# Port Congestion#

We define two congestion indices:

Average Congestion Rate (ACR) — A weighted average of the congestion rates for the top 50 container ports worldwide, with the weights determined by the number of ship visits to each port:

where the congestion rate for each port \(p \in \mathcal{P}\) is computed by dividing the number of delayed ship visits by the total number of ship visits:

\(Delayed_{pt}\) and \(Undelayed_{pt}\) represent the number of delayed and undelayed ship visits at port \(p\) in month \(t\), respectively. The full list of the top 50 container ports can be found using the following link: https://www.worldshipping.org/top-50-ports.

Average Congestion Time (ACT) — The average number of hours a containership waits in an anchorage area of a port before docking at a berth, weighted by the number of ship visits to the top 50 container ports worldwide:

where \(DelayHours_{pt}\) represents the total number of hours that containerships spend in the anchorage areas of port \(p\) in month \(t\), respectively.

The identification of berth and anchorage areas in each port is achieved through the application of the IMA-DBSCAN algorithm, i.e., the Iterative, Multi-Attribute, Density-Based Spatial Clustering of Applications with Noise. The details and pseudo-codes can be found in Bai *et al*. (2023)^{1} and Bai *et al*. (2023)^{2}.

The monthly series of the ACR and ACT indices can be downloaded using the provided link: Aggregated Congestion Indices. Additionally, the disaggregated monthly series of congestion rates for the top 50 container ports are visualized in the following plot: