Synchronized optimization of last trains' timetables in mass rail transit networks based on extra dwell time

Synchronized optimization of last trains' timetables is purposed to improve the connecting effects of last trains by coordinating the arrival and departure times of trains at transfer stations. Due to the great complexities of transfer relationships, it is more and more difficult to solve this problem. In this paper, in order to reduce the number of unable transfer passengers, an optimization model of last trains' timetables is proposed by determining the departure time and extra dwell time. And we minimize the difference between last trains' actual departure time and the optimized ones for the convenience of rolling stocks daily maintenance. Possible optimized solution is investigated through a case study in Beijing subway by using the tool of CPLEX. The results indicate that the volume of unable transfer passengers is reduced by 15.0%, and the number of coordinated trains is improved by 8.9%.