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1 Modeling arrival process Challenge the future Delft University of Technology Modeling the arrival process at dry bulk terminals Delft University of Technology T.A. van Vianen, J.A. Ottjes and G. Lodewijks Faculty 3ME, Transport Engineering & Logistics

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

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3 Modeling arrival process 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)

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4 Modeling arrival process Arrival process (2) How to prevent that ships are queuing before getting serviced? Ships waiting before servicing Quay side capacity Costs Demurrage costs Operational costs Find the optimum

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

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6 Modeling arrival process 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 Arrival process Waiting Servicing

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7 Modeling arrival process 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)

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

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9 Modeling arrival process 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 T1 ~ Erlang-2 T2 Poisson T3 ~ Normal Interarrival time distribution depends on terminal type

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10 Modeling arrival process Average port time (5) Service time relates directly to the carriers’ tonnage Carriers’ tonnage distributions Real-world data does not correspond with the suggested Erlang-2 distribution

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

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12 Modeling arrival process Modeling arrival process (1) Modeling of the arrival process based on Queuing Theory Basic of a queuing systemLabeling 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

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13 Modeling arrival process 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 D/E2/1: Single berth queuing system M/E2/1: E2/E2/1:

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14 Modeling arrival process Modeling arrival process (3) For multiple berths queuing systems, there are hardly mathematical expressions M/M/s: Multiple berths queuing system E2/E2/s: …….. 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

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

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16 Modeling arrival process Modeling arrival process (5) For multiple berths queuing systems, the simulation model was used to determine the average ships’ waiting time

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17 Modeling arrival process 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) Average waiting time, expressed in average service time, versus quay occupancy for multiple berths Multiple berths queuing system

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18 Modeling arrival process 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 * 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

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

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20 Modeling arrival process Continuous quay layout or multiple berths (1) A)Continuous quay layout B)Multiple berths operation Interarrival time distribution typeNED Bulk carriers tonnage distributionTable Input Number of quay cranes [-]4 Max. number of ships at the quay [-]4 Quay crane capacity (free-digging)3,000 [t/h] Annual throughput [Mt]20 – 50 Runtime of simulation [years]5 Simulation input

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21 Modeling arrival process Continuous quay layout or multiple berths (2) Occupied quay length versus annual throughput

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22 Modeling arrival process 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

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23 Modeling arrival process Thank you!

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