Fundamental diagram of ship traffic in the Singapore Strait

The Singapore Strait plays a vital role for the international freight transportation, including containers, bulk cargo and crude oil. In view of the importance of Singapore Strait, it is of practical significance to investigate the ship traffic's speed-density relationship called the fundamental diagram in the Strait, which can be used to estimate the theoretical strait capacity. Despite the availability of large empirical ship traffic data and the long history of traffic flow modeling, the analysis of ship traffic fundamental diagram for the Singapore Strait is still highly deficient. To fill in the gap, we first develop a research framework to address the big AIS (automatic identification system) data for the ship traffic fundamental diagram building. To ensure the correctness of AIS data, a tangible error elimination method is presented. Moreover, a novel weighted least square approach is applied to develop the ship traffic speed-density formulations accurately. Meanwhile, we also show the applicability of the weighted least square approach by a theoretical investigation into the difference between the weighted and non-weighted least square approaches. Finally, we study all the fifteen legs in the Singapore Strait and propose 75 fundamental diagrams based on four classic traffic flow models through mining more than 43 million pieces of AIS data. These fundamental diagrams also indicate the theoretical capacity of each leg in the Singapore Strait.