Figure 6.1: Schematic overview of two groups of 4 QCs, each related to a group of 24 YSs.
simulation constant. Furthermore the number of simulations is 20. For each simulation the jobs of the AGVs are generated according the described Job Generating Algorithm.
For more information about the number of tasks per job and the determination of the 20 simulations see Appendix F.
6.2 Simulation results of 19 different layouts of the TA of the ACT, simulated with 60 AGVs
6.2.1 Performance measures of the AGV system in the ACT
In the simulation results several performance measures have been used to evaluate and compare the performance of the 19 layouts of the ACT. This Section introduces these performance measures. The equations of the most important performance measures are given below in equation 6.1 till 6.7.
Average task time (ATT) =
i=|V|P
i=1 k=nP
k=m
tvki
|V| × (n − m) (6.1)
Average number of tasks per hour (ATPH) = |V| × 3600
AT T (6.2)
60 Chapter 6. Simulation results
Average travelled distance (ATD) =
i=|V|P
Average speed of a vehicle (AS) = AT D
AT T − process time (loading/dispatching process) (6.4)
Standard deviation of the tardiness (STDTR) = vu
Possibility of braking in EZ of TA(PBEZ)) = Average number of braking in EZ of TA Average number of crossings of TA passed per task
(6.7)
• k = task number.
• tvki = time needed by an AGV vi to complete a task k.
• xvki = travelled distance by an AGV vi for performing a certain task k.
• m, n are integers with the requirement that m < n and m > 0.
The value of the ATPH, which can also be described in terms of the ATT, is the most important value for evaluating the performance of the AGV system in the ACT. A small value for the ATT (large value for the ATPH) ensures a high throughput of containers in the container terminal. The value of the STDTR is another very important mea-surement, especially for possible applications of a dispatching algorithm in the future.
A small value for the STDTR indicates that it can be estimated very accurate when a AGV should reach its destination zone. A dispatching algorithm needs this accurate estimation for accurate and efficient dispatching of tasks to vehicles. Therefore a small value for the STDTR is preferred. The measure ATD should be as small as possible,
6.2. Simulation results of 19 different layouts of the TA of the ACT, simulated with 60 AGVs61
since this is preferred from an energy cost point of view. Additionally, the number of braking in an EZ should be low, since accelerating and decelerating by the vehicles is very energy expensive compared to driving with constant speed. Additionally, it causes more brake wear of an AGV.
The next Subsection shows the simulation results of the 19 different layouts of TA of the ACT. The number of AGVs has been 60 for all the simulations that are showed in this Section in order to keep the comparison and analysis of the different layouts simple and clear. This number of 60 AGVs is based on a realistic estimation for the amount of AGVs on a busy day in an ACT with 20 quay cranes.
Moreover, all 19 different layouts of the TA of the ACT are simulated with 20 through 120 AGVs. The results of these simulations are depicted in Appendix G.
6.2.2 Simulation results
Figure 6.2 shows the ATT, ATD and the AS of a vehicle.
Figure 6.3 shows the ATR and the STDTR of a task.
Finally figure 6.4 shows the average number of crossings of the TA passed per task, the average number of braking in an EZ of the TA per task and PBEZ of the TA per task.
The results of the simulations are discussed in the next Subsection.
62 Chapter 6. Simulation results
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50100
150
200
250
300
350Average task time Layout number
Average task time [Seconds]
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5001000
1500
2000Average travelled distance for a task Layout number
Average travelled distance for a task [Meters]
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1
2
3
4
5
6Average speed of a vehicle Layout number
Average speed of a vehicle [Meters/Seconds]
Layout 1 Layout 2 Layout 3 Layout 4 Layout 5 Layout 6 Layout 7 Layout 8 Layout 9 Layout 10 Layout 11 Layout 12 Layout 13 Layout 14 Layout 15 Layout 16 Layout 17 Layout 18 Layout 19 Figure6.2:Simulationresultsof19differentlayoutsoftheTAoftheACT:averagetasktime(ATT),averagetravelled distance(ATD)andaveragespeedofavehicle(AS).
6.2. Simulation results of 19 different layouts of the TA of the ACT, simulated with 60 AGVs63
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20
40
60
80100
120Average tardiness Layout number
Average tardiness [Seconds]
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50100
150
200
Standard deviation of the tardiness Layout number
Standard deviation of the tardiness [Seconds]
Layout 1 Layout 2 Layout 3 Layout 4 Layout 5 Layout 6 Layout 7 Layout 8 Layout 9 Layout 10 Layout 11 Layout 12 Layout 13 Layout 14 Layout 15 Layout 16 Layout 17 Layout 18 Layout 19 Figure6.3:Simulationresultsof19differentlayoutsoftheTAoftheACT:averagetardiness(ATR),standarddeviationof thetardiness(STDTR).
64 Chapter 6. Simulation results
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510
15Average number of crossings of the TA passed per task Layout number
Average number of crossings of the TA passed per task
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1
2
3Average number of braking in an EZ of the TA per task Layout number
Average number of braking in an EZ of the TA per task
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0.1
0.2
0.3
0.4Possibility of braking in an EZ of the TA Layout number
Possibility of braking in an EZ of the TA [percentage]
Layout 1 Layout 2 Layout 3 Layout 4 Layout 5 Layout 6 Layout 7 Layout 8 Layout 9 Layout 10 Layout 11 Layout 12 Layout 13 Layout 14 Layout 15 Layout 16 Layout 17 Layout 18 Layout 19 Figure6.4:Simulationresultsof19differentlayoutsoftheTAoftheACT:numberofcrossingsoftheTApastpertask, numberofbrakinginanEZoftheTApertaskandpossibilityofbrakinginanEZoftheTA(PBEZ)
6.2. Simulation results of 19 different layouts of the TA of the ACT, simulated with 60 AGVs65
6.2.3 Analysis of simulation results
The following major things can be concluded from the simulation results introduced in the previous Subsection:
• Layout 5 provides the smallest value for the ATT as well as for the ATD for a task (see Figure 6.2).
• Layouts with large crossings (layout 5 till 8 and layout 16 till 19) do have smaller values for the ATD for a task compared to the layouts with the small crossings (layout 1 till 4 and layout 9 till 16), see also Figure 6.2 for this conclusion.
• It seems that especially for the layouts with small crossings and less for the layouts with large crossings the ATD for a task correlates with ATT (see Figure 6.2).
• Layout 5 has the smallest value for ATR and the STDTR (see Figure 6.3).
• The layouts with 6 lanes and small crossings have on average a smaller value for the ATR and STDTR compared to the other three groups of layouts (see Figure 6.3).
• From Figure 6.2 and Figure 6.3 it can be concluded that within a group of layouts (see Chapter 4 for these groups) the ATR and STDTR increases if the density of the crossings of the TA decreases (consequently the ATD will increase if the density of the crossings of the TA decreases).
• For the layouts with large crossings the AGV needs to pass on average less cross-ings of the TA compared to the layouts with small crosscross-ings (see Figure 6.4).
• The average number of braking in an EZ of the MT is slightly lower for the layouts with large crossings. Nevertheless, layouts with large crossings provide a larger value for the PBEZ in an EZ of the TA (see Figure 6.4).
4 main groups have been introduced in Chapter 4 in which the 19 layouts of the TA could be divided. The simulation results that has been discussed previously in this Section show that the first layout of each of these 4 groups ensures the best performance compared to the other layouts of the group. A good performance of the layout of the TA is mainly characterized by small values for the ATT, ATD, STD and STDR (as explained in Subsection 6.2.1). Therefore the next Section only investigates the performance of the layouts 1, 5, 9 and 16 in order to be able to give a proper recommendation for the best layout of the TA of the ACT.
66 Chapter 6. Simulation results
20 30 40 50 60 70 80 90 100 110 120
100 150 200 250 300 350
Average time for a task
Average time for a task [Seconds]
Number of AGVs Layout 1
Layout 5 Layout 9 Layout 16
20 30 40 50 60 70 80 90 100 110 120
0 500 1000 1500 2000 2500 3000
Average number of performed tasks per hour
Average number of performed tasks per hour [Tasks/hour]
Number of AGVs Layout 1
Layout 5 Layout 9 Layout 16
Figure 6.5: Simulation results for changing the number of AGVs of layout 1, 5, 9 and 16: average task time (ATT) and average number of tasks per hour (ATP)