Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time

Transcription

1 Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time Peter Sels 1,2,3, Dirk Cattrysse 2, Pieter Vansteenwegen 2 1 Logically Yours BVBA, Plankenbergstraat 112 bus L7, 2100 Antwerp, Belgium sels.peter@gmail.com, corresponding author 2 Katholieke Universiteit Leuven, Leuven Mobility Research Centre, CIB, Celestijnenlaan 300, 3001 Leuven, Belgium 3 Infrabel, Traffic Management & Services, Fonsnylaan 13, 1060 Brussels, Belgium July 22nd 2015

2 Table of Contents 1 Optimising Timetables 2 Reflowing Results 3 Retiming Results Deterministic Results Stochastic Results 4 Conclusions & Future Work 5 Questions / Next Steps

3 Optimising Timetables Challenge / Puzzle Danish Infrastructure Management Company: Banedanmark: Improve timetable in terms of expected passenger travel time (includes: ride, dwell, transfer time and primary and secondary delays) Fixed: Infrastructure, train lines, halting pattern, primary delay distributions Variable: Timing: supplements times at every ride, dwell, transfer action, variable inter-train heading times variable train orders Note: Includes primary and secondary delays opt. efficiency vs. robustness Specifics: One busy day, morning peak hour

4 Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time Reflowing Results Reflowing Results: via OD-Based Passenger Routing Frederikshavn 25 Thisted Aalborg Struer 32 Holstebro 31! Langå Herning 35 Grenaa Aarhus H Helsingør Skanderborg Skjern Lersøen Vejle Taulov Esbjerg Bramming 29 Lunderskov 5 Roskilde Fredericia Nyborg 1 Korsør Ringsted 4 Næstved Tinglev 28 Svendborg Sønderborg 2 Padborg Nykøbing F Rødby Færge Østerport 7 København H 6 11 Kastrup Snoghøj Odense 30 Tønder Kalundborg 3 Gedser Validity period:

5 Retiming Results Deterministic Results Retiming Results for Hard Constraints: Minimum Run Time Violations? Table 1: Realisability. Reduction of the number and size of minimum runtime violations from timetable Orig. Opt. time- distribution: # actions with a violation per size of violation in seconds table: 6s 12s 18s 24s 30s 36s 42s 48s 56s 60s 66s Orig s 78s 84s 90s 96s 102s 108s 114s 120s 126s 132s Orig Table 2: Realisability. Reduction (elimination) of total and average violation from timetable Orig. Opt. timetable weighted sum (s) tot.# avg. (s) Orig Opt

6 Retiming Results Deterministic Results Retiming Results for Hard Constraints: Realisability? From headway histograms: Only Orig. has minimum run time violations. So Orig. is not realisable. Opt. is realisable.

7 Retiming Results Deterministic Results Retiming Results for Hard Constraints: Headway Conflicts? #edges * tot= avg= #edges * tot= avg= Orig_KO_flow1_planned_ms_in_6s_units Opt_KO_flow1_planned_ms_in_6s_units Figure 2: #Edges per Planned headway. m + s < 3 and T 3 < m + s, are problematic. Orig: NOK, Opt OK.

8 Retiming Results Deterministic Results Retiming Results for Hard Constraints: Headway Conflicts? #edges * flow 0e+00 1e+06 2e+06 3e+06 4e+06 tot= avg= #edges * flow 0e+00 1e+06 2e+06 3e+06 4e+06 tot= avg= Orig_KO_flowf_planned_ms_in_6s_units Opt_KO_flowf_planned_ms_in_6s_units Figure 3: #Passengers per Planned headway. m + s < 3 and T 3 < m + s, are problematic. Orig: NOK, Opt OK.

9 Retiming Results Deterministic Results Retiming Results for Hard Constraints: Macroscopically Feasible? From headway histograms: Only Orig. has minimum headway time violations. So Orig. is not macroscopically feasible = not conflict-less. Opt. is macroscopically feasible = conflict-less.

10 Retiming Results Deterministic Results Retiming Results in the Planned Train Time Domain % 12.90% 89.31% 87.10% reduction: 2.53% orig.m original orig.s Plan_Train_Time opt.m optimal opt.s Figure 4: Increase of 2.53% of total planned train time from Orig. to Opt.

11 Retiming Results Deterministic Results Retiming Results in the Planned Train Time Domain Bargraphs show: Orig. Opt. Same planned train minimum ride + dwell time: due to same number of trains and same minima in Orig. and Opt. timetables, (relatively) more planned train ride + dwell supplement time: steered by objective function trading off efficiency with robustness, effectiveness for passenger service of this is to be judged in expected passenger time domain.

12 Retiming Results Stochastic Results Results in the Expected Passenger Time Domain 0e+00 2e+07 4e+07 6e+07 8e % 2.64% 0.22% 70.73% 3.14% 1.39% 5.75% 7.51% KnockOn(s) KnockOn(m) Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) improvement:2.90% 8.88% 2.72% 0.47% 4.57% 72.84% 2.59% 0.68% 7.26% orig.m original orig.s Exp_FullPssngr_Curved_Time opt.m optimal opt.s Figure 5: Reduction by 2.90% of total exp. passenger time from Orig. to Opt.

13 Retiming Results Stochastic Results Results in the Expected Passenger Time Domain Bargraphs show: Orig. Opt. = same (expected) minimum ride + dwell time due to: same train line plan passengers (still) taking same routes + less expected ride + dwell supplement time more efficient + lowered expected knock-on delay better robustness - increased expected transfer time due to: difficulty for solver to plan many transfers with few passengers + overall reduction of 2.90% in expected passenger time Reduction of missed transfer probability from 11.34% to 2.45%

14 Conclusions & Future Work Conclusions practical method to optimise timetables (in 65 minutes) objective = minimal expected passenger time showed Orig. Opt. reduction of 2.90% in exp. passenger. time evaluation reports on hard constraints, deterministic stability (ride & dwell & transfers) feasibility = conflict freeness (headways) evaluation reports on soft constraints, stochastic efficiency versus robustness does not consider resilience

15 Conclusions & Future Work Railway Timetable Performance Indicators Table 3: Railway Timetable Performance Indicators deterministic stochastic stable feasible robust resilient property in realised domain no timetable- timetable- timetable timetable internal internal absorbs common allows dispatching delays delays prim. & sec. to absorb settle delays more rare delays cause or measure taken in planned domain some no supplements timetablesupplements supplements are sufficiently tuned can be negative are negative large dispatching but some are measures compensatingly positive

16 Conclusions & Future Work International Comparison Table 4: Current Quality Levels of some European Railway Timetables deterministic stochastic Level stable...feasible... robust resilient Country realisable no µ-hw-conflicts 0 FR,IT,BE,DK 1 v NL,UK 2 v v v DE 3 v v v v CH,SE 4 v v v v v stable realisable no 3 -HW-conflicts robust resilient Country?,? v,v v,v v,v v,v BE, DK Black text above [Goverde and Hansen(2013)], based on inquiries and timetable process descriptions of 2013, may be incorrect. [Sels et al.(2015a)sels, Cattrysse, and Vansteenwegen] [Sels et al.(2015b)sels, Dewilde, Cattrysse, and Vansteenwegen] [Sels et al.(2015c)sels, Dewilde, Cattrysse, and Vansteenwegen] µ-hw = microscopically calculated min. headway times. 3 -HW = 3 minute macroscopically assumed min. headway times.

17 Conclusions & Future Work Future Work evaluate over only real transfers data? vary parameter a value: 1%.. 5% add parameter r r% of passengers benefit from temporal spreading of trains parameter r value: 0%.. 100%

18 Questions / Next Steps Questions / Next Steps Your questions? here and now, or... sels.peter@gmail.com

19 Questions / Next Steps 89.31% 10.69% reduction: 2.05% 87.51% 12.49% orig.m original orig.s Plan_Train_Time opt.m optimal opt.s 88.77% orig.m original orig.s Exp_Train_Lin_Time opt.m optimal opt.s 88.71% 11.23% 11.29% improvement: 2.33% improvement: 2.42% 86.76% 86.61% 13.24% 13.39% orig.m original orig.s Exp_Train_Curved_Time opt.m optimal opt.s 8.76% 2.02% 71.83% 1.36% 2.25% 6.72% 7.07% Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) reduction: 1.69% 8.61% 1.99% 70.63% 0.36% 4.23% 10.74% 3.44% orig.m original orig.s Plan_OptPssngr_Time opt.m optimal opt.s 8.74% 2.02% 0.10% 7.56% 71.74% orig.m original orig.s Exp_OptPssngr_Lin_Time opt.m optimal opt.s 8.79% 72.14% 3.60% 1.40% 4.83% 3.20% 1.42% 4.52% 2.03% 0.23% 7.66% KnockOn(s) KnockOn(m) Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) improvement:6.49% KnockOn(s) KnockOn(m) Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) improvement:4.53% 9.35% 2.16% 0.17% 4.37% 76.72% 9.21% 75.56% 2.11% 0.50% 4.62% 2.78% 0.58% 4.78% 2.13% 0.46% 4.51% orig.m original orig.s Exp_OptPssngr_Curved_Time opt.m optimal opt.s 8.62% 2.64% 70.74% 1.34% 3.09% 6.62% 6.96% Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) reduction: 3.15% 8.36% 2.56% 68.58% 0.35% 6.39% 10.43% 3.34% orig.m original orig.s Plan_FullPssngr_Time opt.m optimal opt.s 8.57% 2.62% 0.10% 7.41% 70.28% 3.53% 1.37% 6.13% KnockOn(s) KnockOn(m) Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) improvement:5.14% 9.03% 2.76% 0.16% 4.22% 74.08% 2.04% 0.49% 7.21% orig.m original orig.s Exp_FullPssngr_Lin_Time opt.m optimal opt.s 8.62% 70.73% 3.14% 1.39% 5.75% 2.64% 0.22% 7.51% KnockOn(s) KnockOn(m) Sink(s) Sink(m) Transfer(s) Transfer(m) Source(s) Source(m) improvement:3.16% 8.90% 73.04% 2.68% 0.56% 7.30% 2.73% 0.44% 4.35% orig.m original orig.s Exp_FullPssngr_Curved_Time opt.m optimal opt.s Results in all Time Domains e+00 2e+07 4e+07 6e+07 8e+07 0e+00 2e+07 4e+07 6e+07 8e e+00 2e+07 4e+07 6e+07 8e+07 0e+00 2e+07 4e+07 6e+07 8e e+00 2e+07 4e+07 6e+07 8e+07 0e+00 2e+07 4e+07 6e+07 8e+07 Figure 6: Reduction by 3.16% of total exp. passenger time from Orig. to Opt.

20 Questions / Next Steps Goverde, R., Hansen, I., Performance indicators for railway timetables. Proceedings of IEEE International Conference on Intelligent Rail Transportation: ICIRT2013, August 30-September 1, 2013, Beijing, China., Sels, P., Cattrysse, D., Vansteenwegen, P., Jul. 2015a. Practical Macroscopic Evaluation and Comparison of Railway Timetables. Proceedings of the 18th Euro Working Group on transportation (EWGT2015), July 2015, Delft, The Netherlands. URL Sels, P., Dewilde, T., Cattrysse, D., Vansteenwegen, P., 2015b. Reducing the Passenger Travel Time in Practice by the Automated Construction of a Robust Railway Timetable. submitted to Transportation Research Part B URL Sels, P., Dewilde, T., Cattrysse, D., Vansteenwegen, P., Jul. 2015c. Towards a Better Train Timetable for Denmark, Reducing Total Expected Passenger Time. Proceedings of the 13th Conference on Advanced Systems in Public Transport (CASPT2015), July 2015, Rotterdam, The Netherlands. URL