# Simulation Tool for Winter Navigation Decision Support in the Baltic Sea
## 9 Computational Experiments  
The first parameter varied was the number of vessels, increased gradually from 1, 25, 50, 100, to 116 vessels in different runs. Table 7 shows the results of varying the number of vessels in the system. As per the historical data used, all trip itineraries are completed by 15 February, with all vessels exiting the system. If all departure times are adhered to in the simulation run, then this condition will be met, and the last vessel will leave the system by 15 February. If the departure times are delayed, then the overall end time of the simulation may also go beyond 15 February. Table 7 reports the final difference from the overall schedule as a percentage. It is calculated as shown in the equation:  
\[Difference\;in\;schedule=\frac{(Simulation\;completion\;time-actual\; completion\;time)}{actual\;completion\;time}\ast 100\]  
The icebreakers use the Longest Waiting Time First (LWTF) criteria while selecting vessels to assist. According to this method, the requests received by icebreakers are sorted by the duration of time that has elapsed since receipt of the request. Every vessel has an attribute that keeps note of the waiting time until assistance is received. The vessel that has waited the longest is chosen to be assisted first. If LWTF is not used, it is important to define the parameter that specifies maximum allowable waiting time (\(t_{max}\) ). Without this parameter, it is possible that a vessel may remain unassisted till the end of the time period for receiving assistance, while other vessels are prioritized over it. Due to \(t_{max}\), it is ensured that once the waiting time of a vessel crosses the maximum allowable time, it is immediately prioritized over all others and assisted. \[s_{n}=3\;\text{kn},\;C_{on}=1,\;C_{max}=2,\;s_{c}=6\;\text{kn},\;t_{max}\;=12 \;\text{hr}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Parameter** & **Output** & **Current Model** & **Real System** \\ \hline \multirow{2}{*}{**Vessel speed threshold (increase)**} & Number of assistances & Increase & Increase \\ \cline{2-4}  & Average waiting time & Increase & Increase \\ \hline \multirow{2}{*}{**Convoys allowed (on)**} & Number of assistances & Decrease & Decrease \\ \cline{2-4}  & Average waiting time & Decrease & Decrease \\ \hline \multirow{2}{*}{**Maximum allowable waiting time (increase)**} & Number of assistances & Decrease & Decrease \\ \cline{2-4}  & Average waiting time & Increase & Increase \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Validation by parameter variation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Vessels in System** & **Difference in Schedule (\%)** \\ \hline
1 & 0 \\ \hline
25 & 8.38 \\ \hline
50 & 8.38 \\ \hline
100 & 9.18 \\ \hline
116 & 9.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Validation experiments. The difference in scheduling begins to appear when the traffic is increased to 25 vessels or more. Although it can be observed that for the last two scenarios with higher traffic volumes there is a slightly higher difference between the observed schedules and the historical data, the output values are quite close for all the traffic situations. It can be said that system performance is nearly consistent for increasing traffic conditions. The observed difference in schedules is not unexpected since the model at this stage does not capture all the real-life decision-making actions. Firstly, convoy sizes are often larger than two and hence more vessels are assisted at once. Further, icebreakers often optimize their trips to improve overall system performance (reducing average waiting time). Icebreaker assistance mission planning is a complex problem and is beyond the scope of this article. Next, experiments were conducted by varying the icebreaker assistance threshold (minimum speed), \(s_{v}\). Icebreakers can decide whether to let a vessel continue its journey at a given speed or to step in and assist.