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«Spatial, Temporal and Size Distribution of Freight Train Delays: Evidence from Sweden Niclas A. Krüger* a,b,c Inge Vierth a,b Farzad Fakhraei ...»

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Spatial, Temporal and Size Distribution of Freight Train

Delays: Evidence from Sweden

Niclas A. Krüger* a,b,c

Inge Vierth a,b

Farzad Fakhraei Roudsari b,c


Centre of Transport Studies, Stockholm


Swedish National Road and Transport Research Institute


TRENoP, KTH Royal Institute of Technology, Sweden

*Corresponding author:

Phone: +46 70 33 54 599

E-mail: niclas.kruger@vti.se

Abstract: This paper analyzes how freight train delays are distributed with respect to size,

location and time of their occurrence. Arrival delays are analyzed in detail using data covering all freight train departures and arrivals during 2008 and 2009 in Sweden. Moreover, the link between capacity usage and expected delay is analyzed using the fact that demand fluctuates on different time scales, especially due to the economic chock in 2009. Since the distribution of delays on different scales describe reliability and vulnerability in the rail transport system, the results have potentially important policy implications for rail investment appraisal.

Keywords: Fat-tails; Freight; Delays; Rail; Reliability; Vulnerability 1 Introduction Trains that are either delayed, early or cancelled constitute a problem for companies that transport goods by rail. Lack of reliability in the rail transport system means that rail transports have a disadvantage, all things equal, compared to the other modes. Generally reliability is defined as deviation of the transport time compared to the scheduled transport time. To date there is only limited quantitative information in Sweden about freight trains not arriving on time, with major consequences, since without information it is not possible to target appropriately the problem of unreliability. To some extent the lack of reliability is taken into account by planners by building in slack in the scheduled arrival times. However, too much slack will eventually lead to many train arrivals being early, which is also a problem for scheduling the unloading and for the additional storage space and labor required. Cancelled trains (that are often not included in delay statistics) can be seen as very long delays that can cause high costs for firms sending and receiving goods.

Except from extreme situations like very strong winters or large scale accidents, there is also limited knowledge about the reasons for the trains not being on time and the consequences for the rail transport operators and the companies sending and receiving goods. There is moreover limited knowledge about how the capacity utilization, track maintenance and investments in infrastructure influence the probabilities and size of delays. Many networks, because of interdependence in the links, have shown to be vulnerable to extreme events, that is, infrequent but large negative impacts on the functioning of the networks, which makes it hard to identify single causes and remedies to the problem.

This means that benefits of improved reliability, that is, costs saved due to reduced variability in transportation time resulting from investments in rail infrastructure, are not taken into account in a proper way in cost-benefit analysis carried out in Sweden and elsewhere. The benefits of reduced variability in freight transport are not calculated at all or calculated in a very simplified way. A more accurate calculation of the benefits, that is, estimating the value of transportation time variability (short VTTV) requires several steps: a) identification and description of deviations from scheduled times, b) finding appropriate ways to measure benefits from reduction of deviation size, probability and variability, and c) monetary valuation of the benefits.

The Swedish Transport Administration (Trafikverket) has developed a monitoring system covering all trains in the Swedish national rail system. The database includes information about deviations (actual time compared to scheduled time) of both freight trains and passenger trains at a detailed rail segment level. To date information for 2008 − characterized by an economic boom and 2009 − characterized by a recession due to the financial crisis in late 2008 − is available.

This paper studies the distribution of freight trains arriving late at final stations. Trains that depart too late, arrive too early or are cancelled are not analyzed in detail. We investigate reliability − or lack thereof − of rail transportation using a descriptive approach, which is, as we argue above, a prerequisite for valuation of reduced transport time variability in cost-benefit analysis and hence for appraisal of infrastructure investments.

This paper is structured as follows: Previous research is summarized in section 2 and the data obtained from the Swedish Transport Administration is described in section 3. Section 4 analyzes the data. In section 5 we analyze the implications for the estimation of the value of transportation time variability (VTTV) and discuss general policy implications. Section 6 concludes the paper.

2 Previous research The paper addresses several topics that have been studied in detail by previous papers. In order to keep the section tractable, we divide the literature in different topics.

Distribution of delays: The distribution of delays in rail networks is dependent on train routes and types of train, which may vary over time. Delay distributions can be used as an input for analyzing the robustness of timetables and reliability. However, finding a distribution which can generally be used is difficult. Schwanhäuβer (1994) concludes that the tail of arrival delays follows an exponential distribution. This result is confirmed by Goverde et al (2001), Yuan et al (2002), Goverde (2005) and Haris (2006). The exponential distribution for arrival delays is therefore widely used as input for delay propagation models. More flexible distributions are sometimes used to capture the distribution of late arrival and departure times. For example, the Weibull distribution, the gamma distribution and the lognormal distributions have been adopted (Higgins & Kozan, 1998; Bruinsma et al, 1999; Yuan, 2006). Yuan (2006) compares the goodness-of-fit among several distribution models selected for train event times and process times, by fine-tuning the distribution parameters for data recorded at The Hague railway station.

The Weibull distribution is found to be the best fitting distribution model for arrival delays, departure delays and the free dwell times of trains. The model can be used to determine the number of trains that can be accommodating in the network for a given accepted level of knockon delays. Güttler (2006) fits a normal-lognormal mixed distribution to assess running times of trains between two stations using the data for the German railway. Briggs and Beck (2007) find in a study on the British railway network that the distribution of train delays can be described by socalled q-exponential functions (closely related to the exponential distribution).

Primary and secondary delays: Delays can be classified in primary and secondary (knockon) delays. Lindfeldt (2008) studies the distribution of primary delays for passenger and freight trains on the heavily used route between Stockholm and Gothenburg in Sweden and finds that the primary delays are widely spread along the route. A further result is that a reduction of delays of high speed trains would not affect the overall delays in the network significantly, simply because high speed trains make up a small share of total rail transportation. According to Yuan (2006), the propagation of train delays mainly occur during the arrival or departure of trains at stations, since the crossing or merging of tracks are in most cases bottlenecks in highly used rail networks. For passenger trains, the bottlenecks of a rail network are generally situated at stations (Carey & Carville, 2000). An extensive amount of literature addresses sources, impact and nature of secondary delays. Schwanhäußer (1974) calculates an equation for additional delays as a function of buffer time, initial delays, mix of priority classes, headways and overtaking possibilities. The exponential distribution of arrival delays is widely used as input for delay propagation models, including models for propagation of departure delays at stations. Carey and Kwiecinski (1994) estimate the effects of secondary delays between two trains on a single-track due to tight headway by nonlinear regression and heuristic approximations. Higgins and Kozan (1998) present an analytical model that quantifies the expected delay for a passenger train on a track section in an urban area. The authors assume that delayed trains follow with minimum headway speed when a conflict occurs, although in the real world delayed trains need to stop in front of red signals due to occupied route sections or platform tracks ahead. Yuan and Hansen (2007) improve the model developed by Higgins and Kozan by estimating knock-on delays of trains due to speed deceleration and acceleration and the use of track capacity. The model reflects speed fluctuations caused by signals, dependencies of dwell times at stations and stochastic interdependencies due to train movements.

Capacity utilization: The first model that addresses capacity in connection with assessment of delays was developed by Frank (1966). Frank (1966) studies delays on single tracks with both unidirectional and bidirectional traffic. The assumption is that only one train can occupy single-track lines between sidings and by restricting train speeds and travel time to be deterministic, the total number of trains that can travel in the network is estimated. Petersen (1974) improves the model by taking into account two different train speeds and by specifying delays as a function of single and partial double track lines. Petersen (1974) assumes that the departure time is independently and uniformly distributed for a defined period of time and that sidings have equal space and that there is a constant delay for every encounter between two trains. These assumptions are applied to construct a simple expression that shows the number of conflicts that a specific train will meet before arriving at the final station. Chen and Harker (1990) improve the model in Petersen (1974) by relaxing the assumption that trains are uniformly distributed. This makes it possible to provide single track delay functions for different train types with given train schedules and distributional information concerning operational uncertainties.

Moreover, the model can estimate the delays for a given traffic flow using a stochastic approach.

In order to determine the delay probability for a single conflict, the dispatcher’s behavior is modeled, using a district choice model. The model can estimate the mean and variance of a train delay on a single track, which can be used to measure reliability of given schedules. They show that the mean delay and the variance have a direct relationship with inter-station distances (a shorter distance leads to lower means and variance). Harker and Hong (1990) include doubletrack lines and dynamic priorities, that is, train priorities dependent on expected delays. The capacity utilization in the Swedish network is studied by Törnquist (2006), Nyström (2008) and Lindfeldt (2010).

Causes for delays: Nyström (2006) investigates the identification and categorization of causes of delay of a single-commodity train. Delays are categorized into short and long delays and the main finding is that many large delays are caused by failures due to infrastructure items such as turnouts and/or by adverse weather and that many short delays are caused by minor locomotive problems or low contact wire voltage due to many nearby trains. Nyström (2007) analyzes also how different employees at the Swedish Rail Administration assign codes to pictures that describe different delay situations. The finding is that are quite large differences in how same types of delays are reported by different persons and hence, that there is a low level of consistency.

Infrastructure and delays: With respect to rail infrastructure, a range of analytical models focus on the operation of single or double tracks, capacity problems, delay propagation and rescheduling on isolated lines or entire networks (Lindfeldt, 2010). Greenberg et al (1988) develops queuing models to estimate dispatching delays for a low speed, single track rail network with widely spaced passing locations. It is assumed that train arrivals follow a Poisson distribution and that trains follow each other with minimal headway. Using these assumptions they calculate the expected delays for single track segments.

Simulation methods for delay estimation: Murali et al (2010) develop a simulationbased technique to generate delay estimates as a function of traffic conditions and network topology. Their model is tested using delay data in the Los Angeles sub-network and the data can be used to measure expected delays on each train route. A given train can be scheduled on a route that has minimum expected delay. The dispatchers can schedule train routes using their delay estimation procedure in order to minimize the delay propagation. Marinov and Viegas (2011) develop a mesoscopic simulation modeling method for analyzing freight train operations.

To capture the global impact of the freight train operations, the rail network is separated into lines, yards, stations, terminals and junctions. Interconnected queuing systems interact and influence each component. Marinov and Viegas study the network with freight train movements characterized by both insignificant deviations and significant deviations from schedules. Corman et al (2011) studies the problem of coordinating several dispatchers to find the optimal solution in case of disturbances. The objective is to minimize delay propagation; in order to do so the problem is formulated as a bi-level program. Constraints are imposed on the border of each dispatch area. Dispatchers have to schedule the trains within their area by producing a locally feasible solution compliant with the border constraints. The coordination problem can also be solved by branch and bound procedures. The coordination algorithm has been tested on a large rail network in the Netherlands with busy traffic conditions, yielding a proven optimal solution for various network decisions. In simulation software like RailSys (Radtke, 2005), several processes related to delays can be modeled at a high level of detail: primary delays, conflicts (knock-on delays), catch-up effects etc.

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