1 Modeling arrival process 22-05-2012 Challenge the future Delft University of Technology Modeling...

1Modeling arrival process

22-05-2012

Challenge the future

DelftUniversity ofTechnology

Modeling the arrival process at dry bulk terminalsDelft University of Technology

T.A. van Vianen, J.A. Ottjes and G. LodewijksFaculty 3ME, Transport Engineering & Logistics


Content

• Arrival process• Average port time• Modeling arrival process• Continuous quay layout or multiple berths• Conclusions


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 unloading (Courtesy of J.Hiltermann)Ship loading (Courtesy of Richards Bay Coal Terminal)


Arrival process (2)• How to prevent that ships are queuing before getting

serviced?

Ships waiting before servicing

Quay side capacity

Cost

s

Demurrage costs

Operational costs

Find the optimum


Content



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

Carrier tonnage distribution

Nr. of berths

Crane capacityNr. of cranes

Anchorage position

Arrival process

Waiting

Servicing


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)


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

0.02

0.04

0.06

0.08

0.1

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

Freq

uenc

y [-

]

Ships' interarrival time [h]

Poisson

Erlang-2

Poisson and Erlang-2 distributions for ships’ interarrival times with an average of 10 hours


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

• T2: stevedore, import terminal

• T3: single-user, export terminal

Interarrival time distributions

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

125

130

135

140

145

150

155

160

Freq

uenc

y [-

]

Interarrival time [h]

T1 - 345 arrivals - 2.25 yearsT2 - 898 arrivals - 3 yearsT3 - 186 arrivals - 1 year

T1 ~ Erlang-2T2 PoissonT3 ~ Normal

Interarrival time distribution depends on terminal type


Average port time (5)• Service time relates directly to the carriers’ tonnage

Carriers’ tonnage distributions

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

5 15 25 35 45 55 65 75 85 95 105

115

125

135

145

155

165

175

185

195

205

215

225

235

245

255

265

275

285

295

305

315

Freq

uenc

y [-

]

Carriers' tonnage [kt]

T1 - 345 arrivals - 2.25 yearsT2 - 898 arrivals - 3 yearsT3 - 186 arrivals - 1 year

Real-world data does not correspond with the suggested Erlang-2 distribution


Content



Modeling arrival process (1)• Modeling of the arrival process based on Queuing Theory

Basic of a queuing system

Queuing system

Service facility

Queue

-/-/-

Interarrival times distribution

Service times distribution

Number of servers

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 (2)• For single berth queuing systems, the impact of the

several interarrival times distribution was investigated

Average waiting time, expressed in average service time, versus quay occupancy for single berths

0

0.5

1

1.5

2

2.5

3

3.5

4

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Wt [

1/μ]

ρ (λ/μ) [-]

M/E2/1E2/E2/1D/E2/1

D/E2/1:

Anchorage position

Single berth queuing system

134 1tW

112 1tW

114 1tW

M/E2/1:

E2/E2/1:


Modeling arrival process (3)• For multiple berths queuing systems, there are hardly

mathematical expressions

M/M/s:

Anchorage position

Multiple berths queuing system

1

1

,1

sC

sWt

E2/E2/s: ……..

Graphs of UNCTAD can be used, but what if the service time cannot be represented with an analytical distribution?

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

unlo

adin

g ca

paci

ty p

er h

our

[%]

unloading time [%]

50% of load 35% of load 15% of load

Research had shown that the unloading capacity is not constant during the entire ship unloading


Modeling arrival process (4)• A discrete-event simulation model was developed

ShipGenerator

ShipQ

QC1

QC2

QCn

Terminal quay

Ship

Simulation model

Classes with attributes

Distribution Types Options

Ship

MyTonnage

Quay Crane (QC)

MyShip

Capacity

ShipGenerator

MyShipIATDist. Type

TonnageDist. Type

ProcessProcess

IATDist. Type:

Poisson

Erlang-2Deterministic

ShipFile

TonnageDist. Type:

Erlang-2

DeterministicTableDistribution

ShipFile

CraneClass.ProcessMyDistGen.Start(Tnow)While True doBegin

If IsInQueue(CraneIdleQ) then MyDistGen.PauseWhile IsInQueue(CraneIdleQ) do standby; If MyDistGen.Status = interrupted then MyDistGen.Resume(Tnow);If MyShip <>nil thenBegin

if MyShip.Tons > 0 then Begin MyShip.Tons:=MyShip.Tons – GrabTons; Hold(Cranecycle);end;if MyShip.Tons = 0 thenBegin 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 (5)• For multiple berths queuing systems, the simulation model

was used to determine the average ships’ waiting time


Modeling arrival process (6)• For multiple berths queuing systems, the simulation model

was used to determine the average ships’ waiting time

(M/E2/1: 1.75, M/E2/2: 0.75, M/E2/3: 0.58, M/E2/4:

0.28)

0

0.5

1

1.5

2

2.5

3

3.5

4

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Wt [

1/μ]

ρ (λ/sμ) [-]

M/E2/1M/E2/2M/E2/3M/E2/4

Average waiting time, expressed in average service time, versus quay occupancy for multiple berths

Anchorage position

Multiple berths queuing system


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

Tonnage minimum [t]

Tonnage maximum [t]

[%]

0 25,000 5* 25,000 50,000 19.4 50,000 75,000 23.6 75,000 100,000 10.1

100,000 150,000 12.3 150,000 200,000 25.5 200,000 300,000 4.1

* 5% of all bulk carriers were generated with tonnages between 0 tons and 25,000 tons.

Table distribution to represent carriers’ tonnage for T2

Comparison real-world data with analytical models


Content



Continuous quay layout or multiple berths (1)

A) Continuous quay layoutB) Multiple berths

operation

Interarrival time distribution type NEDBulk carriers tonnage distribution Table Input Number of quay cranes [-] 4Max. number of ships at the quay [-] 4

Quay crane capacity (free-digging) 3,000 [t/h]

Annual throughput [Mt] 20 – 50Runtime of simulation [years] 5Simulation input

(A)

BC1 BC2 BC3

(B)

BC1 BC2 BC3

Berth 1 Berth 2 Berth 3 Berth 4

C1 C2 C4C3 C4’

C1 C2 C3 C4


Continuous quay layout or multiple berths (2)

Occupied quay length versus annual throughput

600

700

800

900

1,000

1,100

1,200

1,300

20 25 30 35 40 45 50

Qua

y le

ngth

[m]

Annual Throughput [Mt]

M/G/4M/G/4+ [2]M/G/4+ [3]M/G/4+ [4]


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


Thank you!

1 Modeling arrival process 22-05-2012 Challenge the future Delft University of Technology Modeling...

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