## 1 Introduction  
It is probable that the term marine traffic engineering (MTE) was first used by [PERSON] and [PERSON] [1] in 1971, who defined it in the _Journal of Navigation_ as \"the study of ship traffic and the application of the results of this study from the improvement of port infrastructure and traffic organization\". The first quantitative estimation of marine accident safety was presented by [PERSON] [2] who studied accidents in the Urga Strait. Interestingly, when compared to [PERSON]'s study, the currently accepted collision probability value has decreased significantly (from an accident probability value per operation of \(10^{-4}\) to \(10^{-5}\) today). [PERSON] [2] estimated the probability of grounding as \(10^{-3.7}\), which is also higher than the currently accepted values. In this paper [2], [PERSON] also identified the size of a ship's domain and assumed it to be an ellipse with the parameters of \(6\L\times 1.5\L\). Later research focused on the creation of accident models, of which the McDuff model [3] is now widely used. The MacDuff model distinguishes between geometric probability (resulting from the geometry of the ship's passage) and causal probability, defined by some authors as human error. Various general regression models of navigation safety in maritime and port areas are currently being developed based on the analysis of a large number of real-time ship-maneuvering simulation results [4]. Further research on ship domains was based on the theoretical basis provided by [PERSON] [5]. Currently, research is being carried out that involves automating the processes of domain extraction from real-world data, including primarily using AIS [6]. These methods are mainly applied to coastal waters, and the resulting domains are mainly used for safety management or early notification of navigation incidents [7]. At the same time, advanced methods are being developed for processing AIS-derived data to support ship navigation [8]. In a significant number of marine traffic engineering issues, the ship maneuver simulation method, including the real-time method, is one of the most suitable methods for solving the associated research task. This is because this method is characterized by the following characteristics [9]:  
* A high degree of compliance with reality;
* Low financial expenditure compared to the use of physical models;
* The possibility of studying non-existent systems;
* The possibility of simulating random processes. Several unsolved problems that occur when ships exceed the capacity of the port infrastructure were identified by [PERSON] et al. [10]. Guidelines [11; 12; 13; 14] address the issue of waterway design by standardizing the design process itself. In parallel, one can observe the intensification of national and regional policies on the issue of waterway design by means of ship-maneuvering simulations. Ports are also the subject of strategic risk assessments [15, 16]. General principles of port and waterway design for ships are presented in various studies [17, 18]. Simulation research methods can also be used in other aspects of shipping safety like designing risk-based port regulations [19]. Assumptions for real-time simulation methodologies for waterway and port design are outlined in recent PIANC [11, 12], ROM [13], IALA [14] and Japanese guidelines [20]. An exemplary comprehensive study in this area, particularly for the position distribution of ships on a waterway, was presented by [PERSON] [21]. The process of designing waterways based on real-time computer simulations depends strongly on the experience and knowledge of the simulation team. In the marine simulation sector, compared to other transportation branches such as aviation or road engineering, there is still more \"freedom\" and discretion in the design process itself. Expert knowledge supported by pilots is usually the key factor here for simulations based on their previous design. [PERSON] et al.