基于实际拓扑结构的交通网络客运流量的理论研究

Theoretical Research of Passenger Flow Based on Actual Transport Network

针对de Moura等人提出因特网信息流的费米-狄拉克统计模型,我们提出用玻色-爱因斯坦统计模型来研究一般交通客运网络中的客流分布问题.将交通客运网络抽象成一个与外界有粒子和能量交换的热力学系统,其中粒子代表乘客,适当地定义能级,分析得出交通网络中的每个站点平均客流的解析表述.然后以中国铁路客运网络实际拓扑为基础,用随机行走模型模拟分析交通网络中的客流分布情况,模拟结果显示,无论初态如何,经过足够长时间后,各站点的客流分布趋于平衡,平衡时各站点的客流量与其点权正相关,模拟客流分布曲线与理论结果基本一致.

Comparing with de Moura＇s model of Fermi-Dirac statistics for traffic in a network,we studied the statistical properties of the general passenger transport network with Bose-Einstein distribution.A transport of passenger network can be modeled as a thermodynamics system exchanging particles and energy with its environment,where passengers are considered as particles.With appropriately defined energy-level structure,the analytical expressions of the passenger flow of the transport network can be obtained.Based on the empirical properties of Chinese railway network,we propose an idealized model,in which large numbers of passengers move randomly from one station to another in this railway network.Numerical simulations show that whatever the early state is,in the t→∞ limit the network reaches a stationary state with the passenger flow in proportion with the node weight.The numerical simulations results are shown to be nearly in agreement with the analytical expressions.