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

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 lines, 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. First, 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 addition, 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 deviates from the mean value by less than 1%, the waiting-time parameter conspicuously affects the passenger flow assignment solution.