基于M/M/C排队模型的三峡大坝船舶待闸时长预测研究

为研究三峡大坝船舶在锚地长时间滞留待闸的问题,收集并统计了三峡坝区2013年下行方向上不同类型船舶到达上游锚地和通过船闸的流量数据,并对船舶待闸时间进行了频数统计;引入排队论方法,将船舶在三峡坝上锚地排队待闸到离开锚地的过程构建为随机输入多服务台排队系统,利用M/M/C排队模型求解系统的平均等待时间,平均队长等;将2013年船舶到达率和锚地服务率作为输入,模型计算得出的平均停留时间与实际情况的绝对误差为7.3%,表明了模型的适用性;使用不同的船舶到达率和锚地服务率参数,开展模型敏感性分析,结果表明若船舶到达率降低15%(例如15%的船舶采用翻坝运输),锚地泊位由超负荷状态转为能力充足;相反,若达到率增加15%,系统将处于不稳定状态,无法继续运行;但此时若将锚地服务率提高30%,则系统又能够恢复稳定,泊位可以满足需求. 

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.