ROBUSTNESS IMPROVEMENTS IN A TRAIN TIMETABLE HEADWAYS WITH TRAVEL TIME DEPENDENT MINIMUM. Fahimeh Khoshniyat Anders Peterson

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1 ROBUSTNESS IMPROVEMENTS IN A TRAIN TIMETABLE WITH TRAVEL TIME DEPENDENT MINIMUM HEADWAYS Fahimeh Khoshniyat Anders Peterson Dept. of Science and Technology (ITN/KTS) Linköping University, Norrköping, Sweden March 25, 2015

2 Introduction What is robustness and why is it important? How to improve robustness? One approach is to add more buffer times

3 Introduction Assumption in this study is that as trains travel longer, they lose precisions

4 Delay (min) On-time performance en route Dotted line = average performance Doubled line = 75th percentile Scheduled Travel Time for train No.500 (min)

5 Purpose To implement travel time dependent minimum headways between succeeding trains in a timetable and to measure and evaluate the effects. Location Train 1 Train 2 Origin station Station j H 0 T O T 1 Time

6 Purpose To implement travel time dependent minimum headways between succeeding trains in a timetable and to measure and evaluate the effects. Location Train 1 Train 2 Origin station Reserved time slot for Train 1 Technical minimum headway (H t ) Station j H t H 0 H m =α*(t 1 T o ) T O T 1 Time

7 Purpose To implement travel time dependent minimum headways between succeeding trains in a timetable and to measure and evaluate the effects. Location Origin station Train 1 Train 2 Reserved time slot for Train 1 Technical minimum headway (H t ) Postponed Train 2 Station j T O T 1 Time

8 Step 1: Timetable construction Overall approach Step 2a: Measuring the effects Initial timetable The modified MILP model The modified Timetable Measuring the effects in heterogeneity, number of trains and total travel times Step 2b: Timetable evaluation The original MILP model + delay The original MILP model + delay Initial timetable in case of disturbances The modified timetable in case of disturbances Performance comparison

9 Approach for the model adjustments MILP model Discrete variables represent order of trains and track allocations Continuous variables represent time Correlate headways to trains travel times - Törnquist Krasemann, J., Persson, J.A., N-tracked railway traffic re-scheduling during disturbances, DOI: /j.trb Törnquist Krasemann, J., Design of an effective algorithm for fast response to the re-scheduling of railway traffic during disturbances, DOI: /j.trc

14 Evaluations The experiments in this part are based on the timetables produced with regards to α=1 min/h and fixed order of trains

15 Evaluations Performance measures Total delays Total amount of runtime margin (TAoRM) Total incurred secondary delays Recovery time Number of delayed trains Punctuality Additional running times Deviation from an initial timetable Buffer time reductions Number of violations in overtaking

16 Disturbance scenarios Single delayed train (SD) Speed reduction for one single train (SRT) Speed reduction for one section (SRS)

17 Real case study: Swedish Southern Mainline Alvesta Lund (a part of the Southern Mainline) Ca. 200 km long. Double track. Mixed traffic, fast and slow passenger trains and cargo. Source: The Swedish 17 Transport Administration

18 Timetable instances Timetable instances Trains (#) Train events (#) Sections (#) 2011, 11:00-13: , 16:00-18: , 11:00-13: , 16:00-18:

19 Experiments

20 Single delayed train (SDT) a) Initial timetable c) Modified timetable b) Initial timetable in case of 7min disturbance d) Modified timetable in case of 7min disturbance

21 Speed reduction for one train (SRT) Fixed order Flexible order

22 Speed reduction for one section (SRS)

23 2011, 11:00-13:00

24 To summarize In most of the experiments, timetables with travel time dependent minimum headways outperform the initial ones. In single delayed train (SDT) scenarios, the modified timetables have better robustness. In the scenario for speed reduction for a single train (SRT), although we have reached to a better performance in the modified timetables, the flexible order of trains has also a significant role to improve the performance. In scenario for speed reduction in a single section for all trains (SRS), the modified timetables perform better but the improvements are small.

25 Thank you!

Simulation of modified timetables for high speed trains Stockholm Göteborg

17 18 May 2010, Opatija, Croatia First International Conference on Road and Rail Infrastructure Simulation of modified timetables for high speed trains Stockholm Göteborg H. Sipilä Division of Traffic