Timetable optimization models and methods for minimizing passenger waiting time at public transit terminals

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - urban, mode - rail, operations - scheduling, operations - capacity, operations - frequency, ridership - demand, planning - travel demand management, planning - methods


Train timetabling, public transit terminals, waiting time, mixed integer, linear and non-linear optimization, urban rail, Tehran


This paper focuses on developing mathematical optimization models for the train timetabling problem with respect to dynamic travel demand and capacity constraints. The train scheduling models presented in this paper aim to minimize passenger waiting times at public transit terminals. Linear and non-linear formulations of the problem are presented. The non-linear formulation is then improved through introducing service frequency variables. Heuristic rules are suggested and embedded in the improved non-linear formulation to reduce the computational time effort needed to find the upper bound. The effectiveness of the proposed train timetabling models is illustrated through the application to an underground urban rail line in the city of Tehran. The results demonstrate the effectiveness of the proposed demand-oriented train timetabling models, in terms of decreasing passenger waiting times. Compared to the baseline and regular timetables, total waiting time is reduced by 6.36% and 10.55% respectively, through the proposed mathematical optimization models.


Permission to publish the abstract has been given by Taylor&Francis, copyright remains with them.