## 5 Application to the Liquid Bulk Terminal in the Port of Cartagena (Spain) and Its Evaluation
### Theoretical Terminal Occupancy Decreases without Service Degradation  
A second study was carried out with the aim of estimating the increase in occupancy (and therefore income) that the Port of Cartagena could obtain from the E010 dock without increasing the average congestion anchoring delay above the current 6.3 h.  
In order to simulate the traffic that would arrive to dock E010 with loads higher or lower than those stored in the database, a scaling process of arrival times is used. Let us use U to denote the original average occupation of dock E010 during the observation period (January 2010 to August 2020), with U \(\approx\) 30%. A realistic traffic arrival trace for a different average occupation U\({}^{\prime}\) is artificially created, which can then feed the same tests as the ones described in the previous section. The arrival date of the first vessel in the observation period is denoted as \(t0\). Then, giving a call \(c\), \(t(c)\) indicates the original relative arrival date of the vessel at port, measured as the time between its original date and \(t0\). In order to obtain a scaled version of traffic, the original relative arrival at time \(t(c)\) is exchanged for another arrival at time \(t(c)/x\), keeping the same duration of the operations at port. According to this process, a trace where the port is occupied at 60% (double occupation) would result in a trace where the arrivals are concentrated in 5 years, instead of the original 10 years of the dataset.  
After scaling the traffic arrivals for different simulated occupations U for dock E010, the optimization procedure described in the previous section is applied to each of them, with time flexibilities \(H\) of 6, 12, and 24 h. The results are plotted in Figure 5. The \(x\)-axis is the simulated occupation of E010, while the \(y\)-axis shows the normalized congestion delay observed. \"Normalized\" here means that the average anchoring delay is divided by the average occupation of E010 in each stay. Figure 5 clearly illustrates the benefits that the traffic smoothing effect produced by HADES could provide. In any case, average congestion delay increases in respect to dock occupation. This is a well-known effect of queue systems. The interesting aspect here is the quantification of how the arrival coordination controlled by HADES produces curves that are below the original service curve and are even better when greater flexibility is available. This means that service delays will be lower for the same dock occupation or that more vessels can be served (and thus increase port income) for the same target congestion delay. In this latter approach, the results indicate that exploiting the adjustments limited to 6, 12, or 24 h in the calls would allow them to double the occupation of front E010 (going from 30% to levels of 55% to 60%), maintaining the same level of service (around 6 h of average congestion delay).  
\begin{table}
\begin{tabular}{l c c c c} \hline  & **Data\_0 (h)** & **H = 6 (h)** & **H = 12 (h)** & **H = 24 (h)** \\ \hline Average call time without noncongestion anchoring & 31.50 & 28.77 & 26.88 & 25.71 \\ \hline Average operation time & 25.26 & 25.26 & 25.26 & 25.26 \\ \hline Average congestion anchoring time & 6.23 & 3.50 & 1.62 & 0.44 \\ \hline Reduction of average congestion anchoring time & – & 2.73 & 4.61 & 5.79 \\ \hline Annual freight cost savings (1000s of dollars) & – & 227.5 & 384.3 & 482.2 \\ \hline \end{tabular} Average freight charge: 20,000 dollars/day.  
\end{table}
Table 3: Analysis results after application of HADES.