Maritime traffic models for vessel-to-vessel distances

The maritime traffic is significantly increasing in the recent decades due to its advantageous features related to costs, delivery rate and environmental compatibility. The Vessel Traffic System (VTS), mainly using radar and AIS (Automatic Identification System) data, provides ship’s information (identity, location, intention and so on) but is not able to provide any direct information about the way in which ships are globally positioned, i.e. randomly distributed or grouped/organized in some way, e.g. following routes. This knowledge can be useful to estimate the mutual distances among ships and the mean number of surroundings vessels, that is the number of marine radars in visibility. The AIS data provided by the Italian Coast Guard show a Gamma-like distribution for the mutual distances whose parameters can be estimated through the Maximum-Likelihood method. The truncation of the Gamma model is a useful tool to take into account only ships in a relatively small region. The result is a simple one-parameter distribution able to provide indications about the traffic topology. The empirical study is confirmed by a theoretical distribution coming from the bi-dimensional Poisson process with ships being randomly distributed points on the sea surface