基于生灭过程的场站周转挂车数量配置

Quantity configuration of spare trailers for freight stations based on birth-death process

为了解决甩挂运输中场站备用挂车数量配置问题,引入生灭模型模拟挂车聚散过程,建立当场站发送和接收牵引车频次长期稳定,假定牵引车到达为泊松流,装卸队伍个数确定且装卸时间服从独立负指数分布时,周转挂车状态变化的生灭过程模型;通过研究其平稳分布,给出了牵引车需要等待的概率给定时,场站周转挂车配置数量的计算方法;通过分析排队等待的牵引车数量分布规律,给出需要等待的牵引车平均排队长度计算方法;分析了全部牵引车和等待牵引车的等待时间分布。研究结果表明:车辆的等待时间服从负指数分布,其均值与周转挂车数量无关;为周转挂车数量配置提供了一种有效的计算方法。

In order to solve the quantity configuration problem of spare trailers for freight station in drop and pull transport network,the theory of birth-death process was introduced to model the accumulating-disseminating process of spare trailers. While receiving and sending tractors frequency was long-term stable,spare trailers state transformation was modeled as a birth-death process under the assumption that tractors arrival was regarded as a Poisson stream,the number of loading and unloading service channel was given and the service time was submitted to independent negative exponential distribution.After analyzing the stationary distribution of the birth-death process,the algorithmic method for spare trailer number of freight station was educed when the probability of tractors waiting was given.After analyzing the number distribution of waiting tractors,the algorithmic method for waiting tractors average queue length was obtained,and the waiting time distribution of waiting tractors and all tractors was analyzed.The results show that the waiting time of waiting tractors is sumbitted to negative exponential distributionand its conditional mean is not relevant to the number of spare trailer.This paper provides an effective computational method for quantity configuration of spare trailers for freight station.