# Resource Capacity Requirement for Multi-Terminal Cooperation in Container Ports
## 2 Resource Profiles for Representing Workloads
### Resource Profile Simulation  
A resource profile simulation is developed to generate events imposing workload requirement for resources, such as vessel arrivals, truck transportation, loading and unloading operations, etc. presented in Figure 4, and simulate the workload cascading over the resources across terminals. The events are associated with the random variables provided in the previous section and each event triggers another. The resource profiles simulation estimates the workload distributions for resources to estimate the capacity requirement over time-shifts across the terminals. * \(\mathbf{E_{a}}(i,x)\)-Vessel arrival. This event is triggered when a vessel with type \(i\) arrives at the port and randomly assigned to any of one of the terminals \(x\in M\) with an equal probability, where \(M\) is the set of cooperative terminals at the port. The vessel type is characterized by the attributes such as the category, the TEU quantity, the required QC intensity. When the event is executed, the attributes of the vessel are randomly assigned by referring to Appendix A. The event triggers an immediate execution of \(E_{u}\), \(E_{t}\), and \(E_{s}\) and schedule a new event \(E_{a}(i,x)\) with an exponential interarrival rate \(\lambda\). This event is associated with the workloads \(C_{a}\) and \(C_{a}^{f}\). * \(\mathbf{E_{t}}\)-TEU arrival. This event is triggered when a vessel arrives at the port. The arrivals of TEUs was recorded earlier than the time of executing \(E_{a}\) by tracing back in time. The workload \(C_{a}\) is distributed only in the time ranged from \(t_{open}\) to \(t_{close}\). Both \(t_{open}\) and \(t_{close}\) are dependent on the generated \(T_{arrive}\). * \(\mathbf{E_{u}}\)-Unloading. This event is triggered when the first vessel in the queue arrives at a randomly selected terminal. The event execution time is delayed until \(t_{unload}\) as both the vessel and the QCs operations must be ready for the unloading operations (which generally takes 2 h) to be performed. The event allocates QCs to the vessel as requested (generated) in the event of \(E_{a}\). It is set that the required number of QCs is always available at a terminal. The time window for the unloading operation \(T_{switch}-t_{unload}\) is conditionally determined by the generated \(H_{Q}^{U}\). When the event is triggered, the amount of TEUs in the yard increases at the rate of \(H_{Q}^{U}\). The workloads \(C_{b}\) and \(C_{b}^{f}\) are associated with the event. The simulator sets unloaded TEUs to leave the terminal within 5 days following the unloading. The unloading event \(E_{u}\) triggers the execution of the loading event \(E_{l}\) through determining \(T_{switch}\). * \(\mathbf{E_{l}}\)-Loading. The event is triggered immediately upon the completion of the unloading operation on the vessel. \(T_{switch}\) is used to execute the loading event \(E_{l}\) but the event execution time is delayed until \(T_{load}\). Similar to the unloading operation, the loading time window \(T_{end}-T_{load}\) is conditionally determined by the generated \(H_{Q}^{L}\) while the TEUs at the yard also decreases accordingly. The workloads \(C_{c}\) and \(C_{c}^{f}\) are adjusted with the event. The event triggers the execution of the vessel departure event \(E_{d}\) though determining \(T_{end}\). * \(\mathbf{E_{d}}\)-Vessel departure. The execution time of this event is delayed until \(t_{depart}\), which is determined by the generated \(T_{end}\) as the both the vessel and the QCs operations must be ready to be released. When executing this event, the vessel returns the assigned number of QCs, releases the quay space of the terminal, and triggers an immediate execution of \(E_{a}\). Figure 4: Event entity diagram for resource profile simulation. \(\mathbf{E_{s}}\)-TEU Transfer. This event is triggered when the event of vessel arrival \(E_{a}(i,y)\) where \(y\in M\backslash\{x\}\) is executed.