On Probability Distributions of the Time Deviation Law of Container Liner Ships Under Interference Uncertainty

Abstract

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.

A study on the distribution characteristics of the arrival time interval of different ship types

“…Wu Di et al analyzed the deviation between the actual arrival time of the container liner and the shipping schedule, and proved that the probability of the container liner's arrival at night follows the gamma distribution [4] . Song Yunting et al concluded that the deviation probability of container liner arrival time conforms to Erlang distribution under the conditions of scheduling constraints and disturbance uncertainty [5] .…”

Effect of Service Priority on the Integrated Continuous Berth Allocation and Quay Crane Assignment Problem after Port Congestion

“…In order to mitigate container port congestion when the number of feeders is evidently larger than the number of deep-sea vessels, Jia, et al [44] studied the way to allocate berths to deep-sea vessels and schedule arrivals of feeders. Song and Wang [45] indicated the waiting time of ships is an important indicator of port congestion. The causes of port congestion were not discussed in depth in this article, but the evacuation strategy of vessels after port congestion was mainly analyzed.…”