# Resource Capacity Requirement for Multi-Terminal Cooperation in Container Ports
## 2 Resource Profiles for Representing Workloads
### Resource Profile Simulation
The event generates \(C_{d}\) over the time window \(T_{finish}-T_{transfer}\) for interterminal trans-shipment at each cooperating terminal, with the time window for trans-shipment TEUs being 2-3 days after unloading at a terminal. Hence, the TEU transferring activities are recorded earlier than the time of executing \(E_{a}(i,y)\). \(T_{transfer}\) is generated by the execution of \(E_{a}(i,y)\) and \(T_{finish}\) is dependent on the transferring productivity of trucks. \(\mathbf{E_{t}}\)-Truck transport. This event is triggered when \(E_{a}(i,y)\) determines \(T_{transfer}\). An amount of TEUs at a terminal, \(C_{d}\), will need to be transported to terminal \(y\) from \(x\) by trucks. A generated single truck typically transports 1.5 TEUs at a time. When a truck transports transferring TEUs from a terminal to another, the process takes a number of time-units including the congestion on traveling paths. The congestion has the effect of reducing the speed of truck flows. Underwood formula is used to adjust the truck speed for the traffic congestion on a traveling path, taking into account parameters such as length of the travel path, free flow speed, and a predetermined amount of maximum number of trucks. The effective traveling speed \(u_{n}\) in a traveling path between two terminals with \(n\) trucks is estimated by  
\[u_{n}=u_{f}exp\left(-\frac{k_{n}}{k_{0}}\right), \tag{8}\]  
where \(u_{f}\) is the free speed and \(k_{0}\) is the traffic density at maximum flow. For \(L^{t}\) representing the length of the traveling path, \(k_{n}=(n-1)/L^{t}\) is the traffic density in the traveling path with \(n\) trucks. The event triggers an immediate execution of \(E_{g}\) with the delay of traveling and congestion of a truck. \(\mathbf{E_{g}}\)-Gate check-in. The execution time of this event is delayed until the arrival of a truck, as the traveling time and delays caused by congestion should be included. Since the gate is a resource with limited capacity, the queue length will be a meaningful measure for gate workload. The gate is modeled as a single server machine and its service times are adjusted for multiple pass lanes. Whenever a truck arrived at a gate (i.e., the execution of \(E_{g}\)), it joins the gate queue and waits for the check-in service. The truck queue length is affected by the workload distribution of Equation (4) and counted as the gate congestion measure in the simulation. The gate check-in event triggers an immediate event \(E_{c}\). \(\mathbf{E_{c}}\)-Arrival of Transferred TEU. This event is triggered when a truck passes the gate, but the execution time is deferred until the truck is processed at the gate. It increases the TEU workload in the yard accordingly at most \(C_{d}\). This event generates \(T_{finish}\), and calls the event \(E_{s}\) to transport TEUs continuously until cumulative probability for TEU workload, \(P[C_{d}|T\leq i]\), becomes 1. Transferring time window \(T_{finish}-T_{transfer}\) essentially includes the two delay elements, namely, congestion and queueing that increase uncertainty.