## 3. Maritime Traffic Conditions  
Maritime traffic conditions refer to the comprehensive state of ship operators, ships, and the environment that constitute maritime traffic, and there are various ways to express them using quantitative indicators. Maritime traffic congestion is an index that can be expressed as the percentage of the actual maritime traffic volume against the maritime traffic volume of a navigational passage. It is often used as a simple indicator of the average traffic volume and congestion of a navigational passage [29; 30]. Maritime traffic congestion is also used as an index to select traffic conditions to evaluate the efficacy of the collision avoidance algorithms of autonomous ships [31]. Equation (1) is an expression for calculating maritime traffic congestion. \[T_{c}\ (\%)=\frac{Q_{t}}{Q_{p}}\cdot 100(\%) \tag{1}\]  
where  
\(T_{c}=\) Maritime traffic congestion,  
\(Q_{t}=\) Actual maritime traffic volume,  
\(Q_{p}=\) Practical maritime traffic volume. Since the area required for safe navigation of a vessel is usually proportional to the squared length of the ship, the actual maritime traffic volume is the summation of the length squared conversion traffic volumes by tonnage group, which is calculated as the product of number of ships and the length squared coefficient. Equations (2) and (3) are the expressions for calculating actual maritime traffic volume and length squared conversion traffic volume. \[Q_{t}=\frac{\sum_{m=1}^{m}V_{n}}{D\cdot T} \tag{2}\]  
where  
\(V_{n}=\) Length squared conversion traffic volume by tonnage group,  
\(D=\) Port operation day,  
\(T=\) Port operation time,  
\(m=\) Number of tonnage group. \[V_{n}=N_{n}\cdot\left({L_{n}}^{2}\right) \tag{3}\]  
where  
\(N_{n}=\) Number of ships by tonnage group,  
\(L_{n}=\) Length coefficient by tonnage group. Length coefficient is ratio of the representative length to the standard length of ships, representative length of ships is proportional to the cube root of average tonnage of ships, and standard length of ships is a weighted average of the representative length of ships by tonnage group. Equations (4) and (5) are the expressions for calculating length and representative length of ships. \[L_{n}=\frac{R_{n}}{S} \tag{4}\]  
where  
\(R_{n}=\) Representative length of ships by tonnage group,  
\(S=\) Standard length of ships. \[R_{n}=\sqrt[3]{250\cdot AT_{n}} \tag{5}\]  
where  
\(AT_{n}=\) Average tonnage of ships by tonnage group. Practical maritime traffic volume is the value obtained by multiplying the maximum maritime traffic volume by the practical maritime traffic capacity coefficient, and the practical maritime traffic capacity coefficient generally has a value of 0.2 to 0.25. This refers to the practically allowable traffic volume depending on sea and weather conditions, maritime traffic conditions, and maritime traffic management methods, which means that it is 20 to 25% of the maximum maritime traffic volume. Equation (6) is an expression for calculating practical maritime traffic volume. \[Q_{p}=Q_{m}\cdot C_{p} \tag{6}\]  
where  
\(Q_{m}=\) Maximum maritime traffic volume,  
\(C_{p}=\) Practical maritime traffic volume coefficient. Maximum maritime traffic volume is a theoretical value that can be accommodated on a passage of width \(W\), assuming that ships of a certain size are continuously navigating at speed \(V\). The size of the ship is determined by the elliptical ship domain, which is the area necessary for the ship to navigate safely, and \(\alpha\) and \(\beta\) mean the major and minor axes of the ship domain. There are many theories about the shape and size of a ship domain, the elliptical ship domain is common. \(\alpha\) usually has a value of 6.0 to 8.0 and \(\beta\) has a value of 1.6 to 3.2. Equation (7) is an expression for calculating maximum maritime traffic volume. \[Q_{m}=\frac{W\cdot V}{\alpha\cdot\beta\cdot S^{2}} \tag{7}\]  
where  
\(W=\) Width of passage,  
\(V=\) Velocity of ship,  
\(\alpha=\) Major axis coefficient,  
\(\beta=\) Minor axis coefficient.