# Resource Capacity Requirement for Multi-Terminal Cooperation in Container Ports
## 3 Simulation Experiment
### Simulation Results with Low Transferring  
The proportion of TEUs for inbound and trans-shipment-inbound are set to 20% and 80%, respectively, and the same proportion applies to the TEUs for outbound and transshipment-outbound. The proportions of TEUs remaining in a terminal and transferring to the other terminals are set to 40% and 60%, respectively. All the other terminals have equal probabilities to take the transferred TEUs and the transferring is only limited to trans-shipment TEUs. Based on the collected samples, \(\overline{X}-R\) Charts for QC intensity, the TEU workload at the yard, and the queue length at the gate can be drawn with the estimated control limits consisting of upper control limits (UCLs), central lines (CLs), and lower control limits (LCLs) for each set of output [21]. Specifically, the simulation plots the QC intensities currently serving all vessels at the terminal whenever a vessel leaves a terminal (\(E_{d}\)). Figure 5 shows the simulation results of QC intensities over time-shifts. The mean requirement of QC intensity for vessel service is 8.12 and the upper limit is estimated as 9.78. It means that a terminal needs to prepare 9.78 QCs to meet the handling capacity requested by the incoming vessels, even though on average only 8.12 QCs are needed to meet the capacity request. The storage space requirement in TEUs is plotted when any of these three events takes place: (i) a vessel arrives at the terminal (\(E_{a}\)); (ii) the interterminal transferring is completed (\(E_{c}\)), and (iii) a vessel departs (\(E_{d}\)). Figure 6 shows that the mean storage capacity required to support the requested vessel service is estimated to be 117,109.64 TEUs, with 125,006.81 and 109,212.50 TEUs as the upper and lower control limits, respectively. The mean difference between maximum and minimum storage requirements is estimated as 13,686.60 TEUs. Gate availability is critical for the smooth execution of interterminal transferring activities. A long truck queue is usually an indication of gate congestion. Figure 7 plots truck queue length at every instance when a truck reaches the gate (\(E_{g}\)). The estimated queue length is 1.56 trucks, and the upper limit shows 2.32 trucks in the queue. Thus, it can be inferred that the gate needs to possess adequate capacity to clear an average queue length of 1.56 trucks to provide the handling service requested by vessels during the transferring activities. Note that the truck queue is estimated only for transferring containers. The results are summarized in Table 1.  
Figure 5: \(\overline{X}-R\) charts over time-shifts (x-axis) for QC intensity (y-axis) when trans-shipment and nontrans-shipment (inbound and outbound) TEUs are 80% and 20%, respectively, and 60% of arrived TEUs are transferred to other terminals. Figure 6: \(\overline{X}-R\) charts over time-shifts (x-axis) for storage space requirement (y-axis) when trans-shipment and nontrans-shipment (inbound and outbound) TEUs are 80% and 20%, respectively, and 60% of arrived TEUs are transferred to other terminals. The simulation results of QC intensities for all vessel arrivals over the run-time suggest that a terminal is expected to prepare 9.71 QCs if it wishes to meet the handling capacity requested by the incoming vessels entirely, but on average 7.92 QCs are sufficient to meet the capacity request (Figure 8). The QC intensity is generally lower than what was found previously in Section 3.1. It indicates the workload in the quayside operation will be reduced by 2.5% when the transferring rate increases from 60% to 75%. Figure 9 shows that the mean storage capacity requirement to support the requested vessel service is estimated to be 107,120.78 TEUs, with 127,060.92 and 87,180.64 TEUs as UCL and LCL, respectively. Compared to the results in Section 3.1, the increase of transferring rate has helped reduce the storage capacity requirement by 8.5% on average. However, the gap between the two limits has also widened by 152.5% at the same time.