# Improving the Maritime Traffic Evaluation with the Course and Speed Model
## 3 Maritime Traffic Flow Model  
Traffic flow, or traffic stream, pertains to the movement of people and vehicles proceeding in the same direction. It can be envisioned as traffic traversing across one, two, or even more lanes [18]. Traffic flow models illustrate the relationship among the three variables of velocity, density, and traffic volume. These models can elucidate traffic flow characteristics, such as delay, congestion, and bottlenecks. While typically employed in road traffic facilities, various single-mode models have been studied, with Greenshields (linear model) [19], Greenberg (algebraic model), and Underwood (exponential model) [20] being representative examples. A recent study assumed that excessive speed was the cause of accidents in road traffic and compared the deviation of driving speed by vehicle type to the speed limit [21]. To investigate the applicability of these traditional traffic flow models to maritime traffic, the data were collected and compared. The results exhibit significant similarities to road traffic flow. However, the effectiveness was found to be low in the velocity-density model [22], which could be attributed to the inherent properties of maritime traffic. Maritime traffic flow refers to one or more courses or flows that manifest when sea vessels move at specific speeds over a designated period. The key terms in the maritime traffic flow assessment encompass comprehensive environmental stress, navigation risk, and ship operating difficulty. These terms assess the operational burden of a ship as a risk. Prominent models include ES, PARK, BC, and SJ, each displaying unique characteristics (Table 1). Maritime traffic necessitates a distinct approach compared to road traffic. In road traffic, once the mode of transport and route to the destination are established, the primary variables influencing the arrival time are velocity, density, and traffic volume [23]. However, in maritime traffic, after setting the mode of transport and route, several other considerations come into play. These include variables such as weather conditions, sea state, water depth, course-keeping quality based on ship movement characteristics, turning capacity, ship age, surrounding traffic volume and navigation, port regulations, ship operator characteristics, optimal speed, and more [24; 25]. Hierarchical and coupling models have been used to propose mechanisms of factors affecting marine traffic flow [26]. Therefore, the characteristics of maritime traffic can be broadly categorized as spatiality, continuity, specificity, and safety. Among these, spatiality is the most significant property distinguishing maritime traffic from road traffic. It refers to spatial autonomy. Maritime traffic enjoys navigational autonomy in navigable sea areas. This means that a suitable course can be chosen during navigation planning within a sea area or route, as long as seaworthiness is not compromised. Furthermore, the COLREGS applies to ships, allowing maneuvers, such as overtaking and crossing, to be considered relative to other vessels. Thus, while maritime traffic is autonomous, recognizing and utilizing historically used navigation patterns or conventional routes can enhance efficiency and minimize risks. This is because these are routes that have been tested and proven over time. Continuity pertains to the consistent velocity of maritime traffic. There are no traffic lights or stop signs at sea, resulting in an uninterrupted flow similar to that of highways. Moreover, except for some smaller vessels, speed adjustments are not immediate. Ships typically sail at an optimal speed suitable to their specific characteristics, such as type, size, and cargo type. As a result, changes in a ship's speed are gradual and not overly pronounced. Specificity refers to the environmental and human factors influencing maritime traffic. Unlike road traffic, maritime traffic is significantly impacted by external factors, such as climate and sea conditions.