Train Timetabling on double track and multiple station capacity railway with useful upper and lower bounds

Abstract

Abstract. Train scheduling has been one of the signi cant issues in the railway industry in recent years since it has an important role in e cacy of railway infrastructure. In this paper, the timetabling problem of a multiple-tracked railway network is discussed. More speci cally, a general model is presented here in which a set of operational and safety requirements is considered. The model handles the trains overtaking in stations and considers the stations' capacity. The objective function is to minimize the total travel time. Unfortunately, the problem is NP-hard, and real-sized problems cannot be solved in an acceptable amount of time. In order to reduce the processing time, we presented some heuristic rules, which reduce the number of binary variables. These rules are based on problem's parameters, such as travel time, dwell time, and safety time of stations, and try to remove the impracticable areas of the solution space. Furthermore, a Lagrangian Relaxation algorithm model is presented in order to nd a lower bound. Finally, comprehensive numerical experiments on the Tehran Metro case are reported. Results show the e ciency of the heuristic rules and also the Lagrangian Relaxation method in a way that the optimum values are obtained for all analyzed problems.

Capacity of Main Railway Lines – Analysis of Methodologies for its Calculation

“…Then, from our example the time of occupation, T obs = 540 min and based on the formula t medz = 0.420 + 0.564.t obs , the total gap time T medz = 304.98 min and consequently the use of permeable performance will be K prakt = 58.68%. The slight deviation between these values and the values based on ŽSR methodology, is caused by estimation of the regression correlation equation parameters, which has the reliability value R2 = 0.999 [15][16][17][18].…”

A Scheduling Approach for the Combination Scheme and Train Timetable of a Heavy-Haul Railway

“…The TTP model is the optimal integration of a heavy-haul railway combined scheme and train timetable. It is a difficult problem since both the train formation problem and the train timetabling problem are NP-hard problems [22,33,34]. Therefore, to solve the TTP model, we developed a genetic algorithm-based framework.…”