
ShipGenerator
QC2
ShipQ
Ship
Terminal
quay
Simulation model
Ship
Quay Crane (QC)
MyTonnage
Classes with attributes
IATDist. Type:
QCn
MyShip
ShipGenerator
Capacity
MyShip
IATDist. Type
Process
TonnageDist. Type
Process
Poisson
Erlang-2
Erlang-2
TonnageDist. Type:
Deterministic
Deterministic
TableDistribution
ShipFile
ShipFile
Distribution Types Options
CraneClass.Process
MyDistGen.Start(Tnow)
While True do
Begin
If IsInQueue(CraneIdleQ) then MyDistGen.Pause
While IsInQueue(CraneIdleQ) do standby;
If MyDistGen.Status = interrupted then MyDistGen.Resume(Tnow);
If MyShip <>nil then
Begin
if MyShip.Tons > 0 then
Begin
MyShip.Tons:=MyShip.Tons – GrabTons;
Hold(Cranecycle);
end;
if MyShip.Tons = 0 then
Begin
If (IsInQueue(MyBerth.MyCranesQ)) and
(MyBerth.MyCranesQ.Length > 1) then
Begin
LeaveQueue(MyBerth.MyCranesQ);
LeaveQueue(CraneActiveQ);
End;
if (IsInQueue(MyBerth.MyCranesQ)) and
(MyBerth.MyCranesQ.Length = 1) then
Begin
LeaveQueue(MyBerth.MyCranesQ);
LeaveQueue(CraneActiveQ);
MyBerth.MyShip.Destroy;
MyBerth.LeaveQueue(BerthOccupiedQ);
MyBerth.EnterQueue(DeberthQ);
end;
EnterQueue(CraneIdleQ);
end;
end;
End;
Modeling arrival process
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Modeling arrival process (5)
• For multiple berths queuing systems, the simulation model was used
to determine the average ships’ waiting time
Modeling arrival process
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Modeling arrival process (6)
• For multiple berths queuing systems, the simulation model was used
to determine the average ships’ waiting time
4
M/E2/1
M/E2/2
M/E2/3
M/E2/4
3.5
3
Anchorage position
Wt [1/μ]
2.5
2
1.5
1
0.5
0
Multiple berths queuing system
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ρ (λ/sμ) [-]
Average waiting time, expressed in average service time,
versus quay occupancy for multiple berths
(M/E2/1: 1.75, M/E2/2: 0.75, M/E2/3: 0.58, M/E2/4: 0.28)
Modeling arrival process
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Modeling arrival process (7)
• Can analytical models be used for an accurate arrival process
modeling?
• The simulation model was used to compare terminals’ real-world
arrival data with analytical models
Comparison real-world data with analytical models
Table distribution to represent carriers’ tonnage for T2
Tonnage
minimum [t]
0
25,000
50,000
75,000
100,000
150,000
200,000
Tonnage
maximum [t]
25,000
50,000
75,000
100,000
150,000
200,000
300,000
[%]
5*
19.4
23.6
10.1
12.3
25.5
4.1
* 5% of all bulk carriers were generated with
tonnages between 0 tons and 25,000 tons.
Modeling arrival process
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Content
•
•
•
•
•
Arrival process
Average port time
Modeling arrival process
Continuous quay layout or multiple berths
Conclusions
Modeling arrival process
19
Continuous quay layout or multiple berths (1)
BC1
C1
C2
C3
BC1
Berth 1
A) Continuous quay layout
B) Multiple berths operation
C4
C4’
(A)
BC3
BC2
Berth 2
C1
BC3
BC2
Berth 3
C2
Berth 4
C3
Interarrival time distribution type
Bulk carriers tonnage distribution
Number of quay cranes [-]
Max. number of ships at the quay [-]
Quay crane capacity (free-digging)
Annual throughput [Mt]
Runtime of simulation [years]
C4
NED
Table Input
4
4
3,000 [t/h]
20 – 50
5
Simulation input
Modeling arrival process
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(B)
Continuous quay layout or multiple berths (2)
1,300
1,200
Quay length [m]
1,100
1,000
900
M/G/4
M/G/4+ [2]
M/G/4+ [3]
M/G/4+ [4]
800
700
600
20
25
30
35
40
45
50
Annual Throughput [Mt]
Occupied quay length versus annual throughput
Modeling arrival process
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Conclusions
• Serving ships on time and at correct speed is crucial for terminal
operators
• Modeling the ships’ arrival process is required to design the
terminal’s quay side
• The ‘wilder’ the arrival pattern, the greater the average waiting time
• Modeling the arrival process must be based on Queuing Theory
• However, for multiple berths there are hardly analytical solutions and
a discrete-event simulation is proposed
• For an accurate modeling, it is proposed to use a table distribution
which represents the carriers’ tonnage instead of using analytical
models for the service time distribution
• A continuous quay operation results in a higher annual throughput or
less required quay length
Modeling arrival process
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Thank you!
Modeling arrival process
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