Quantitative Assessment on Navigation Impact of the Controlled Waterway in the Upper Yangtze River Using Queuing Model

As an important transportation link between eastern and western economic zones of China, the Yangtze River waterway has been globally ranked first in relation to freight volume since 2010, and the density of ship traffic has also increased significantly. However, the inland navigation system has been increasingly threatened by traffic congestion, which is more serious in the controlled waterways of the upper Yangtze River. In this study, the distribution laws of ship traffic flow and service time in the controlled waterway were analyzed, indicating that the traffic flow obeys the Poisson distribution, and the service time obeys a negative exponential distribution. Thereafter, by simplifying the queuing processes and rules, the M/M/1 queuing service model was established to calculate ship queuing indicators in a controlled waterway. It was found that the ship queuing indicators varied greatly among different controlled waterways. Compared with downstream ships, upstream ships usually had longer queuing lengths and times, which were also more affected by the increasing number of ship arrivals and service times. Consequently, a dimensionless loss coefficient was proposed to quantify the influence of the controlled waterway on the navigation capacity. As the service time and number of ships increased, the loss coefficient also increased. The results of this study could provide references for understanding the ship queuing problem, and thereby the assessment of navigation capacity and anchorage constructions in a controlled waterway.