路网应急疏散理想与保守疏散时间流研究

摘要

Studying ideal evacuation time flow and conservative evacuation time flow for emergency evacuation problem is significant to predict the evacuation time in the situation of emergency. In view of this objective, a mathematical programming model for ideal and conservative time flow is built, meanwhile, two flow-augmenting algorithm to solve this model is developed by means of theory of the shortest path, the longest path and the minimum profit flow, the algorithm can not only calculate the flow assignment in ideal and worst evacuation situation, but also can calculate the corresponding value of evacuation time respectively, further, identify the range of total evacuation time. Finally a demonstration example is used to demonstrate the calculation process of ideal and conservative time flow, as well as discussing its evolution properties.%研究应急疏散问题的理想疏散时间流及保守疏散时间流对于估计真实突发事件下的疏散时间具有重要的指导意义。为此构建了理想疏散时间流与保守疏散时间流问题的数学规划模型，并借鉴经典网络流理论的最短路、最长路、最小费用流算法原理，设计了求解理想疏散时间流与保守疏散时间流的两个增广路算法。该算法不但可以求得理想疏散情况及最坏疏散情况下的流量分布，还可以计算出各自对应的理想疏散时间和保守疏散时间，从而识别出应急疏散总时间的范围域。最后通过算例演示了理想疏散时间流及保守疏散时间流的求解过程，并讨论了他们的变化特征。