The use of railway simulation as an input to economic assessment of timetables

Journal of Rail Transport Planning & Management xxx (2016) 1e16

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The use of railway simulation as an input to economic assessment of timetables Jennifer Warg*, Markus Bohlin Department of Transport Science, Royal Institute of Technology (KTH), 100 44, Stockholm, Sweden

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 January 2016 Received in revised form 11 August 2016 Accepted 21 August 2016 Available online xxx

Assessment of capacity for highly-used railways is an important and challenging task. This paper describes a method for evaluation of timetables based on capacity and economic assessment. Common methods from both fields are combined. For developing and analysing purposes, the model is first tested with historical delay data for express trains on a double-track line with dense, mixed traffic in Sweden. An assessment aiming to compare the departures is made by combining common weights for different variables. Differences in the results based on the model structure are discussed. In the second step, microscopic simulation is used to reveal delay characteristics of timetable alternatives that are then compared and discussed in a similar way to step 1. The presented method using simulation makes it possible to reveal and evaluate characteristics that are important for both timetable planning and economic analysis, for example evaluation of strategies. Timetable and delay times are important input variables that affect the travellers' choice. Using simulation and other methods from capacity planning gives the opportunity to find characteristics for analysing alternatives and improve economic evaluation, at the same time as the use of economic parameters provides more possibilities to make a relevant capacity analysis. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Capacity evaluation Railway simulation Economic assessment Delays

1. Introduction Service reliability has always been an important topic in railway traffic contexts as low punctuality and long delays make people choose other means of travel or transporting their goods, thus lowering the service demand. Time savings and passenger valuations are a cornerstone in evaluating capacity usage and socio-economic benefits to achieve a cost-efficient and well-functioning system. However, capacity analyses rarely contain economic approaches. On the other hand, capacity characteristics are hardly ever included in economic assessments although they can affect the results significantly and their importance is highlighted in many economic studies and guidelines. Choosing and measuring the right parameters for these assessments can be difficult, especially if changes are to be analysed and input data difficult to estimate. The main purpose of this article is to introduce a method for evaluating different timetable alternatives based on capacity and passenger valuations. Unlike in previous research on economic evaluation of capacity, the method uses microscopic simulation to retrieve input data. Advantages and experiences from both fields are combined. In the paper, characteristics of delays and ways to include these and other measurements for describing capacity will be demonstrated and analysed. For this

* Corresponding author. E-mail address: [email protected] (J. Warg). http://dx.doi.org/10.1016/j.jrtpm.2016.08.001 2210-9706/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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purpose, timetable data, delay statistics and simulation data for the Swedish Western Main Line, an important, highly-used double-track line in Sweden, are used. With the help of commonly used variables and valuation parameters for describing capacity, alternatives are compared and the choice and combination of parameters and variables for the model discussed. The purpose is to develop a method that combines economics and capacity and can easily be applied for timetable and capacity planning but also supports processes where decisions are based on economic evaluation. Focus is on reliability and travel time, but the possibility for extending the model with other variables as for example frequency is prepared. This paper describes a novel method for including capacity parameters in an economic model, thus making it possible to estimate the effect of changes in a timetable. In the first part, statistics are used, while the second part contributes a model application where simulation is used to reveal characteristics that are used for evaluating alternatives. This is a new approach and combines capacity and economics. The article begins with a short description of common practice in capacity analysis, transportation and cost benefit analysis and how they are connected. The introduction closes with a description of capacity measurements and recommendations for valuation. The model is then presented. Different input combinations are tested for statistical and simulated data. Finally, results and model structure as well as the need for further work are discussed. 2. Capacity and transport economics 2.1. Capacity analysis Capacity analysis aims to estimate the maximum number of trains that can use an infrastructure during a time period without exceeding given circumstances (Abril et al., 2008). Variables influencing capacity are divided into infrastructure, traffic and operation. Block and signalling system, single/double track, definition of lines/routes, network effect, track structure/speed limits and lengths of subdivisions are pointed out for the infrastructure. Regarding the traffic parameters, new/existing lines, train mix, regularity of timetables, traffic peaking factor and priority were included. Track interruptions, train stop time, maximum trip time threshold, time window and quality of service/reliability/robustness were chosen as operational characteristics. The goal of a capacity analysis can also be to determine the properties of an infrastructure and timetable as a baseline for reducing delays by using the existing capacity in a better way (Goverde et al., 2013). Often, the relationship between key factors, such as train homogeneity or number of trains on a line, and their impact on delays is analysed (see e.g. Lindfeldt, 2015) and trade-offs between conflicting aims have to be made. Several methods and tools have been developed to improve the way of analysing capacity. Vromans et al. (2006) describe different kinds of analytical and stochastic models and railway simulation. Abril et al. (2008) also mention optimisation and recommend a combination using an analytical method before optimising and finally simulating. Nicholson et al. (2015) describe an evaluation framework for comparison and evaluation of timetables and control methods that includes several important KPIs such as punctuality, the delay at selected stations as well as the recovery time, maximum delay and delay area. Further, Andersson et al. (2013) quantify timetable robustness by considering critical points. An approach for calibration of simulation disturbance parameters can be found in Cui et al. (2016). Pouryousef and Lautala (2015) use a hybrid approach to improve level of service parameters (maximum, total, average and standard deviation of dwell time, and timetable duration). 2.2. Transportation cost and benefit analysis In order to make decisions, cost and benefit analysis is used to evaluate advantages and disadvantages for different alternatives. As for capacity analysis, many different objectives have to be balanced in order to find the most efficient solution. The value of travel time savings (VTTS) is a crucial measurement in transport economics and transport policy. The theory about allocating time based on income initiated by Becker (1965) has been redefined by many authors and also adjusted for use in transport economics. The VTTS is often used in combination with costs in order to evaluate alternatives using the parametric utility function

Utility u ¼ ac þ bt

(1)

where c stands for cost and t for time, while a and b are parameters to be estimated. Assuming the parameters to be constant, a change in travel time or cost would affect the utility. The consumer surplus describing the customers' willingness to pay can be calculated by converting the utility to a monetary value. If we know the parameters, the travellers' monetary value of time (in money/time) can be expressed as

Value of travel time VOTt ¼

b a

(2)

The resulting consumer surplus for existing travellers can be calculated as

Consumer surplus CS ¼ VOTt *Dt

(3)

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Assuming that consumers try to maximise their utility, the alternative with the highest CS would be the preferred one. 2.3. Combining capacity and economics Research in this area mostly focuses on passenger satisfaction conducted by revealed or stated preference. In a study made in the UK, punctuality and reliability were pointed out as the dominating influence factors regarding passengers' satisfaction (Passenger Focus, 2010). Satisfaction decreases already if the train is one minute late and continues to fall by an average of 0.75% per minute. The importance of reliability for travellers was also demonstrated in a recent quantitative study on express trains between Stockholm and Gothenburg (Warg, 2013). The respondents showed an interest in delay data for the specific train before choosing an appropriate departure. Knowing the delay properties can influence the travellers' choice. Several other studies and also common practice in socio-economic evaluation confirm that the use of data describing capacity and its usage is important. However, the use of variables describing capacity in socio-economic analysis is limited. In the German recommendation for future infrastructure investments (Intraplan, 2006), time losses due to delays are for example only included if the investment is expected to improve on-time performance and to have significant impact on the estimation results. If included in cost-benefit analysis (CBA), they are often expressed by assigning a higher value for positive average delay than for undisturbed travel time. This will be discussed in more detail in the following section. The way capacity parameters are CBA can € rjesson and Eliasson (2011) for timetable parameters. Inadequate moreover give misleading results, as demonstrated by Bo input may be a cause of bias. A more detailed approach to include quality in assessments is taken by Frank (2013), who uses a parametric method in rez Herrero (2014) compares the evaluation of scheduled services to combination with analysis of stations and bottlenecks. Pe common practice in road traffic, using explicit formulas for expressing congestion. A major difference is pointed out in that the relationships between number of trains and resulting perturbations cannot be described in an easy way although delays can be observed from reality and the effects of adding more trains can be estimated. The reason given for this is that perturbations are dependent on many other factors, for instance the characteristics of the train, infrastructure or timetable. Investments in additional capacity have to be evaluated by CBA based on expected results as well as demand. However, there is a lack of studies where quality parameters are included in economic models in a way that makes it possible to estimate the effects of changes regarding delays. That is what this paper contributes. 2.4. Common ways of measuring and valuing quality Punctuality as the percentage of trains arriving on time or not more than a certain time late is a common measure of reliability. Five minutes' (or less than six minutes') delay is a common limit for passenger trains' punctuality and is for example used in an international quality study for rail traffic (Finger, 2012) as well as for long-distance trains in Sweden. But there are also other limits, for example 2:59 min for commuter trains in Sweden and 4 min for passenger trains in Norway. For €rnquist Krasemann, 2014). a time, 15:59 was used for long-distance trains in Sweden (To The choice of limit should be based on the passengers' point of view. A study by Passenger Focus for the UK's East Coast (2010) examined how passengers' satisfaction is influenced by the actual delay and how these perceived thresholds map the official ones specified by the regulator. 2e4, 5e6 and 8e10 min' delay were considered break points for the passengers' €, satisfaction with punctuality. In a Swedish questionnaire study performed on express trains between Stockholm and Malmo it was found that travellers underestimate delays (Paulin, 2011). Low delays might be neglected and the lowest breakpoint for passengers' satisfaction is expected to be higher than in the UK. In addition to the limit that defines when a train is on time, methods differ for example according to whether to include cancelled trains, where to measure, and which services to aggregate. In Sweden, punctuality is now presented for important stations with high passenger volume in addition to the services' final station and cancelled trains are included as late trains based on a result of collaboration between the Swedish Transport Administration (Trafikverket) and representatives from the industry that aimed to improve the applied methods (Trafikverket, 2013, 2014b). There might also be variations regarding departure, time of the day, part of the line/country, etc. An example can be found on the Swedish operator SJ's website, where punctuality for arrivals/departures to/from Sweden's three largest cities between 6 and 9 a.m. and 3:30 and 6 p.m. is shown (SJ.se). This means that the choice of how to aggregate data in the model has to be done accurately. While punctuality describes the number of trains arriving less than a certain time late, it is also valuable to know the delay distribution, which for example can be described by average delay of all services, delayed services or services exceeding the punctuality limit. Median and standard deviation are other interesting measures. As stated earlier, average delay is a popular input in transport-economic studies that consider reliability and often expressed by assigning a higher value for positive average delay than for undisturbed travel time. In the German recommendations for CBA (Intraplan, 2006), average delay is weighted 2.7 times travel time, in the Swedish recommendations (Trafikverket, 2016) 3.5. In Denmark, 1e3 is used, in the UK 1e5 (OECD, 2010). 5 is supposed to be used to cover delay variation; the standard parameter is 3. According to Wardman and Batley, 2014, 2 is the standard parameter in Denmark and 3.7 in New South Wales in Australia. In Norway, 2.8 is recommended for short trips (<50 km), 2.1 otherwise. Warg (2013) also Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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found that the relationship between improvements in travel time, punctuality and average delay was 1:0.45:2.4 for express trains between Stockholm and Gothenburg in Sweden. Standard deviation as a measure of how the values differ from the average is often used to assess reliability in public transport with many departures (Paulley et al. 2006). A common measure is the reliability ratio (value of 1 min of standard sz deviation compared to the value of 1 min of travel time) defined by Eijgenraam et al. (2000). According to M atrai and Juha (2012), the focus often lies on road traffic. In Sweden, the recommended value for car mode in CBA is 0.9 (Trafikverket, 2016). For public transport, no value has been defined except in a study focussing on destinations with rare connections (ratio 2.4). In the Netherlands and the UK, 1.4 is used. In Norway, 0.54 is the recommended standard deviation for travel time by longdistance train. For car and bus, the variation in early arrival is also included, but for trains it is assumed to be 0. 1.49 is recommended for the variation in late arrival (TOI, 2010). The USA uses reliability ratios between 0.8 and 1.1 (Wardman and Batley, 2014). In a study of travel time reliability, Beaud et al. (2012) concluded that travellers are willing to pay 34.54 V/h for travel time saving and 21.96 V for a reliable travel time, implying that reducing standard deviation by 1 min was worth 0.64 min' additional travel time. All references consider the relationship of reliability to travel time. However, reference to delay time is also a relevant measure. If both average delay and standard deviation are used in a CBA, 3 and 0.84 are recommended in Denmark and 3 and 0.8 in the UK (OECD, 2010). In a study in Hungary, 2.5 and 1.4 are combined and a recommendation is made to decrease the trai and Juha sz, 2012). national value for delays if both parameters are used in combination (Ma Time supplements, also called scheduled delays, are connected to capacity shortage. They are added to the minimum possible timetable time to cover variations and improve reliability. In the timetable process, supplements are also used to homogenise speeds in order to schedule more services. In analytical or optimising approaches, this extra time is often one of the parameters that the analysis focuses on. Basically, supplements belong to the static timetable parameters as they are part of the given travel time. However, they are an indicator for capacity usage and lead to negative delays if not completely used, which means a train can reach a destination before the scheduled arrival time. This makes it reasonable to handle time supplements separately from travel time. However, it is usually included in travel time. In addition to the discussed measurements, the literature describes further characteristics of reliability that might be potential input to the model developed in this paper. From a passenger's point of view, long delays that occur rarely have a €rjesson and Eliasson, 2011). The importance of major delays is also demongreater effect than smaller, regular delays (Bo €m and Krüger (2013), who state that the worst 10% of all delays account for more than half of the total delay strated by Bergstro in Sweden. They suggest using standard deviation for the 90% of delays with more concentrated spread and including the remaining 10% of long delays in another way. On the other hand, a questionnaire study on express trains between Stockholm and Gothenburg showed that the length of a substantial delay does not affect the travellers' choice significantly (Warg, 2013). The importance of presenting and accumulating delays in an adequate way is demonstrated by Staav (2014). During a week in 2011, the average punctuality for a regional connection in Sweden was 83%. However, a popular departure for commuters (departure time 16:55) was late on 4 of 5 days, which raises the question of whether passenger-valued measurements should be used. What information is helpful to a traveller can also be discussed e and if this is a relevant question when choosing parameters for a model. For example, for a traveller, the value of knowing that the train arrives on average 9 min late might be questionable if this only occurs in 1.25% of cases. This section described common methods of capacity analysis and socio-economic evaluation. It was referred to work linking these fields and ways of measuring and valuing quality were shown. This paper makes use of these works by combining methods from both fields and using common ways of valuation. The approach is further explained in the following section. 3. Method and model As described earlier, capacity is an important input in economic assessments, at the same time as economic assessment is relevant for capacity analysis. The purpose of this paper is to develop a utility function for evaluating timetable alternatives with a focus on capacity. This section describes the framework, idea and the method used. 3.1. The model The model developed here is based on the user's utility expressed as their value of time (Equations (1)e(3)). The focus is on the demand side described by the timetable, excluding explicit arrival/departure times. Producer surplus as well as investment and external costs are not included so far. As time is an important unit in the field of capacity and timetabling, it was chosen to express the value as a time equivalent. This means that for each alternative, a time is estimated that expresses the alternative's characteristics. This metric sets the characteristics in relation to the travel time. The lower the value, the better the alternative. This can be more illustrative than a monetary value, at the same time as it can be converted into such quite €rjesson and Eliasson (2014) recommend for longdistance train easily, for example by multipying with 7.3V/h, the VOT that Bo trips. A time might also be suitable for international comparison as converting into national currency becomes unnecessary. As described in Section 2, economics often uses monetary values, but sometimes also in relation to travel time. Time is a resource that is similar for everybody, even if individuals' value of time differs. If, for example, the value of a change for one departure of a train is to be estimated, the monetary value requires the number and kind of travellers on the train and their Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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value of time to be known, whereas a time equivalent can describe the result independently. The utility is expressed as average time for a certain category of train services and can be applied for different systems. As stated earlier, the time equivalent aims to describe an alternative based on its characteristics converted into travel time. The most obvious comparison is between two different services, represented as train paths in the timetable: Let's include the scheduled travel time and the average delay in the metric. If both kinds of variable are valued equally, the metric would be their sum, in which case the average real travel time is as illustrated in Fig. 1. As more variables are relevant and weights might differ, the timetable value Ss for each train slot s is defined. It is the sum of the service-specific values for each included variable wsi multiplied by the associated parameter ci, which describes the variable's relation to normal travel time.

Train slot value Ss ¼

n X

csi *wi

(4)

i¼1

To evaluate a timetable alternative a, the average for all train slots s is compared:

Pd Timetable value Va ¼

i¼1 Ss

s

(5)

The variables describing each alternative are divided into static and dynamic variables according to Warg (2013), see Fig. 2. The first group describes properties of the timetable, for example travel times, frequency of service and scheduled delays. Dynamic parameters are the outcome of operation or simulation of a timetable, for example delays and on-time performance. Dependencies between variables exist. Starting with the most obvious input variable, scheduled travel time, the model in this paper is developed by adding variables and associated parameters. Different departures of the same category are compared with the help of their train slot value S. Based on the assumption that variables that are not included can be disregarded, S represents the value a specific departure has for a traveller, the lowest value being the preferred one. In the second step, the method is applied for timetable alternatives. The effect of changes on dynamic data is estimated with the help of the microscopic simulation tool RailSys. In Warg (2013), simulation was shown to be an adequate method to reveal delay data for future scenarios. Modelling a railway system and simulating traffic with introduced primary delays (Radtke and Bendfeldt, 2001) makes it possible to compare different scenarios for parameters like timetable and infrastructure, but also, for example, extremely long/short primary delays. Unlike analytical methods and optimisation, simulation gives an idea of how traffic might work if a certain strategy, encoded as simulation rules, is applied instead of one optimal solution. Simulation is therefore directly applicable for testing changes prior to their implementation. Infrastructure, trains and timetable are modelled according to actual conditions or the situation to be analysed. Traffic is simulated for a certain number of days with primary delays that are applied statistically at the starting station for the trains, at stations with passenger exchange and/or on the line. Alternatives are compared using the timetable value. V. The purpose of the method that is to be developed is to make it possible to estimate the effects of changes in the timetable, as shown in Fig. 3. The variables describing the timetable are converted into the train slot/timetable value by weighting them in relation to travel time. Dynamic variables are revealed through simulation of the timetable with primary delays. By adjusting the timetable according to the resulting value, a better timetable/train path solution can be found. 3.2. Application and development of the model in this paper In this paper, the train slot value S and timetable value V are expressed as a time equivalent of the travel time for an express train on the Swedish Western Main Line between Stockholm and Gothenburg. Depending on number of stops and amount of time supplement, the scheduled travel time varies between 169 and 191 min, including technical minimum running time and supplement. The line is also used by numerous other services that differ concerning stopping patterns, speeds, used part of the line, etc. For autumn 2013, the Swedish Transport Administration (Trafikverket) estimated the capacity utilisation to be high (81e100%) on several parts of the line, especially during peak traffic (Trafikverket, 2014c). As the Swedish market has been deregulated, there are new operators entering the market, and fast connections between Stockholm and Gothenburg are attractive with high travel demand and travel times competing with air traffic. For the 2014 timetable, a new operator applied

Fig. 1. Graphical illustration of time equivalent for two different services.

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 2. Examples of static and dynamic timetable criteria.

Fig. 3. Structure of the planned method.

for slots for long-distance train that were in conflict with slots that other operators had applied for. Based on the described differences between services, Trafikverket concluded that timetable adjustments were necessary to resolve the conflicts. This affects at least one operator negatively, but resolving the conflicts by means of infrastructure investments would have been expensive (Trafikverket, 2014a). Even during the timetabling process for 2015, conflicts occurred and more are expected in the future. This background and characteristics make the line appropriate for this study. The analysis focuses on arrival at the final station for the operator SJ's express trains between Stockholm and Gothenburg. These timetable and delay characteristics were considered to be appropriate for this study. Records of actual arrival time were compared to scheduled time for weekdays during the first six months of 2014. Apart from three exceptions, only trains with regular departures (more than 100 registrations) during this period are considered. In the second step, simulation was performed for the last 80 km of the line. Fig. 4 shows the deviation from scheduled arrival time for all departures in the data set. In addition, several measurements demonstrate how dynamic characteristics could be measured and included in the model. The median for all registrations is 0 min. The average delay is 9 min for the complete data, 13.5 if only positive delays are considered, and 36/54 min if only delays exceeding the punctuality limit of 5 or 15 min are included. For the negative delays, the average is 3 min. The distribution is widely spread, with standard deviation 28 min. Early departures and short delays occur with high frequency but there are also some very long delays (maximum 285 min). 4. Application 1: Train slot value based on historical delay In the first application of the model, different express train departures are compared based on their train slot value calculated with timetable and historical delay data. Different variables and parameter values are tested. The comparison is independent of train path times and alternatives are compared as if they were available simultaneously so that the traveller Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 4. Deviation from the scheduled arrival time in Gothenburg (number of trains arriving x minutes early/late and cumulative percentage) and different statistical measurements for the arrival distribution. Delays exceeding 120 min are grouped (121e180 min, 181e240 min and more).

can choose the most adequate one. This makes it possible to compare train slots instead of departures where arrival and departure times play an important role. In the basic model, where the travel time for an express train is the only input, the departure with the shortest travel time is the preferred one. The travel time can be split into minimum running time ts and time supplement tss. A time supplement is added to the minimum travel time for timetabling reasons or to improve reliability. This is because it makes sense to include a supplement for each specific departure s as a separate input variable. As the first step in the development of the model, the dynamic variable average delay as is added. This is a commonly used variable for describing the performance of services. Inserted into Equation (4), it results in the following equation:

Train slot value Ss ¼ ts *wt þ tss *ws þ as *wa

(6)

Fig. 5 shows the resulting time equivalent Ss for the different departures if all variables are weighted equally. Differences depend mainly on the stopping patterns (the fast departures are non-stop services, the others have between two and four stops) or timetable restrictions. If average delay ads is included with weight wa ¼ 3.5 according to the Swedish recommendations, the result is as shown in Fig. 6. In both models, train slot 403 would be the preferred one. This preference differs from the basic model, where the utility of train number 401 with the shortest given travel time exceeds that achieved by trains 443, 405 (both 5 min' longer given travel time) and 403 (þ7 min). The departure with the longest scheduled travel time, 435 (þ27 min compared to the shortest one), becomes more preferable compared to the others when delay data is included. In the first case (Fig. 5), 413, 439 and 447 have the highest time equivalent and thus the lowest utility. With the second model configuration, train 413 becomes even worse. On the other hand, train 403 has become much better than the others. Increasing the delay factor from 3.5 to 5 (as occasionally used in the UK) leads to further changes in the ranking between the departures. As Fig. 4 shows, the deviation from scheduled arrival time varies for the analysed data. Times are concentrated around 0, but with a long tail of widely spread positive registrations reaching a maximum of 4:45 h delay. The positive average delay that was included in the examples above is 12 min. Exactly 12 min' delay only occurs in 0.55% of cases e otherwise, the trains are delayed more or less. Variability can be described by the standard deviation, expressed as reliability index rd (see section Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 5. Train slot value for different departures if wt ¼ wts ¼ wa ¼ 1.

Fig. 6. Train slot value for different departures if wt ¼ wts ¼ 1 and wa ¼ 3.5.

2). Standard deviation describes how the values differ from the average: in the case of the express trains arriving in Gothenburg 28 min if all registrations are considered. For the different train numbers, the value varies between 6 and 70 min. trai and Juha sz (2012) to reduce the parameters if average delay and reliability are Following the recommendation of Ma used, it seems reasonable to reduce the quite high Swedish value for delay from wa ¼ 3.5 to 3 combined with a reliability index with wr ¼ 1.4 as a starting point for the model in this study:

Train slot value Ss ¼ ts *wt þ ss *ws þ as *wa þ rs *wr

(7)

Fig. 7 shows the resulting time equivalent for the studied arrivals: Including standard deviation in this way extends the scale of the bars to a higher level and increases the differences between departures. Train 429 has become the most unattractive one. On the other hand, departure 413, which was worst with the previous model configurations, becomes much better here. In these calculations, average delay and standard deviation are based on positive values only. Early arrivals are considered to be on time, meaning with 0 min' delay as this is the common way of treating them in both registration and analysis. Including the true value for negative delays in the average delay and standard deviation data changes the result. In would then be reasonable to include punctuality or another variable that takes the negative delays into account. Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 7. Time equivalent with delay value d 2.5 and reliability ratio dv 1.4.

As stated in Section 2.4, rules for measuring punctuality differ. As our data is from Sweden, we consider trains arriving not more than five minutes late to be on time and apply the relationship 1:0.45:2.4 between improvements in travel time, punctuality and average delay found in Warg (2013). The proportion of trains arriving late (pd) is expressed as a percentage and converted into time with the help of weight wp. Standard deviation was added with reliability ratio 1. This is lower than in the previous case as more parameters are included.

Train slot value Ss ¼ ts *wt þ ss *ws þ as *wa þ rs *wr þ ps *wp

(8)

This results in the following time equivalents:

Fig. 8. Time equivalent (delay value 2.4, punctuality value 0.45 and reliability ratio 1).

The resulting time equivalents seem reasonable. The value of average delay is reduced but punctuality is added instead and the impact of standard deviation is not as great as in the earlier examples. However, it still exceeds the effect of other parameters. A further decrease should be considered. Fig. 9 shows how the different departures are ranked among each other in comparison for the different model configurations. Rank 1 is the most attractive. It can be seen that the assessment varies according to the chosen input parameters and values. This impact differs between departures. For some, the result is strongly dependent on the value of dynamic parameters in the model (for example trains 405, 413, and 443 and with the opposite effect in particular for 435); others perform more stably, Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 9. Comparison of rankings for different model configurations.

especially train 403. This shows the importance of including these parameters e without them, departures with lower utility are chosen. Because of differences in primary delays, timetable dependence and other restrictions, it is not possible to plan all departures, for example departure 403. However, how differences affect the outcome must be analysed in order to find a way to make improvements. That can be done by means of simulation, which is demonstrated in the following section. When the effect on different trains is estimated, the number and kind of travellers have to be considered. In the analysis above, these variations were not included as the focus was on the passengers' choice of train according to delay distribution. If the focus is instead on socio-economic effect, the whole timetable should be considered and it is important to differentiate between different trains. This is partly realised in the Danish method, where the average delay per train with value 2 is multiplied by the number of passengers on the train to calculate passenger-delay-minutes (Fosgerau et al., 2008). In addition, the effect of including early arrivals with their true values and including punctuality with different limits and weights is an interesting approach. In the examples, time supplement was treated in the same way as travel time. Travellers do not know the difference between minimal and planned time whereas it does not influence their decision other than via the total travel time. This is a reason for weighting supplements equally to pure travel time. If negative delays are included in the average, the actual average travel time is considered, which means that early arrivals improve the services. However, negative delays should be valued lower than positive ones to avoid an early arrival being ranked higher than an on-time arrival with a shorter scheduled time. This question is of particular interest to analyse in cases where many trains arrive before timetable, as is the case in the studied material. Shorter travel times could be stated but would cause longer delays. The effect of removing the supplement is tested and the evaluation discussed in an example in application 2. 5. Application 2: Timetable value based on simulation data After a comparison of different departures based on real timetable and delay data, the timetable value is then used here to compare different alternative timetables. This is done as a first step in developing the method presented in Fig. 3, where different timetable suggestions can be compared and the effect of changes tested. According to Equation (5), the timetable value Va for each alternative a is the sum of the train slot values Si divided by the number of departures.

Pd Timetable value Va ¼

i¼1 Si

s

(9)

If the relationships between services differ between the alternatives, the equation has to be adjusted, for example in relation to the journey distance. In the application here, only express trains are considered since the differences were assumed to be negligible. Analysis of arrival statistics has shown characteristics for the express trains between Stockholm and Gothenburg. Several parameters have been used to assess and compare the performance of different departures during the day. In the next step, the traffic is simulated and alternatives compared to test the applicability of the model structure.

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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5.1. Input Simulation focuses on the last 80 km of the line (Herrljunga-Gothenburg, see the graphical timetable from RailSys in Fig. 10). Quite homogeneous but dense traffic with commuter trains operating with high frequency on the last 45 km of the line and a lot of time supplement for the express trains make this part suitable for the analysis.

Fig. 10. Graphical timetable Herrljunga-Gothenburg, T14. Each line represents a train slot with timetable times on the x-axis and planned location of the train at a certain time on the y-axis (abbreviations of station names). Analysis focus on high-speed trains (red). Freight trains in blue, regional, IC and commuter trains in green. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The main idea of simulation is to analyse how a system reacts to delays that are applied on a timetable according to how it might look like in real operation. This allows alternatives to be compared. In the studied case, there are also large differences between the departures regarding on-time arrival in Herrljunga. Modelling the delays as accurately as possible means coding separately for all departures. However, the objective here is to reveal general dependencies and to develop a method that can be used more widely and only one entry distribution based on all records was modelled. In RailSys, trains arriving ahead of schedule are considered to be on time, which in contrast to the analysis means that negative delays are not included in the entry delay distribution in Herrljunga. Input to the simulation model is provided by Trafikverket. The model is validated and € (2009) and Sipil€ calibrated concerning different aspects for related cases by Lindfeldt and Sipila a (2011, 2015) and in various studies shown to model train operation in Sweden well. For example, in Rmcon (2015), validation of the simulation model was done by verification of the train behaviour compared to real operation. Trafikverket (2015) shows how a RailSys model is used on the Western mail line for evaluating future timetables. In this paper, times in RailSys were also verified against timetable times.

5.2. Scenarios To choose relevant scenarios for the simulation, the characteristics of the line are further analysed. The average travel time for the high-speed trains is 42 min on this part of the line, including a 2-min stop for 35% of the registrations in the analysis, compared to a total scheduled travel time of 189 min between Stockholm and Gothenburg (including 0-4 stops). The scheduled travel times on the analysed part include between 9% and 27% supplement, with absolute values on the same level as for the whole first part of the line (375 km). This is why several departures arrive in Gothenburg with negative delay. Removing the supplement on the last part of the line increases the delays in Gothenburg but also makes them more evenly distributed (Fig. 11): Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 11. Delay distribution JanuaryeJune 2014, departure from Herrljunga and arrival in Gothenburg (with and without time supplement). The x-axis shows deviation from the scheduled arrival time, the y-axis the number of arrivals for each deviation. Aggregated for delays >15 min.

With supplements, delays increase by 5.2% between Herrljunga and Gothenburg, compared to a 2.2% decrease if supplements are added. Valuing delays higher gives worse results for the alternatives without supplements. However, removing the supplement can have positive effects too, as travel time can be further reduced. The fact that the time supplement is connected to both static and dynamic timetable parameters describing capacity also makes it reasonable to separate it from travel time in the model. In order to analyse the impact of the time supplement, different alternatives without supplement are simulated and analysed. The effect of increasing and degreasing the frequency of express train departures is also evaluated. All alternatives are also simulated without entry delay to analyse the effect on the resulting values in Gothenburg. This results in the following scenarios: -

T14: Original timetable with entry delays for the express trains from statistics S1: Without supplements for the express trains (technical minimum running time only) S2: As S1 but 8 min' later departure from Herrljunga for express trains S3: As S1, but later departure, avoidance of conflicts where possible F1: Increased frequency for express trains (30 instead of 19 departures) F2: Decreased frequency for express trains (15 instead of 19 departures, only regular services, fast non-stop services cancelled) - All scenarios simulated without entry delays (called T14_0, S1_0, etc)

Fig. 12 shows the timetable slots for the express trains between the slower commuter trains and the effect of later departure times, which resolves the conflicts in this case. In the scenario with increased service supply for the express trains, eleven trains were added to the 19 existing trains (scenario F1). As the train slots of other trains are not moved, these services were scheduled in gaps. This results in a not evenly spread distribution. Scheduling was made as attractive to passengers as possible, but sometimes fleeting could not be avoided. Considering that services do not need to have the same stopping pattern on the rest of the line, this might not be a disadvantage, especially if the services are operated by another company with a different business strategy. In particular during the afternoon (arrival time between 17:30 and 19:30), it is difficult to schedule more express trains. Instead of adding new services with even greater supplements than the other express trains, it was decided to skip adding new services during this period. The average headway is then 29 min instead of 48. In the scenario with reduced traffic (F2), express services were removed. This gives an average frequency of around one hour with fairly regular traffic.

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 12. Graphical timetable Alingsås-Gothenburg with block occupation for alternatives without supplement (RailSys). Time on the x-axis, distance on the y-axis. Express trains yellow, commuter trains light green. Left: S1 (cross-sections mark conflicts). Right: S2 (no conflicts in the shown area). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5.3. Analysis and results Scenarios S2 and S2_0 perform considerably less well than the other scenarios and are excluded from further analysis. There are scheduled conflicts, leading to delays for departures without entry delay adding to increased delay for late trains. The remaining alternatives are evaluated with the help of the time equivalent. The analysis focuses on the timetable slots and their quality, especially as expressed by dynamic variables. Changed frequency affects the demand by offering more or fewer departures and departure/arrival times closer to the desired times. In this first application, these effects are not yet considered as the focus is on the effects on quality of changes in capacity. This means that the positive impact of increased frequency is only mentioned but its effect on capacity is included in the metric. Fig. 13 shows the results with parameters valued equally. The scenarios without entry delay perform considerably better than the corresponding ones with entry delay. Within these groups, S1, the scenario without supplement and scheduled departure from Herrljunga as in T14 performs best with a short stated travel time plus a considerably shorter delay. Without entry delays, even S3 (without supplement but later and more conflict-managed slots in the timetable) has a low total value. However, the resulting average delay in Gothenburg is highest for this scenario when the same timetable is simulated with an entry delay distribution according to the data from JanuaryeJune 2014. But it is still better than T14 and F2 (decreased frequency). Minimum travel time and supplement differ for the scenarios with increased and decreased service supply (F1 and F2) because the values are an average for all train slots, including faster and slower departures. In F2, all express services are cancelled. In F1, regular services are added, resulting in a lower/higher average time than in scenario T14.

Fig. 13. Time equivalent for simulated scenarios (value 1 for all parameters).

Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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Fig. 14. Time equivalent for simulated scenarios (value 3.5 for average delay).

Valuing delay time at 3.5 times travel time makes scenario S3 the worst one if real entry delays are applied in Herrljunga (Fig. 14). Without entry delays, the scenario performs even better than the ones where average delay adds to the scheduled supplement: In the scenarios without supplement, punctuality is close to zero if no delayed trains are included. A majority of the trains, however, arrive between 0 and 6 min late, implying that the measured punctuality is higher. The scenarios without supplement perform better than those where punctuality is adjusted (0 min' level for real ¼ 7 min' level for those without supplement). In future work, changes in static timetable parameters due to increased/decreased frequency should be considered by including the effects for travellers when the total results for the timetable alternatives are compared. Investment/operating costs for the trains might also be considered. 6. Discussion, conclusions and future work The approach in this paper uses simulation to estimate and measure the expected level of quality as an input to an economic evaluation model to estimate the benefits of changes, for example adjustments of the timetable. It contributes a novel method that makes it possible to combine capacity and economics by using simulation for estimation of delay characteristics. The analysis results in a time metric, which describes how one alternative performs, compared to others. Examples demonstrate the use of the method with different combinations of input variables and parameters based in particular on travel time and dynamic variables. Results describing the performance of alternatives are expressed by a time equivalent, in the first part for different departures based on statistics, and in the second for simulation of timetable alternatives. Analysis of a delay distribution and other characteristics of an important railway line in Sweden revealed how the variables look like on such a line. Further, it was shown that the model configuration highly influences the result described as the relative utility of a train slot. Including dynamic variables changes the preferences. For instance, a service with short travel time is preferable if no other characteristics are known. However, its attractiveness decreases if it has lower reliability than one with better ontime performance but slightly longer scheduled travel time. Knowing these preferences and judging accordingly are important for decision-making with regard to both investments and timetabling. Input parameters have to be chosen properly. In this paper, different configurations for the metric were shown. In the analysed case dealing with express trains on the Swedish Western Main Line, a combination of minimum running time, supplement, average delay, standard deviation and punctuality with the parameters used in Fig. 8 gives reasonable results. The model structure and input parameters that were found to be relevant in the first part were also applied on simulation data in the second part. It was shown how different scenarios can be compared with the help of the method developed. Following the aim of the paper, it could be demonstrated how dynamic timetable data can be used for evaluation of different services and that simulation is a suitable method for determining the dynamic characteristics of each alternative as input to the model. A combination of several variables is recommended, but adjustments according to the data available are possible. The model can be used in various ways depending on the data available or the specific aim. The value of parameters might have to be reduced when several variables are combined, as the example with the standard deviation showed. The choice of model configuration affects the results to a large amount. In addition to configure the combination of variables and parameters in future work, the way of including standard deviation, punctuality and positive delays or supplements as well as an alternative treatment of outliers should be further analysed. Alongside the model's development, some capacity variables were analysed further. Input delay was shown to have a large effect on the output. For making a general analysis, it is reasonable to have aggregated entry delay data, but on several levels. The analysis with the help of simulation showed that the input delay can have a substantial impact on the final result. In case of major delays, the method developed in this paper could be used to adjust the timetable. Another variable examined was Please cite this article in press as: Warg, J., Bohlin, M., The use of railway simulation as an input to economic assessment of timetables, Journal of Rail Transport Planning & Management (2016), http://dx.doi.org/10.1016/j.jrtpm.2016.08.001

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time supplement. In particular, if the risk of delay is low, the resulting time equivalent can perform less well for alternatives with a substantial supplement compared to solutions with a lower supplement. If the real supplement is known, including it in the model using a higher value compared to travel time should be considered as it is removable, and often a sign of high capacity usage. Here again, a microscopic simulation tool like RailSys is adequate as it makes it possible to distinguish between travel time and supplement. The method used in this article is a new evaluation approach for estimating how an alternative satisfies the market demand and can provide valuable support for decision-makers when planning investments, during train path allocation and for dispatching. It can also be helpful to operators and clients who want to estimate the effects of investments and changes in a timetable. By comparing train slot values, inefficient slots can be detected and adjustments be tested in order to reach improvements. This application can also be used to test how much adding a new slot contributes. It can for example be useful in regular-interval timetables where adding relatively unattractive slots might lead to intuitive results, expressed by a worse timetable value, even if there is no impact on reliability. The method is based on existing methods and weights for CBA, which are adjusted and tested in different configurations during the method's development. The close connection to existing methods simplifies the possible implementation of the findings. Results are presented as a time equivalent, making them more independent of costs, which are only included indirectly through the use of weights. Using a time equivalent also facilitates understanding of the results, as it is easier for a user to see that a measure for example leads to two minutes' shorter travel time than a societal benefit of a certain amount of money. This simplifies the use of the model and offers the possibility to include capacity parameters in an economic assessment, for example for timetabling and dispatching, but also evaluation of new investments and timetable adjustments. As has been shown, it is important to include both socio-economical parameters and capacity in analyses that result in such a decision. It can further be discussed if a basic model should be defined and any additional variables included, such as additional time, or if results should be normalised, for example in relation to the total time of one of the chosen journeys or the average, to increase comparability but which might make it less illustrative for users. Adjusting the resulting time equivalent according to the occupation of a departure would also be interesting. One aspect of interest is how to include the fact that the common customer does not know about the delay statistics, which means that they base their decision on facts (travel time including supplement ¼ basic model) and perhaps experience (for example earlier journeys with/without delays, etc). Experiences and their impacts are difficult to predict, but important for estimating effects. In future work, more scenarios should be evaluated and more model configurations tested. For further conclusions and analyses of relationships between factors and estimation of the usage of values in a more advanced way. How punctuality, perhaps as a combination of several levels, can be included and how this is related to negative delays needs to be tested. For application of the model for changed systems (e.g. changed services, infrastructure, timetable), it might be relevant to use multiple simulation methods such as TigerSim (Lindfeldt, 2015) or use RailSys as a timetable generator, as Sipil€ a (2015) does). In contrast to merely simulating one fixed timetable as done here, several timetables are simulated in order to ensure that characteristics of the system are revealed, not of a single timetable. In further studies, scenarios with a more homogeneous service supply should be included to increase comparability and draw more general conclusions. In addition, the number of commuter trains should be varied and more static timetable effects included in the way the model structure is described. A connection to UIC406 would be interesting, too. Producer surplus, investment and external costs could also be included. A future extension of the model might be differentiation of the train types, use of line, stations, time during the day/week, etc. Including more limitations (e.g. more services, differences between services/departures) and using passenger-valued delays are other suggestions. Using only 90% of the total delay to calculate the standard deviation and including the remaining 10% (worst) in another way should also be tested. For the simulation, more homogeneous traffic should be analysed and compared in more detail for one departure or different situations. The composition of travellers on the trains should also be considered as they have different values of travel time savings. Once a configuration is decided, the framework proposed in this paper could also be used as a basis for optimization of timetables, with the objective of maximizing socio-economic benefits. In particular, by using delay statistics in the construction of timetables together with the socio-economic model proposed here, it may be possible to optimize timetables by allocating supplements to times and locations so that socio-economic effects are maximized. Especially in light of the fact that delays grow during the course of the day, supplements may need to be added to trains departing later during the day. References Abril, M., Barber, F., Ingolotti, L., Salido, M.A., Tormos, P., Lova, A., 2008. An assessment of railway capacity. Transp. Res. Part E 44, 774e806. €rnquist Krasemann, J., 2013. Quantifying railway timetable robustness in critical points. J. Rail Transp. Plan. Manag. 3 (3), Andersson, E.V., Peterson, A., To 95e110. phan, M., 2012. Value of travel time reliability: two alternative measures. Procedia - Soc. Behav. Sci. Volume 54, 349e356. Beaud, M., Blayac, T., Ste Becker, G.S., 1965. A theory of the allocation of time. Econ. 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