Timetable Design for Urban Rail Line with Capacity Constraints

Abstract

To design an efficient and economical timetable for a heavily congested urban rail corridor, a scheduling model is proposed in this paper. The objective of the proposed model is to find the departure time of trains at the start terminal to minimize the system cost, which includes passenger waiting cost and operating cost. To evaluate the performance of the timetable, a simulation model is developed to simulate the detailed movements of passengers and trains with strict constraints of station and train capacities. It assumes that passengers who arrive early will have more chances to access a station and board a train. The accessing and boarding processes of passengers are all based on a first-come-first-serve basis. When a station is full, passengers unable to access must wait outside until the number of waiting passengers at platform falls below a given value. When a train is full, passengers unable to board must wait at the platform for the next train to arrive. Then, based on the simulation results, a two-stage genetic algorithm is introduced to find the best timetable. Finally, a numerical example is given to demonstrate the effectiveness of the proposed model and solution method.

Timetable Design for Minimizing Passenger Travel Time and Congestion for a Single Metro Line

“…The research papers [12,14,15] have considered the passenger waiting time and the capacity of trains under time-dependent or dynamic demand for the fact that the waiting passenger may not be able to board the next arriving train under over-saturated conditions. Zhu et al assumed that the passenger demand is steady, and created an efficient timetable with minimal passenger cost and operation cost through considering the capacity of trains and stations [24]. However, the real passenger demand is dynamic, and C n -number of congestion events on platforms.…”

Timetable Optimization of Rail Transit Loop Line with Transfer Coordination

“…Time timetabling can be classified into single-line timetable optimization and network timetable synchronization. The former one always focuses on the waiting time of passengers [12], the number of waiting passengers [13], operational cost [14,15], travel time [8], vehicle delay [11,16], and energy consumption [17,18]. Given that single-line timetable optimization only focuses on a single line without the passenger interchange with other lines in the network, the demand of transfer passengers has not been considered thoroughly.…”

Pareto optimal train scheduling for urban rail transit using generalized particle swarm optimization

“…With a reasonable description of passenger loading and departure events, they proposed a nonlinear train scheduling model, whose objective is to minimize the total number of waiting passengers and weighted remaining passengers. Zhu et al 17 also studied the urban rail timetabling with capacity constraints. In their study, the capacity constraint of station is also considered and a simple simulation model is proposed to calculate the passenger waiting cost.…”

“…In most of the above studies, simple weighted aggregation is used to integrate the multiple objectives. [12][13][14]16,17 However, the practicability of these weighted aggregation methods cannot be guaranteed, since there is still no definite unified opinion on how to determine the weight proportion of each aspect. In contrast, Pareto optimality method is more practical, which can provide more information to operators when determining an optimal train timetable, that is, list more compromise solutions to let the operator choose according to the circumstances of urban rail system.…”