## 3 Description of the Simulation Model
### Model Structure and Working Principle  
As per Figure 1 presenting an example simulation model structure, the simulation model consists of different types of blocks representing navigation legs (L), ports, crossings, borders between different IB operating areas, and ship entry/exit gates. Ships are represented by entities, each of which has a set of predetermined attributes specifying the technical characteristics (e.g., ice-going capability) and voyage characteristics (destination ports, port-turnaround times) of the ship. IBs, on the other hand, are represented by \"resources\". Specifically, an individual IB is represented by an individual IB resource that, when assisting a ship, is attached to the ship being assisted. Figure 1: Simulation model example. Entry/Exit A is used by ships arriving from or leaving towards Kvarken, Entry/Exit B is used by ships arriving from or leaving towards Lulea (Sweden). Letter L stands for (navigation) leg. Each ship entity enters the simulation model at a specific date and time (determined based on maritime traffic data) through an entry gate with an assumed geographical location (e.g., Kvarken, Bay of Bothnia). Once entered, a ship entity will progress towards its first port of destination, where it will stay for a predetermined period corresponding to the total port turnaround time. Thereafter, the ship entity will either continue towards another port within the simulation model or towards a port located outside the simulation model. In the latter case, the ship entity will progress towards an exit gate with an assumed geographical location and then leave the simulation model. Navigation legs are here defined as the geographical distance between two waypoints. The time it takes for a ship entity to complete a leg depends on the leg distance, the ice conditions, the operating mode (independent or assisted operation), the ship's estimated speed in the prevailing ice conditions and operating mode, and the waiting time for IB assistance (in case the ship must call for IB assistance). Specifically, navigation legs are modelled as per the schematic diagram in Figure 2 whose various elements are described as follows:  
* A--Date definition. When a ship entity (with or without IB assistance) arrives at a waypoint, the present date is determined in terms of the number of days elapsed since the start of the simulation. * B--Ice conditions. The prevailing ice conditions are determined following a predefined table defining the ice conditions by navigation leg and date. The prevailing ice thickness along the leg is defined in terms of the average equivalent ice thickness (\(H_{eq\_avg}\)) (cm) and the maximum equivalent ice thickness (\(H_{eq\_max}\)) (cm). \(H_{eq\_avg}\) is defined as the average thickness of all major ice features (level ice, ice ridges, openings) over the whole leg. \(H_{eq\_max}\), in turn, is defined as the average thickness of the same ice features over the part of the leg with the most difficult ice conditions (e.g., an area with severe ice ridging). In order to account for uncertainty and stochasticity, during an individual simulation run the applied \(H_{eq\_avg}\) and \(H_{eq\_max}\) values are multiplied by randomly determined coefficients representing their uncertainty. In addition, based on the location and prevailing ice conditions, an assumption is made as to whether a brash ice channel is present. Specifically, depending on the location of a leg and the prevailing ice conditions there, a brash ice channel is assumed to be (a) present at all times, (b) present with a certain probability, or (c) never present. If an ice channel is assumed present with a certain probability, whether an ice channel is present at a specific date is determined based on a binary number (0 = no ice channel, 1 = ice channel) drawn from an assumed distribution. * C--Speed without IB assistance.