# Improving the Maritime Traffic Evaluation with the Course and Speed Model
## 4 Evaluation of Maritime Traffic Flow with the CS Model  
### Overview  
Changes in course and speed are the outputs of a ship's navigation, which are based on the combined judgment of the ship's operator and the ship's navigation instruments as the ship sails. Based on this concept, we designed a course-speed (CS) model. This model serves as a method for evaluating maritime traffic flow by tracking changes in the course and speed. This model emphasizes spatiality and continuity, which are essential characteristics of maritime traffic. When a ship sails, numerous variables influence its movement. However, the CS model primarily focuses on course changes and speed variations, using these factors to assess the fluidity of maritime traffic flow.  
When a ship navigates a specific sea route or area, the distribution of its sailing trajectory generally follows a normal distribution across the cross-section of traditional maritime traffic flow [27]. Any behavior deviating from this norm implies a disruption in the smoothness of the maritime traffic flow. For instance, changes in the typical course or navigational patterns in certain situations, deviating from conventional navigation routes, indicate a failure to maintain spatiality. Likewise, any changes in speed that do not adhere to the ship's optimal speed, considering its specific characteristics, suggest a failure to uphold continuity.  
The CS index (Ics) is calculated based on the spatiality index (Ispa) and continuity index (Icon) as follows:  
\[\mathrm{I_{cs}}=\mathrm{mean}(\mathrm{I_{spa}}+\mathrm{I_{con}}), \tag{1}\]  
The spatiality index (Ispa), as defined in Equation (2), quantifies the disparity in speed and acceleration between the ship under assessment and the standard plan. In contrast, the continuity index (Icon), as defined in Equation (3), measures the variance in the course  
Figure 1: Evaluation method according to maritime traffic characteristics.  
over ground (COG) and rate of turn (ROT) between the ship under assessment and the standard plan:  
\[\mathrm{I_{spa}}=\frac{1}{2n}(\sum_{k=1}^{n}\mathrm{D_{k}(v)}+\sum_{k=1}^{n} \mathrm{D_{k}(a)}), \tag{2}\]  
\[\mathrm{I_{con}}=\frac{1}{2n}(\sum_{k=1}^{n}\mathrm{D_{k}(\theta)}+\sum_{k=1}^{ n}\mathrm{D_{k}(r)}), \tag{3}\]  
where n represents the number of target ships for assessment and Dk(x) represents the difference between the standard plan and the target ship.  
The standard plan entails collecting AIS data over a specific period as ships traverse the assessment sea area. These data are then categorized based on ship size and traffic volume, yielding an average and dispersion for each ship at distinct points. The differences in velocity (v), acceleration (a), course over ground (\(\theta\)), and rate of turn (r) between the standard plan and the ship under assessment are calculated as shown.  
\[\mathrm{D_{k}(x)}=\int\left(\frac{\sqrt{\left(\overline{x}(t)-x_{k}(t)\right) ^{2}}}{\mu(t)}\right)\mathrm{dt},x\in v,a,\theta,r, \tag{4}\]  
where \(\overline{x}\) refers to the average of the standard plan, \(u\) represents the standard deviation of the standard plan, and \(x_{k}(t)\) denotes the value of ship k at location t.