The main goal of the traffic system modelling is successful running a business and continuously searching the possibilities for its improvement. With the application of the model set in this paper one can get the valuable results for managing the port system. These results should route the port managers to bring appropriate decisions in order to enhance the business efficiency and enlarge the port competitiveness. The model presented is based on the general systems theory. The port system can be presented as a physical system which over time changes its status to a random manner i.e., exceed from one state to another under the influence of random factors that cannot be predicted in advance. Here, the system "serving ship at quay" is defined with the universe of discourse and couplings (UC-structure), dividing it on elements and links between them. Next, the states and the transitions between the states are identified, along with the scheme (ST-diagram). From the ST-diagram the system of differential equations is set and the computer program for solving is recommended.