Analysis of Crossing of Pairs of Ship's Routes and Its Application

Abstract

Based on the queing theory, authors have constructed the mathematical model which describes the marine traffic system where pairs of ship's routes with opposite directions and apart by arbitrary distances cross each other. At each crossing point the effective traffic intensity (the ratio of an arrival rate of ships to an effective passable rate) and probabilities of collision avoidance have been analytically derived from the model. They are numerically simulated by means of a computer, changing such parameters as the traffic intensity and the number of ships between two crossing points. Numerical analyses indicate the critical traffic intensities at which ships jam up on every route. The computed probability of the collision avoiding compares favorably with the actual rate of avoiding collision maneuvers which were observed on board at the congested water in Japan.