Bull, Simon Henry

Burggraeve, Sofie

Lusby, Richard Martin

Vansteenwegen, Pieter

In this paper we study the impact of the `turn conditions' in end stations on the performance of a line plan. If trains have to turn on their platform in an end station, the yoccupy the platform for several minutes. A more preferred option, from a timetabling point of view, would be that a train disappears from the platform in its end station after dwelling and only appears again when departing for a subsequent trip. In this case, the train will not interfere with other trains that dwell on the platform during the time between these events. However, this option is only possible if the train can stay in a exible and large enough shunt. Starting from a given line plan, we compare two timetables, one where trains have to turn on their platform and one where trains can turn in a shunt. We evaluate the impact on the performance of the line plan by its feasibility for timetabling,the minimum overall buffer time between trains, the sum of the buffer times and the buffer times in individual stations. A case study on the DSB S-tog in Copenhagen (Denmark) is performed

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Downloaded from orbit.dtu.dk on: Nov 08, 2017Train turn restrictions and line plan performanceBurggraeve, Sofie ; Bull, Simon Henry; Lusby, Richard Martin ; Vansteenwegen, PieterPublication date:2016Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Burggraeve, S., Bull, S. H., Lusby, R. M., & Vansteenwegen, P. (2016). Train turn restrictions and line planperformance. Paper presented at 9th Triennial Symposium on Transportation Analysis , Oranjestad, Aruba.Train turn restrictions and line plan performanceSofie BurggraeveKU Leuven Mobility Research Centre - CIB, KU Leuven, BelgiumSimon BullDTU Management Engineering, Technical University of Denmark, DenmarkRichard M. LusbyDTU Management Engineering, Technical University of Denmark, DenmarkPieter VansteenwegenKU Leuven Mobility Research Centre - CIB, KU Leuven, BelgiumEmail: sofie.burggraeve@kuleuven.be1 IntroductionIn this paper we study the impact of the ‘turn conditions’ in end stations on the perfor-mance of a line plan. If trains have to turn on their platform in an end station, theyoccupy the platform for several minutes. A more preferred option, from a timetablingpoint of view, would be that a train disappears from the platform in its end station afterdwelling and only appears again when departing for a subsequent trip. In this case, thetrain will not interfere with other trains that dwell on the platform during the time be-tween these events. However, this option is only possible if the train can stay in a flexibleand large enough shunt. Starting from a given line plan, we compare two timetables, onewhere trains have to turn on their platform and one where trains can turn in a shunt. Weevaluate the impact on the performance of the line plan by its feasibility for timetabling,the minimum overall buffer time between trains, the sum of the buffer times and the buffertimes in individual stations. A case study on the DSB S-tog in Copenhagen (Denmark) isperformed.2 State of the artRailway network characteristics affect the performance of a railway service, for example,the use of tracks or junctions by trains in opposite directions, the number of platforms inthe stations, the existence of alternative routes, the layout of the shunt in end stations,etc. In (Mar´ın et al., 2009), an iterative approach is presented to integrate robust network1design and line planning. They focus on the construction of connection links that offer analternative in case of link failure. However, we focus on the design of the terminal stations.Line plan characteristics also influence the performance of a railway system, for ex-ample, the number of lines that use the same infrastructure, the frequency of a line andthe combination of frequencies, the trip lengths (catching up due to skipping stations),etc. Goerigk et al. (2013) analyse different line planning models by comparing typicalcharacteristics of line plans, but also by comparing their impact on timetables and theirrobustness against delays. Therefore, they calculate a timetable for each line plan. In thispaper, we also calculate timetables in order to evaluate line plans, but we focus on theimpact of an infrastructure change and we don’t compare line plans mutually.3 MethodologyWe create a set of diverse line plans. For each of these line plans we test if it is possibleto generate a feasible timetable with and without turning on the platform. The majorityof the initial line plans are not timetable feasible with turning on the platform. Then, weupdate the line planning model by including information on why timetables are infeasible.If the line plan is timetable feasible with and without turning on the platform, we findoptimal (or near optimal) solutions to both timetable problems. We then compare theperformance of both.3.1 Line planningRailway line planning is a long term planning problem which consists of the determinationof the routes, stopping patterns, and hourly frequencies that should be operated in therailway network. We use a mixed integer linear program (MILP) to create line plans.Passengers are simultaneously routed, each picking a route with best estimated traveltime, waiting time (estimated from headway times) and additional transfer penalties,but subject to capacity constraints. Operator line cost is estimated based on the rollingstock unit requirements and running times for the plan. A feasible line plan satisfiesoperational requirements and contractual service levels, satisfies conditions for feasibletimetabling (though no all-embracing set of conditions is known), and provides capacity forall expected passengers. Line plans are either found by minimizing total passenger traveltime or running cost, with a constraint on the other, or a weighted sum of each. We reportaverage passenger travel time, which is similar across line plans as the majority of passengerdemand is between stations that are well-served by all “reasonable” line plans but thedifferences are important as they are large differences for a minority of passengers. To findtimetable feasible plans, additional constraints are introduced and tightened iteratively;these constraints are concerned with the shared use of end stations. Additionally, specificline combinations meeting certain unfavourable conditions for timetabling, e.g. one linethat would certainly catch up with another one due to different trip lengths, are forbiddenfrom appearing together.3.2 Timetable modelRailway timetabling is a mid-long term planning problem, which consists of the determi-nation of train arrival and departure times in stations. We use a MILP to build a cyclictimetable with a period of one hour starting from a line plan. The trains of a line areequally spread over the period. The goal function of this timetable model maximizes theminimal buffer time between every two trains. Reserve and release times of station areasare taken into account in the calculation of the buffer times between the trains. There isonly one type of constraint that is necessary to allow for feasible turnarounds in the endstations of the lines. A train reserves the platform in its end station until the next trainin the opposite direction departs from that platform (because that is the same physicaltrain). This constraint is necessary to connect the schedule of trains in opposite directions,but it shortens the buffer time between trains of the same line in the same direction.4 Case studyThe DSB S-tog is a high frequency railway service that transports 30 000 to 40 000 pas-sengers per hour at peak times between 84 stations. An illustration can be found onhttp://www.dsb.dk/Global/STog/S%20kort%20udk%202015%233%20(3).pdf. This net-work has seven terminal stations with two platforms and eight intermediate stations inwhich one platform is constructed as a terminal. Each train turns on the platform inits end station and thus occupies this platform for several minutes. A train’s occupationtime of this platform is bounded below by the minimum time needed to turn and boundedabove by the time until the arrival of the next train. The DSB S-tog network is designedso that trains crossing in opposite directions, with a few exceptions, only affect each otherin an end station. We assume that trains occupy every station area on their trip for 60seconds. Trains of the same line are equally spread over the period of one hour.The results of the case study can be found in Table 1. The first line plan was previouslyused by DSB S-tog. The second line plan is designed to be better for the passengers thanline plan 1, the third line plan to have a better operator cost than line plan 1 and thefourth line plan to outperform on both characteristics. The upper part of the table showssome general information on the line plans. The passenger and operator cost are estimatedby the line plan model. The number of interactions are the number of train pairs thatshare a platform in at least one station. In the lower part, we report four indicators on thespreading of the trains in time. All the timetables are constructed with a calculation timeLine plan 1 2 3 4# lines 9 8 8 7# interactions 1434 1362 1434 1434passenger cost 1172 1158 1198 1171line cost 679 829 653 665Turn restrictions DSB yes no yes no yes no yes noMin buf time (min) -1 1 0,178 0,667 0,250 0,5 0 0,250 0,355 0,667(upper bound) (0,667) (0,667) (0,583) (1) (0,250) (0,250) (0,467) (0,667)#stations with min buf time 1 12 52 34 29 24 10 19 19#stations with buf time ≥ 2 64 53 30 21 31 43 46 50 47∑buf times (min) 18 450 18 969,6 20 196 17 985,2 19 086 19 085,8 20 166 19 180,9 20 308(upper bound) (21 066) (21 786) (19 602) (20 298) (20 580) (21 306) (20 214) (20 946)Table 1: The minimal buffer times improve if the infrastructure allows to turn in a shunt.limit of 5400 seconds. We see that the minimal overall buffer time (Min buf time) and thesum of the minimal buffer times (∑buf times) improve if turning on the platform is notrequired. The values of the number of stations with a buffer time bigger than two minutesor equal to the minimum buffer time (which itself increased) show no clear trend, butthey show that the turn restrictions affect the buffer times in the whole network. Optimalvalues give railway companies the information on how much the performance could beincreased if flexible large enough shunts would be built in end stations.5 Conclusion and future researchWe analysed the effect of train turn restrictions on railway service performance. Weconclude that for different kinds of line plans, the probability of propagation of delayscan significantly be improved if the terminal stations have an appropriate shunt so trainsdon’t need to turn on (and occupy) their platform. Moreover, with our approach we cancalculate the magnitude of this performance improvement. Furthermore, we found thatinformation on trip lengths and frequency combinations in end stations is useful for findingline plans that are feasible for timetabling with train turn restrictions. Future researchconsists of further integration of line planning and robust timetabling.ReferencesM. Goerigk, M. Schachtebeck, and A. Scho¨bel. Evaluating line concepts using travel timesand robustness. Public Transportation, 5:267 – 284, 2013.A´. Mar´ın, J.A. Mesa and F. Perea. Integrating Robust Railway Network Design and LinePlanning under Failures. In R. K. Ahuja, R.H. Mo¨hring, C.D. Zaroliagis, Robust andOnline Large-Scale Optimization, volume 5868 of Lecture Notes in Computer Science,pages 273–292, Springer-Verlag Berlin Heidelberg, 2009.1One station has overlapping occupation times. This allows for bigger buffer times in other stations.

Train turn restrictions and line plan performance

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Train turn restrictions and line plan performance

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