Abstract: Owing to the low utilization rate of airspace, lack of quantitative models for managing air traffic flow, congestion of air routes and intersections and capability to deal with emergencies, the system for optimal distribution model was improved from the civil aviation actual operation characteristics of air traffic control. Based on the multi-commodity flow theory, the air traffic flow with different performances was transformed into multi-commodity flow on the network. Meanwhile, a mathematical model considering the three-flow synergy was established and the approximate algorithm to reduce the difficulty was expressed. First, the traffic flows of huge, medium and small aircraft with different performances were considered, and the necessity for distinguishing aircrafts different performances with different flows was explained; second, the cost function of the en-route with flow change, based on en-route length, aircrafts speed and fuel coefficient was defined; third, considering network connectivity, route capacity, controller work load and flow type, multi-commodity flow theory and improved system for the optimal allocation model, in which the total cost in the route network is minimum, were used to establish a mathematical model that considers the three-stream synergy. At the same time, aiming at improving the low efficiency of multi-commodity flow calculation in the Ford-Fulkson algorithm, an approximation algorithm for the phased distribution of air traffic flow was designed according to the characteristics of dynamic changes of route network cost; finally, a numerical example was constructed based on some airspace in the North China Control Zone. The simulation results show that the model can complete the coordination of three traffic flows in real time with a large-scale air traffic flow, and it has a greater efficiency in scale calculation than the traditional algorithm.

Key words: air transport, multi-commodity flow, capacity, aircraft performance, traffic distribution

摘要： 针对目前空域利用率低、管制员分配空中交通流量依靠自身经验，缺乏量化模型提供决策和面对突发事件处理能力不足等问题，从民航管制实际运行特点出发，改进了系统最优分配模型，并基于多品种流理论将不同性能的飞机流转化为网络上多品种流，建立了一个考虑了三流协同的数学模型，设计了阶段式的近似求解算法，从而降低求解难度。首先，考虑了大型机、中型机与小型机尾流强度不同的特点，说明了以不同品种流区别飞机性能差异的必要性；其次，考虑航路长度、速度和燃油系数等因素构建了航路随流量变化的费用函数；再次，针对空中交通的运行特点，以航路网络中总航行费用最小为目标，考虑了航路容量、管制员负荷、网络连通性和三流的优先级建立了最优化模型。同时，针对Ford-Fulkson算法求解多品种流计算效率低的问题，结合航路网络费用动态变化的特点，设计了一种实时阶段性分配空中交通流量的近似算法。最后以华北管制区的部分空域为例构建了算例，仿真结果表明：模型能够在大流量下实时的完成3种交通流的协调，比起传统的算法在大规模运算时具有效率优势。

关键词: 航空运输, 多品种流, 通行能力, 飞机性能, 流量分配