A Study on Prediction of Waiting Time of Ships Crossing Three Gorges Locks based on M/M/C Queuing Models

In order to study the issue of serious delay of ships during the process of crossing Three Gorges Locks, downstream traffic flow consisting of different types of ships arriving at anchorages and passing Locks in 2013 is collected and analyzed.Frequency distribution of different waiting durations of ships are also summarized and presented.Queuing theory is used to conceptualize the anchorages of Three Gorges Dam as a queuing system with random arrival rate and multiple servers, M/M/C queuing model is used to best represent the system and used to model average waiting time and average queuing length, etc.of the system.The observed arrival rate of ships and service rate of anchorages in 2013 are used as inputs of the model, average delay time estimated from the model is compared with the actual data, and the absolute percent error (APE) is found to be 7.3%, which suggests that the accuracy of the model is acceptable.Then sensitivity analysis of the model is carried out by specifying different arrival rates and service rates.Study results show that decreasing arrival rate by 15% (e.g.the goods from 15% of all of the ships arrived will be transfer to road transportation) would change the status of the anchorages from overloading to operating within the capacity.On the other hand, if increasing arrival rate by 15%, then the system will be unstable and fully congested.However, if, at the same time, the service rate of the anchorages increases by 30%, the system will return to its stable status and the parking demand of arriving vessels can be accommodated.