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Estimating containership arrival rate is a key element in harbor operation and management; however, it is not easy to be described because of a wide range of external factors. Most of the literature discussing arrival processes is based on a homogeneous Poisson process, which is unable to describe the fluctuation status of growth or recession. In the paper, we propose the Non-Homogeneous Poisson Process to analyze the arrival process of containership. The Maximum Likelihood Method is used to estimate the parameters and the performance of the models. Finally, a real case of Taichung Harbor in Taiwan is taken as an example. The result shows that power law intensity function and logarithmic linear intensity function models all estimate that the containership arrival shows slow growth trend. Relative to power law intensity function, logarithmic linear intensity function is a model with better goodness-of-fit.