## 3 Description of the Simulation Model
### Model Structure and Working Principle
The assumed independently achievable speed (knots) of a vessel is determined both for \(H_{eq\_avg}\) and \(H_{eq\_max}\) based on ship and operation type-specific hv curves that determine the speed of a ship as a function of the ice thickness. As per the example hv curves presented in Figure 3, two different types of independent operation are considered:
* Independent operation in a brash ice channel (\"Channel\" as per Figure 3). Here, the ship is operating in a pre-existing brash ice channel without IB assistance. Ice resistance is higher than when operating with IB assistance because broken ice is distributed over the channel area. \(H_{eq\_r}\) relates to the prevailing thickness of the unbroken ice in the area. * Independent operation in level ice or through a large ice floe (\"Level ice\" as per Figure 3). * D--Need for IB assistance. Whether a ship needs IB assistance (or continued assistance in case the ship is already assisted by an IB) to complete the next upcoming leg is determined based on its estimated independently achievable speed (knots) in the worst expected ice conditions (\(H_{eq\_max}\)) along the leg (calculated in block C). If a ship is not assisted by an IB, the ship will stop and call for IB assistance if its estimated independently achievable speed in \(H_{eq\_max}\) falls below a defined threshold (e.g., 1.5 knots). Otherwise, the ship is considered able to continue independently. If a ship is assisted by an IB from before, the assistance will continue until the ship's independently achievable speed in \(H_{eq\_max}\) exceeds another higher threshold value (e.g., 8 knots). This means that an IB is assumed not to leave an assisted ship in ice conditions in which it can barely continue independently, but to assist a ship until it has reached open water or ice conditions in which it can continue independently without difficulty. * E--Junction 1. A ship entity's choice of path at Junction 1 depends on whether the ship that it represents is considered to be in need of IB assistance. If the represented ship is considered able to continue independently, the ship entity continues to block F. In this case, if the ship is assisted by an IB, the resource representing the assisting IB is released from the ship and becomes available to assist other ships. On the other hand, if the represented ship is considered to require IB assistance, the ship will proceed to block G.
* F--Leg time without IB assistance. In the case of independent operation, the time a ship needs to complete a leg is calculated in hours based on the leg distance and the ship's independently achievable speed (determined in block C). The ship entity will remain in the block for a period corresponding to the calculated leg time. * G--Junction 2. A ship entity's choice of path at junction 2 depends on whether the ship that it represents is assisted by an IB. If the ship is assisted by an IB, the ship entity continues to block L. Otherwise, it continues to block H.
* H--Convoy formation. Typically, IBs assist ships one by one. However, if multiple ships need IB assistance over the same distance at the same time, a convoy operation can be carried out in which an IB assists more than once ship at a time. Convoy operations are challenging as they, among others, require a significant safety distance between the assisted ships [20]. This limits the feasible convoy length as the hull ice resistance of assisted ships tends to increase as a function of the distance to the escorting IB. In the present simulation model, an IB is assumed to assist a maximum of two ships at a time. Specifically, a convoy is formed if a ship entity arrives at block H while another ship entity is already waiting for IB assistance in block I. In that case, the arriving ship entity proceeds to block K. If another ship entity is already waiting in block K, the ship proceeds to block I. * I--Acquisition of IB assistance. A ship entity arriving at block I will trigger a call for IB assistance and wait until an IB resource becomes available.