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The first uses real data from the Swedish rail network, train operation and delays to analyse how different factors influence available capacity and train ...
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Stockholm 2015
KTH Royal Institute of Technology TRITA-TSC-PHD 15-002 School of Architecture and the Built Environment ISBN 978-91-87353-65-9 Department of Transport Science
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Acknowledgements
Trafikverket (Swedish Transport Administration) provided funding for this research.
I would like to thank my supervisors Bo-Lennart Nelldal, Lars-Göran Mattsson and Markus Bohlin for their support and advice. Thanks also to Magnus Wahlborg, a member of the reference group and contact person at Trafikverket responsible for the research program financing this thesis. Thanks to Magdalena Grimm and Pär Johansson at Trafikverket, members of the reference group, and the “railway simulation team” at Trafikverket: Per Köhler, Magnus Backman, Johan Mattisson. Thanks to Anders Peterson and Mats Berg for valuable comments regarding the thesis. Thanks to Hans Sipilä, my roommate during all these years, for the endless discussions about work and everything. It is possible that without you, I would have finished my PhD faster, but more probably not at all. Thanks to Jennifer Warg, Behzad Kordnejad, Jiali Fu, Oskar Fröidh, Anders Lindahl, Hans E Boysen, Josef Andersson and Fredrik Hagelin for all the stimulating discussions and their valuable inputs. Thanks to all colleagues and fellow PhD students at Department of Transport Science for making work fun. Special thanks to Olov Lindfeldt and Leif Broberg for introducing me to the field of railway capacity.
To my family: mother, father, brothers, uncles, aunt and friends, without you it would not have been possible. Min kone Nadire, köp rachmet jinim! Maen sinni jikk soymaen xikirim apigim!
Stockholm, August 2015
Anders Lindfeldt
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List of Publications
I. Lindfeldt, A., 2010. A study of the performance and utilization of the Swedish railway network. Published in: Proceedings of the First International Conference on Road and Rail Infrastructure, Opatija, Croatia.
II. Lindfeldt, A., 2011. Investigating the impact of timetable properties on delay propagation on a double-track line using extensive simulation. Published in: Proceedings of Railway Engineering, 11th International Conference, London, UK.
III. Lindfeldt, A., Sipilä, H., 2014. Simulation of freight train operations with departures ahead of schedule. Published in: Proceedings of the 14th International Conference on Railway Engineering Design and Optimisation. (CompRail XIV), Rome, Italy.
IV. Lindfeldt, A., 2013. Heterogeneity Measures and Secondary Delays on a Simulated Double-Track. Published in: Proceedings of the 5th International Seminar on Railway Operations Modelling and Analysis (RailCopenhagen2013), Copenhagen, Denmark.
V. Lindfeldt, A., 2015. Validation of a simulation model for capacity evaluation of double-track railway lines. Published in: Proceedings of the 6th International Seminar on Railway Operations Modelling and Analysis (RailTokyo2015), Tokyo, Japan.
VI. Lindfeldt, A., 2015. Scheduled waiting time and delay in capacity evaluation of double-track railway lines. Submitted to Journal of Rail Transport Planning & Management
Nelldal, B-L., Lindfeldt, A., Lindfeldt, O., 2009. Kapacitetsanalys av järnvägsnätet i Sverige, delrapport 1. Capacity analysis of the Swedish rail network, part 1. In Swedish.
Lindfeldt, A., 2009. Kapacitetsanalys av järnvägsnätet i Sverige, delrapport 2. Capacity analysis of the Swedish rail network, part 2. In Swedish.
Lindfeldt, A., 2014. Kapacitetsutnyttjande i det svenska järnvägsnätet. Uppdatering och analys av utvecklingen 2008-2012. Capacity utilisation of the Swedish rail network. Update and analysis of the development 2008-2012.
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1 Introduction
Railway is an attractive mode of transportation with a wide range of applications. It is used to provide high capacity local transportation of passengers in large cities, haul large quantities of ore from inland located mines to seaside ports and to connect cities by comfortable high- speed services offering short travel times from city centre to city centre, just to mention a few. It is energy efficient and it can be powered by renewable energy sources, hence its attractiveness is bound to increase further as awareness increase of the issues associated with air pollution and climate change.
The demand for railway transportation is steadily increasing around the world (UNECE, 2014). The increase in demand generates increase in traffic load. Many railway lines are already used close to their maximum capacity and in order to meet the new demand, actions need to be taken. Such actions include building new railway infrastructure, upgrade existing infrastructure or use existing infrastructure more efficiently. Constructing new railway infrastructure is expensive, and it is therefore of importance that the right actions are taken at the right time. This in turn requires an understanding about how the railway system works and responds to increased capacity utilisation.
Analysing and describing railway capacity is a multifaceted task. It involves several complex systems, e.g. railway infrastructure, rolling stock, timetable and human behaviour. Some of the factors influencing capacity are: number of tracks connecting the stations, station track layout, signalling system, train performance, speed difference between train services, market demand, reliability and delay acceptance of railway customers. Because if its complexity, railway capacity can be defined in many different ways. Barter (2008), quoting (Nock, 1980), gives a good general definition of railway capacity that includes the most important aspects:
The number of trains that can be incorporated into a timetable that is conflict free, commercially attractive, compliant with regulatory requirements, and can be operated in the face of anticipated levels of primary delays whilst meeting agreed performance targets.
Figure 1.1: Capacity balance (UIC, 2004).
There is no simple way to tell what the capacity of a railway infrastructure is because it depends to such a high degree on how it is used (UIC, 2004). Figure 1.1 shows that capacity is a balance between number of trains, average speed, stability and heterogeneity. Capacity is the length of the chord connecting the four axes. It shows that railway capacity is a trade-off between quantity and quality, i.e. between number of trains that are operated and how much delays they will experience. Increased traffic load leads to higher sensitivity to delays with
Average speed
Heterogeneity
Stability
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MixedMetro‐‐traintrain workingworking
The capacity of a railway can be defined in many ways. In this thesis capacity is referred to as the number of trains/h that can be operated on a railway line. Consequently it does not include parameters like for example train size or limitations in availability of the infrastructure due to maintenance. Also when referring to capacity, it is neither that of specific stations or short line sections, nor that of a large scale network, but rather that of a longer railway line.
Effects of capacity utilisation are in this work limited to primarily SWT and delays rather than economic evaluations. However, many of the results presented in this thesis can serve as input to economic evaluations.
The analysis performed in this thesis addresses railway traffic during normal operation. With normal operation in this case means operation without too large delays. Sources of large delays, disruptions, can e.g. be complete stops caused by vehicle or catenary failure on a line section. In situations like these trains are cancelled and redirected to use other routes in the railway network and the timetable is no longer relevant. Consequently, it requires other methods of analysis than is employed in this thesis (Cacchiani et al. 2014).
Many of the studies presented in the thesis are based on Swedish conditions. This includes for example infrastructure design, timetable construction guidelines, train vehicle models and primary delay levels. However, the developed methods and many of the major conclusions are general.
Primary delays are modelled as independent in the simulations performed in this thesis. This is a simplification of reality. Examples of common events that generate delays that are not independent are trains operating at reduced traction power, temporary speed restrictions or headway dependent dwell times. These kinds of delays are not separated from delays of more random nature when delay distributions used in the simulation studies are compiled from data from real operation.
The most important factor for capacity is the number of tracks on the line. The most common configurations are single- , double- , and quadruple tracks. In general the capacity of a double- track is four times that of a single track, and a quadruple track three times that of a double- track given a fairly heterogeneous traffic. Going from single track to double-track means that trains can meet everywhere on the line without being restricted to do this only at crossing stations. Besides increasing the capacity, traffic in different direction becomes almost independent, i.e. less risk of delay transfer. On quadruple tracks, trains going in the same direction can preferably be separated according to mean speed, and is the reason why the potential capacity of a quadruple track is more than two double-tracks.
Signalling combined with track layout can be crucial to capacity. For a conventional signalling system with fixed block sections, the length of the block sections on the line is of importance for the minimum headway between two consecutive trains in the same direction. A block section is a section of track that can only be occupied by one train at a time. Shorter block sections give shorter minimum headway times, figure 1.2, and given a limited number of block sections on a line section, they should be designed so that they have as equal occupancy time as possible. This implies that the block sections should be shorter where trains are moving slower, e.g. around and at stopping locations. For single track lines, short inter-station distances and simultaneous entry capability to decreases crossing time are crucial. Minimum headway is the shortest time interval between two successive trains that is possible to have without the second being interfered by the first.
In this work, station is used for points in the network where overtaking, crossing or direction reversal is possible. Line sections are the sections of track between the stations. Distance between crossing/siding stations affects capacity in a similar way as the speed of the trains. Shorter distances mean that crossings and overtakings can be performed more often and more trains can be scheduled. For a given traffic density, more frequent siding/crossing possibilities also decreases need for scheduled delay.
Train operation can be either structured or unstructured. If the structured operation , trains are operated according to a planned timetable. In unstructured operation no timetable exists and train can depart whenever ready without consideration of the pre-planned timetable. Most passenger services are operated according to a timetable while it is more common with unstructured operation of freight trains, especially in the United States.
Figure 1.2: Example of minimum technical headway on a double-track section equipped with Swedish ATC2 with infill (Lindfeldt 2008).
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Passenger train, 3 km block sections Passenger train, 1.5 km block sections Passenger train, 0.75 km block sections Passenger train, 0.25 km block sections Freight train, 3 km block sections Freight train, 1.5 km block sections Freight train, 0.75 km block sections Freight train, 0.25 km block sections
Figure 1.3: Left, observations of arrival and departure lateness at scheduled stops for some Swedish stations. Period of measurement: September-October 2008 (Lindfeldt, 2009).
Allowance is extra time in the timetable that is added to the scheduled time of the trains. It can both be used to extend the running time between stations, running time allowance, or to make longer stops, allowance at stations. In both cases, the allowance can be used by the train to recover from suffered delays. The allowance may increase stability, but longer scheduled running times are negative from a market perspective. It is common to apply allowances before large junctions in the network to compensate for interference with other train movements (including shunting) and before the last station to improve the punctuality at the terminus.
Buffer time is the time between trains in the timetable. Larger buffer times reduce the probability of delay transfer between trains but also decrease the capacity. The amount of buffer time needed between trains depends on signalling system, infrastructure layout and expected severity of the delays. Often, minimum values for buffer times in different situations are used in the timetable construction, e.g. at crossings and overtakings.
On a general level, delays can be categorized into two different groups: primary delays and secondary delays. Primary delays can be delays caused by faults in technical systems, human behaviour or other external factors such as severe weather conditions. Examples of sources of primary delays are faults on switches, signalling and rolling stock or stops taking longer time than planned. Primary delays can be influenced by choice of technology, education of personnel, weather conditions, wear and maintenance of infrastructure and rolling stock.
A secondary delay occurs when the source of the delay is another train. The most common reason for this delay transfer is that several trains need the same resource at the same time and thus one train has to wait. Such resources can e.g. be signal block sections, switches or platform tracks at stations. A source for secondary delay that is not due to lack of resources is when a connecting train gets delayed because it awaits the late arrival of another train.
When an isolated part of a bigger train network is analysed, two additional types of delays need to be defined: entry delay and exit delay. That means the delay the trains have when it enters and leaves the analysed system.
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2 Related research
There are several different methods of analysing railway operation. Different methods can be divided into analytical, combinatorial and simulation based, Mattsson (2007). All approaches have their advantages and disadvantages. Typically, the advantages of analytical and combinatorial methods are that they do not necessarily require detailed information about for example the timetable. This makes them suitable to long-term planning where a timetable may not exist and general results are needed. Among the disadvantages are that perturbations often are modelled in a simplified manner, if at all, and that the effects of dispatching are not considered. Simulation on the other hand can model the perturbations in detail, but is in general time consuming and requires detailed knowledge about timetable and infrastructure. In general, methods based on less detailed models may be better for drawing general conclusions. On the other hand, more detailed models are required to perform more thorough studies, but they do also require more data as input and risk generating results that are only valid for a specific setup.
Harrod (2012) gives an overview of optimisation based model structures used for railway scheduling. He classifies models according to if the track structure is modelled explicitly and if the timetable is periodic or not. Four different fundamental model structures are discussed: Mixed integer sequencing linear problems (MISLP), Binary integer occupancy programs (BIOP), Hypergraph formulation and Periodic event scheduling. The fundamental properties of each model are described together with their advantages and disadvantages.
De Fabris et al. (2014) develop a heuristic for timetable generation in large networks. Infrastructure model is mesoscopic, which makes it possible to calculate timetables fast at the same time as it is possible to consider e.g. restrictions incurred by signal blocking times and train route dependencies in station switch regions. The mesoscopic model can be used to calculate train running times and minimum headway times between trains, which is an advantage compared to macroscopic models where this have to be provided as input. The heuristic can calculate a timetable for the network in north-east Italy in a few minutes. The timetable has such quality that it is accepted by timetable planners.
Goverde and Hansen (2013) give several timetable performance indicators: Infrastructure occupation. Can be obtained by compression of timetables, UIC 406 (2004), and gives infrastructure occupation as a percentage of a time period the infrastructure is occupied by train movements. Timetable feasibility. A feasible timetable should not have any conflicts between trains, i.e. that several trains are scheduled to use the same infrastructure at the same time. Scheduled running times and dwell times should not be shorter than is possible for trains to perform in reality. Timetable stability is the ability of a timetable to recover from a primary delay without active dispatching. Can be measured as the combination of the size of the primary delay and the corresponding settling time, i.e. how long time it takes before all trains return to their scheduled train paths. Is dependent on timetable allowances and buffer times. Timetable robustness. A robust timetable can handle the variance in process times that often occur in real operation, .e.g. due to different driver behaviour and passenger volumes and weather. Both primary delays and secondary delays are minimized in a robust timetable. Is dependent on timetable allowances and buffer times.
heterogeneity and allocation of running time allowance. However, primary delays are modelled in a simplified manner as only one primary delay is inserted at a time. The methods are good to establish how fast a timetable can recover from a disruption, which is indeed one definition of robustness, but is not designed to analyse real life operation with multiple disturbances.
Deadlocks occur in situations when several trains are blocking each other so that train movements cannot continue. Problems with deadlocks are present in synchronous simulation of train operation, while it is not a problem in asynchronous simulation and situations of rescheduling (Pachl 2007). He further illustrates the problem of deadlocks and he gives two different approaches for avoiding deadlocks that can be implemented in simulation software: Movement Consequence Analysis and Dynamic Route Avoidance. Deadlocks are dependent of infrastructure layout and occur on track sections with bidirectional traffic, e.g. single track railway lines. It is emphasized that it is a necessity that proposed methods for deadlock avoidance must not be complicated and computational intense in order to avoid long simulation times. It is a process that has to be continuously ongoing in the simulation since trains might be disturbed by primary delays at any moment. Hence, methods applied for rescheduling is not applicable.
Andersson et al. (2015) use a MILP model to increase the robustness of an existing timetable. The model is an extended version of the one presented in Törnquist and Persson (2007). The robustness of the timetable is calculated by identifying critical points, RCP (Andersson et al. 2013), where the risk for train interaction in case of disturbances is high. Critical points occur in locations where train systems enter the line and overtakings are scheduled. They are calculated pairwise between two trains and are composed of three parts; running time allowance before the critical point, running time allowance after the critical point and headway between the two trains in the critical point. After all critical points have been identified, the model is used to calculate a new timetable by redistributing existing running time allowance and shift trains in the timetable, without changing train order, to increase the robustness in the critical points identified. That the robustness has indeed increased is verified by reusing the optimisation model to simulate a real-time rescheduling where trains are delayed by entry delays. Compared to the original timetable, train delays are smaller in the modified timetables where RCP values have been increased.
In a similar study, Khoshniyat and Peterson (2015) use the same MILP model to study the effect of travel time dependent minimum headways on train delays. The underlying assumption is that trains accumulate delays as they run from origin to destination, which was shown in an empirical study performed by Peterson (2012). An existing timetable is adjusted so that headways increase with distance travelled, where they are more efficiently used to avoid secondary delays. Three different delay scenarios are used, delay of a single train at a random location, speed reduction of a single train (the entire trip) and speed reduction for all trains passing a specific location. It is concluded that delays do indeed decrease when headways are redistributed and increased towards the end of the train runs.
Medossi et al. (2011) introduces stochastic blocking times instead of deterministic times that are normally used in blocking time models. Stochastic blocking times make it easier to determine the probability that two trains will interfere with each other and cause secondary delays. GPS data is used to analyse train run characteristics in detail, including acceleration, cruising, coasting and braking. For each motion phase, separate performance parameters are estimated, including e.g. reduced rate of acceleration, cruising speed, coasting time interval
and braking rates in different situations. The variability in the estimated parameters are used to create the stochastic blocking times, but does also reveal interesting details about driver behaviour. The proposed method can also be used to provide input to and calibrate micro- simulation tools. The stochastic blocking times are estimated for each single train run individually but do not include effects due to secondary delays.
Cerreto (2015) proposes a micro simulation based method for estimation of timetable robustness. Primary delays are applied to a single train in the timetable and the consequences in terms of e.g. settling time and the number of delayed trains is measured. Which train that receives the primary delay is systematically varied and the simulation process repeated. A technique is also presented that reduce the large number of simulations needed.
The differences between and limitations of micro, meso and macroscopic infrastructure models are discussed in Gille et al. (2008) and one of the conclusions is that station areas should preferably be modelled in higher detail than at macroscopic level. Cui and Martin (2011) argues for the benefits of simulation models that can combine all three levels of detail in a flexible way. The balance between accuracy and performance, i.e. computational workload, should be considered when the model is constructed. A microscopic infrastructure can be evaluated according to certain criteria in order to determine the importance of different components. Important components can remain at microscopic level while less important components can be aggregated to be mesoscopic or macroscopic. The lover level of detail of appropriate parts of the infrastructure model makes computation faster without losing accuracy.
Büker and Seybold (2012) describe an analytical model for analysis of delay propagation in railway timetables. Delays are modelled by cumulative distribution functions and train interaction calculated by means of an activity graph. A challenge that is addressed in the paper is to find a suitable class of distribution functions that can be used to model delays realistically and can be used in the analytical calculations. The analytical approach makes the model faster than running simulations. Dispatching decisions is modelled in a simplified manner and higher-order second secondary delays are neglected. However, the effects of the latter are considered to be small in real world scenarios. The methodology is implemented in a software tool. Another analytical method for timetable stability analysis of cyclic timetables using max-plus algebra is presented in Goverde (2007).
Kroon et al. (2008) use stochastic optimisation to improve robustness of an existing timetable by reallocating buffer times and running time allowances with the objective of minimising train delays. It is applied to cyclic timetables, but can be used on non-cyclic as well. However, cyclicity reduces computing time. The method is a two stage recourse model that includes a timetabling part and a simulation part that evaluates the robustness of the timetable. The simulation part of the model does not include dispatching functionality, i.e. it assumes that trains always run in the same order as in the scheduled timetable. Timetables optimised by the model have less delay compared to the original timetable, both in simulation and real world experiments. An example of another model that can create optimal timetables with respect to both train running times and timetable robustness is presented in Fischetti (2009).
