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Summary The 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.

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Container liner shipping is a kind of transportation mode that is operated according to a schedule. Although the goal is to operate container liner ships on time, the actual arrival time and handling time often deviate from the schedule due to uncertain factors. The identification of a proper probability distribution to describe time deviation law will have a significant impact on accurately recognizing the uncertainty of the operation of container liner ships. In view of this problem, this paper discusses the basic characteristics of container liner ships’ operation time, analyses the properties of relevant probability distributions, and selects representative container ports around the world to collect data on the container liner ships’ operation time for statistical verification. The results show that under schedule constraints and interference uncertainty, the time deviation presents a specific state between a fixed length and random distribution that conforms to the properties of an Erlang distribution. Given that container liner shipping follows the same operation rules worldwide, it is reasonable to deduce that the time deviation law could be generalized to other container ports. Finally, the practical value of this study is demonstrated through quantitative evaluation of port congestion degree under various probabilistic models.