Calculation of the traffic capacity of channels is based on analysis of congested traffic flow, especially the behaviours of the giveway action. This study improves the previous model describing the ship behaviours in giveway motion as the results of navigators' choice of giveway action. The generalized cost function consisting delayed time and loss of ship damage by collision are newly introduced. The influence of traffic congestion to the choice between overtaking and following can be cleary explained. Moreover, the giveway motions become to be described not only by the distances between overtaking and overtaken ships in rateral direction, but also by the giveway course. This result expands the model calculating effective ship domains from one-dimentional to two-dimentional.