随机路网的最短路径问题研究

主要研究随机路网中的最短路径问题,首先给出随机路网的定义,建立了随机路网的模型,假定路段的费用是满足正态分布的随机变量,并给出从历史数据中得到此变量的均值和方差的统计学方法;然后得出路径出行费用的均值及方差的递推公式,将费用的方差当作一个限制条件,从而在Dijkstra算法的基础上,提出了带单一限制条件的最短路径算法,同时给出了算法的具体流程;最后用一个简单例子演示了算法的具体步骤,并在南京路网中验证了此算法的实用性。

The Study on Shortest Path Problems in Stochastic Traffic Network

The shortest path problem in the stochastic traffic network is studied.First,the definition of stochastic traffic network is given and the stochastic network model is built.Assuming the link cost is the normally distributed random variable,a statistic method is proposed to get this random variable from historical data.Then the formulas to acquire the mean and variance of path cost is proposed.An algorithm of shortest path based on Dijkstra with single restriction(variance of link cost) is proposed.Finally,an example is given to show the algorithm.