SummaryThe probability distribution of the operational law of container liner ships in port is the significant theoretical basis for the study of container liners and ports, but there has been a lack of corresponding statistical analysis and theoretical research on that distribution since maritime container transportation came into being. The main purpose of this paper is to identify probabilistic models of the operational law of container liners by statistically analysing the operation data collected from Dalian, Kaohsiung and Rotterdam ports. The results demonstrate that both the interarrival time and the handling time of container liner ships follow higher order Erlang distributions. Under the combined influence of schedule constraints and the interference of some uncertain factors, container liners run between randomness and certainty, presenting the same feature as higher order Erlang distributions. In addition, the world container trade in container ports is subject to similar operational rules and time limits, so it is reasonable to deduce that the above conclusion could be generalized to other container ports. Finally, this paper quantitatively evaluates the degree of port congestion under various probabilistic models, which shows that the study not only has theoretical significance but also values in application.