城市轨道交通线路客流控制整数规划模型

Integer Programming Model of Passenger Flow Assignment for Congested Urban Rail lines

针对客流过饱和的城市轨道交通线路难于充分发挥旅客输送能力的问题,基于网络拓扑与客流需求定义建立了以旅客周转量最大为目标的线路客流控制整数线性规划模型.该模型首先建立了客流-运行图网络模型用以描述旅客在时间和空间上的移动;其次,在客流OD参数定义中,将旅客出行时间推算为旅客期望乘坐列车,定义了旅客在站等待时间参数;最后,使用优化软件GAMS24.3进行了建模求解.在网络规模为1 000对客流FOD和909个顶点的过饱和客流城市轨道交通线路客流控制问题算例中,耗时0.01 s得出了最优解与分时段客流控制方案.计算结果表明:饱和情况下,不同的在站等待时间下线路旅客总周转量与平均值的偏差低于1%,等待时间对各个车站具体控流方案有结构性的影响.

Urban rail transit lines are often hard to give full play to its passenger transport capacity in condition of oversaturated passenger flow. In order to maximize the passenger transportation capacity of congested urban rail transit l in e s,a linear integer programming model for urban rail transit passenger flow control is built on the basis of network topology and definition of passenger demand. F irs t,a flow- timetable network model is proposed to describe passenger movements in the rail line with timetable guidance. Then,by converting a passenger’s departure time to the expected train by the passenger, origin-destination （ OD ） parameters of passenger flow, including origin, destination and expected train , are defined along with the parameter of passenger’s waiting time in station. Based on these definitions, the linear integer programming model is finally built to maximize the passenger turnover volume. In ad dition, to verify the effectiveness of the model, a case study on a urban rail transit line with a network scale of 1 000 passenger OD pairs and 909 nodes is conducted,and the model is solved with software GAMS24.3. The results show that the optimal solution can be obtained in 0. 09 s. In saturated situations, the total passenger turnover volume under different in-station waiting time deviatesfrom the mean value by less than 1 % , the waiting-time parameter conspicuously affects the passenger flow assignment solution.