## 3 Description of the Simulation Model
### Model Structure and Working Principle
Once a ship entity has been assigned an IB it will proceed to block J. In case multiple ships are waiting for assistance in block I, the ships will be assisted in the order in which they arrived. * J--IB transfer and maneuvering time. Although an IB is assumed to remain within its operating area at all times, the exact position from which an IB starts to move towards a ship calling for assistance is not known. Therefore, the related \"transfer time\" (hours) is determined probabilistically based on an assumed distribution. Once an IB has reached a ship or convoy in need of assistance, before the assistance may start, the IB must maneuver itself into an appropriate position ahead of the ship(s) that are to be assisted. Additionally, in case the ship(s) are stuck in ice, the icebreaker must first cut loose the ship(s) by breaking the surrounding ice. The corresponding maneuvering time is determined probabilistically based on an assumed distribution. The ship entity will remain in the block for a time corresponding to the sum of the determined IB transfer and maneuvering times. * K--Ship waiting to join a convoy. A ship entity waiting in block K will form a convoy with the first IB-assisted ship entity exiting block J. The IB-assisted ship entity arriving from block J is assumed to have priority access to the IB, meaning that it will be assisted by the IB until it has reached its destination or is deemed able to continue independently (see description of block D--\"Need for IB assistance\"). The ship entity joining the convoy from block K, on the other hand, will be assisted over one leg only after which it needs to call for further IB assistance if needed. * L--Speed with IB assistance. The speed (knots) of a ship assisted by an IB is determined as the lower of the achievable speed of the assisted ship and the achievable speed of the assisting IB. In other words, the speed is either limited by the assisted ship or by the IB. The achievable speed of the assisted ship is determined based on ship model-specific hv curves for \"Assistance at distance\", examples of which are presented in Figure 3. The achievable speed of the IB is determined as per the description of block C--\"Speed without IB assistance\". In the case of convoy operation, as a simplification, the speed of each assisted ship is determined separately as described above. * M--Leg time with IB assistance. The leg time (hours) for an IB-assisted ship or convoy is determined based on the leg distance and the speed as determined in block L. The ship entity or entities will remain in the block for a time corresponding to the calculated leg time. The performance of the FSWNS depends on many stochastic factors. In the simulation, as explained above, random variables are generated by drawing random numbers from variable-specific distributions. It can be noted that using MATLAB, the generation of streams of random values is as default repeatable, meaning that separate simulation runs result in identical streams of random values. This is well suited to analyze the influence of variations in single parameter values or distributions. However, in order to analyze how the system performs under different combinations of parameter values, independent sets of random values must be generated. A general challenge related to the modelling of stochastic factors of the FSWNS is the lack of relevant data. In this study, four stochastic variables are considered: (a) the presence of brash ice channels as determined in block B, (b) the time it takes for an IB to reach a ship in need of assistance as determined in block J, (c) the duration of the IB maneuverings required before an IB assistance can start, and (d) uncertainty in the assumed \(H_{eq\_avg}\) and \(H_{eq\_max}\) values. Examples of how these variables can be specified are presented in Section 4. Figure 3: Examples of hv curves for different ship models. The hv curves determine the speed of a ship as a function of the equivalent ice thickness (\(H_{eq}\)). Figure 2: Leg model structure.