DELAY DISTRIBUTIONS IN RAILWAY STATIONS

Transcription

1 The 9th World Conference on Transport Research, Seoul, Korea, July 22-27, 2001 Paper No Topic Area: C Method of Presentation: OHP DELAY DISTRIBUTIONS IN RAILWAY STATIONS Rob M.P. GOVERDE, MSc 1 Prof.Dr.-Ing. Ingo A. HANSEN 1 Dr. Gerard HOOGHIEMSTRA 2 Dr. Hendrik P. LOPUHAÄ 2 1 Delft University of Technology Faculty of Civil Engineering and Geosciences Transportation Planning and Traffic Engineering Section P.O. Box 5048, 2600 GA Delft, The Netherlands Phone: , fax: , goverde@ct.tudelft.nl 2 Delft University of Technology Faculty of Information Technology and Systems Statistics, Probability Theory and Operations Research Section P.O. Box 5031, 2600 GA Delft, The Netherlands Abstract: The estimation of the precise arrival and departure times of trains at stations is done by means of a software tool that extracts the occupation and clearance times of each train per track section of the Dutch Railways network. The software tool was applied to the whole automatically collected set of signal data of the area of Eindhoven during one week in September 1997 comprising 140 MB. A total of 1846 trains were detected and used for further analysis. The detailed statistical analysis of the distribution of the train arrivals, dwell times and departures shows a systematic mean arrival delay of almost every line (InterCity, InterRegio, AggloRegio) ranging up to 138 sec per train. All of the IC-lines except the line starting nearby at Heerlen showed a punctuality of less than 90 % when punctuality is defined as having less than 3 minutes of delay. The IR- and AR-lines arrived more punctual. The dwell times of all the lines lasted on the average 30 to 90 sec longer than scheduled and more than two thirds of the trains arriving late extended the planned dwell time. Consequently, the mean departure delays per line ranged between 1.5 and 2.5 minutes. There is much statistical evidence that the arrival delays and the dwell times fit to normality, whereas the departure delays have a clear negative exponential distribution. Keywords: Train Operations, Punctuality, Delay Distributions, Rail Privatisation

2 1 INTRODUCTION Punctuality of transport services has become a major issue during the last decade due to increased mobility of people, globalisation of trade, competition with other transport modes, saturation of infrastructure capacities, and deregulation of the transport sector. Road congestion, and air and railway traffic delays are daily phenomena and seem to increase continuously. The franchising of railway services in Great Britain in 1996/97 led to contractual agreements concerning the aimed level of punctuality and reliability and financial incentives in the performance regime (Edmonds, 2000; Wolmar, 2000). Its impact on punctuality, however, is still unclear: During the first years after privatisation of British Rail the train delays decreased, but since 1998 it has increased significantly (CRUCC, 1999) because of an increase of the number of trains operated while the network remained in principle unchanged. According to an estimation of Railtrack a 1% increase in the number of trains leads to a 2.5% rise in congestion-related delays (Wolmar & Ford, 2000, p. 168). The German Railways launched in 1997 a broad campaign for the reduction of train delays within one year by 50%, consisting of computerised dynamic train operations monitoring, monthly punctuality reports at every major station, and incentives for the railway staff. Three years later, the campaign was cancelled because of growing frustration of the public about decreasing punctuality of train services and unsatisfied managerial staff. European railway experts have studied the level of service of the Japanese Railways and were very impressed by its extraordinary high degree of punctuality with less than one minute average delay per train (Weigand, 1996). However, they did not succeed in applying the same methods and achieve similar performance due to institutional, organisational and cultural differences. Recently, the Dutch Minister of Transport and the Dutch Railways agreed upon the determination of punctuality levels including a yearly improvement by 1% to be assured, as well as the introduction of fines and payback regulations to railway customers in case of insufficient performance (Netelenbos & Huisinga, 2000). As there exist different methods of measuring and perception of train delays on behalf of the Dutch Railways and the rail user s interest group, the development of a new punctuality monitoring system until the end of 2002 was decided. The aim of the paper is to discuss the following research issues: - How can train delays be defined and measured in a scientifically consistent manner and be investigated independently from the operating companies? - Which statistical distributions and parameters characterize delays in train operation? - Which are the main reasons for train delays and how can they be identified? The paper is organized as follows: First a number of current definitions of delays and punctuality by different railways in Europe are discussed. Then the principal modes of measuring train delays are described. Further on an example of a detailed statistical analysis of delays at the Dutch railway station Eindhoven is presented. 1

3 2 DEFINITION OF PUNCTUALITY Punctuality of train services, in general, is expressed as the percentage of trains passing, arriving or departing at given locations of the railway network no later than a certain time in minutes. Delays smaller than 5 minutes are usually not considered as delays by the European railway companies because of limited precision of the applied modes of measurement, tolerances of the timetable and insufficient means of control of operations in practice. As there are no standard definitions and the mode of measurement of delays is varying, the punctuality rates of the railways differ a lot (Ackermann, 1998; Zhu, 2000). As the time difference with regard to the scheduled time can be determined only on the basis of a timetable the latter s degree of precision determines the precision of the punctuality estimation. As the railway timetable for the public indicates only hours and minutes, the train delays could be defined as being 1 or more minutes behind schedule. A computerised timetable design enables, however, to determine the planned arrivals and departures by fractions of a minute, e.g. in steps of 5 or 10 sec. A high timetable precision of seconds is applied in Japanese Railways and even some European railway companies use this for internal purposes. But, so far, the punctuality levels published by most of the railway companies do not include a lot of trains with small delays and therefore create a much too positive image compared to reality. In any case, the definition of delays should not be influenced by political or marketing aspects in order to assure a scientifically objective measurement and estimation. As delays may occur also during train stops, thus creating eventually differences, both arrival and departure delays should principally be considered. Whether it is suitable to publish arrival, as well as departure delays depends on the railway network. In first instance, departure delays are considered as being more important because they include dwell time delays. For reasons of practicability of control of operations and public perception, statistics of punctuality of train services do not need to include delays smaller than one minute. The setting of a larger minimal limit than one minute delay for the estimation of punctuality seems to be no longer justified for railways with state-of-the-art automatic train detection systems. Therefore, the proposed definition for delays in railway operations should be: Trains are considered delayed if they arrive, pass or depart later than scheduled at the stopping position of the platform or stabling track. Early or late arrivals and departures are treated separately. Punctuality of train services is expressed as the percentage of trains that arrived, passed or departed no later than 60 sec compared to all train movements in the same time period at predefined representative network locations. 3 MEASUREMENT OF TRAIN DELAYS The presence of trains is detected automatically by means of axle counters, coils, induction loops, or track circuits. In general, the start and the end of the occupation of a signal block or a track section by a passing train is recorded and the data is saved a certain time for safety reasons. The location of the devices, however, varies and depends on the track layout and the design of the signalling system. In most cases the last measurement point before a station is situated some hundred meters or even more than a kilometre upstream of 2

4 the platforms, whereas the first one after a station is located typically close to the departure signal. Moreover, the stop position of trains at a platform may vary if the length of trains is changing over time-of-day or day-of-week and the passenger access to the platform is not located at only one end. Therefore, the distances between the last (first) train detection devices before (after) the station and the stop position of the different trains at the platform are to be determined in order to estimate the remaining deceleration (acceleration) time of the trains until (from) the stop. Accurate data of Dutch railway operations has been obtained from information of interlocking and signalling systems by so-called TNV-systems. A TNV-system is continuously recording in real-time the actual state of all relevant signal controls and monitoring information in a traffic control area, including the attached track, signals, points, and route relays, in so-called TNV-logfiles. The data flows between, to and from TNV-systems are shown in Figure 1. Each TNV-logfile of a single day consists of about 25 MB ASCII-format. traffic control TTCS process control PSS passenger info Bepac train describer TNV signal control EBP, EBS interlocking relays,vpi, EBS train detection / railway infrastructure track circuits, points, signals Figure 1. Data flows of the TNV-system of the Dutch Railways We have recently developed at Delft University of Technology the tool TNV-Prepare (Goverde & Hansen, 2000) that converts TNV-logfiles into tables per train series (line) and route suitable for data analysis. Within TNV-Prepare, the rail infrastructure and signals are implemented as a set of coupled and connected objects. TNV-Prepare filters the files on the relevant objects, automatically tracks the (standard and non-standard) train routes from the data, recovers the signalling and interlocking events corresponding to individual train movements along the route, and checks the consistency of the results. TNV-Prepare runs on MS Windows 95 and NT operating systems. TNV-logfiles of several periods and traffic control areas of the Dutch Railways have been obtained, which have been converted off-line using TNV-Prepare into separate files corresponding to individual train series and (sub) routes. This gives reliable and compact tables of successive events along a train route, including for instance successive section entrances and clearances, proceed and stop signals, and point switches. The user can choose to view/export a subset of events such as for instance the successive section entrances (see Figure 2). 3

5 Figure 2. TNV-Prepare overview of successive section occupation times of individual trains for a specific train line The columns of TNV-tables correspond to the successive sections on the route of a train including the attached objects. Three events are reported for an occupied section: the previous clearance time, the start of occupation, and the next clearance time. Likewise, three events are reported for a signal: the previous proceed time, the stop, and the next proceed time. Concerning the points the last switch to the left or straight and the next switch to straight and right respectively are reported. The accuracy and reliability of the (logged) event times has been tested by means of a check whether synchronous events show equal occurrence times, e.g. start of occupation of a track section, the attached TNV-step and the stop sign of the previous signal. The computation time has been found negligible and the transmission of messages from the signalling system noise-free. Another logical test is related to the chronological sequence of events, e.g. the consecutive occupation of track sections along the routes of a train in one direction. It results in discarding inconsistent data. The number of empty cells caused by missing or inconsistent data, however, is found negligible even during peak traffic and communications periods. It can be concluded that the logged event times equal the real event times with an error smaller than one second. Thus, the estimated arrival, departure and dwell times of every train at a station on the basis of the last reported event before the stop and the first event after the stop represent the real times with a precision of about a second. The actual train length and speed of each train at the last block signal upstream of the station can be estimated simply on the basis of the difference of the check-in and check-out times and the scheduled train characteristics. Estimation errors due to train speed and deceleration variations during the approach are filtered by means of a least squares method and comparison of the calculated speed with the design speed, e.g. at the signals and turnouts (Goverde, 2000). 4

6 The train detection at the platform track section itself lasts until the clearance time of the train at the departure signal. The precise moment of the train stop and the start of acceleration at departure, in general, is not recorded automatically, except when the train is equipped by an on-board processor and the data is transmitted to the track-side control system. The remaining deceleration and acceleration time of the train from and to the signals, however, can be estimated on the basis of the known standard deceleration and acceleration rates per type of train. The arrival and departure times of each train at the platform tracks are determined with a precision of about one second, which is sufficient for the empirical analysis of train delays (Goverde, 2000). 4 STATISTICAL ANALYSIS OF DELAYS The train detection data of one week in September 1997 at the Dutch railway station Eindhoven has been used for testing the tool TNV-Prepare and analysing the train delays (Goverde et al., 2001). The statistical analysis has been done by means of the software tool S-Plus. For each line serving this railway station several event and process times have been analysed, including the arrival delay, departure delay, dwell time, and occupation times of sections on the inbound and outbound routes. In total, 1846 trains have been recorded, 30% IC-trains, 30% IR-trains and 40% local trains (AR). Freight trains have been discarded in this analysis. For each train line the mean and standard deviation of each event or process time distinguished by time period (morning peak, daytime, evening peak, and evening) has been determined. Analogously, the mean and standard deviation distinguished by type-of-day (Sunday, weekday, Friday, and Saturday) has been analysed. Moreover, appropriate theoretical distributions of the event and process times have been assessed and tested on goodness-of-fit, including data separations in time period and type-of-day. The data of the various train series has also been compared mutually for correlation of train type (local, interregional, and express trains) and originating route. 4.1 Arrival time In general, about 40% to 80% of the trains of a line arrived more or less late (Table 1). If delays up to one minute are neglected the percentage of delayed trains was between 17 and 67%. In case the common definition of delays (> 3 minutes) is used the percentage of punctual local trains varies from 94% to 100%, and for the other trains this ranges from 66% to 96%. The results show that the random behaviour of the arrival delays during the evening peak differs considerably from the other parts of day (Figure 3). The behaviour of the arrival delays also fluctuates significantly over the type-of-day (Figure 4). There is some evidence that the arrival delay follows a normal distribution with respect to a time period or type-ofday, except for the evening hours and the weekdays, although the empirical distributions are all rather skewed to the right (Figure 5). There is some evidence that the arrival delay during the entire week is normally distributed for two of the IC-lines and all of the IR-lines (Figure 6). The hypothesis of normal arrival delays is rejected for the other three IC-lines and the local (AR) lines. The standard hypothesis of a negative-exponential distribution of train delays, introduced first by Schwanhäusser (1974) is not confirmed in the case of the 5

7 train arrivals in Eindhoven where delays of less than one minute and early arrivals have been included. Table 1. Arrival delays of the trains at station Eindhoven (September 1997) Line From To Average [s] St. dev. [s] Share of late trains Share of delays > 1 min Share of delays < 3 min Average of late trains [s] IC 800 Haarlem Maastr IC 800 Maastr. Haarlem IC 900 Haarlem Eindh IC 1500 Den Haag Heerlen IC 1500 Heerlen Den Haag INT1800 Keulen Eindh IR 1900 Rotterd. Venlo IR 1900 Venlo Rotterd IR 2700 Venlo Eindh IR 3500 Utrecht Eindh AR5200 Deurne Tilb.Wt AR6400 Weert Eindh AR9600 Utrecht Eindh Figure 3. Histogram and kernel estimate of the arrival delay of IC 1500 Den Haag-Heerlen at station Eindhoven by part of day (September 1997) 6

8 Figure 4. Histogram and kernel estimate of the arrival delay of IC 1500 Den Haag-Heerlen at Eindhoven by type of day (September 1997) ehv IC 1500f arrival delay [s] Figure 5. Histogram and kernel estimate of the arrival delay of IC 1500 Heerlen-Den Haag at station Eindhoven (September 1997) 7

9 ehv IC 800f arrival delay [s] Figure 6. Cumulative distribution and exponential fit of the arrival delay of IC 800 Haarlem-Maastricht at station Eindhoven (September 1997) A considerable number of trains coming from line terminals that are situated about km towards the east and south of Eindhoven, e.g. Venlo, Heerlen and Maastricht, arrive too early. If the early and punctually arrived trains are excluded from further analysis the late arrivals can be investigated in more detail. The late arrivals can be fit in most of the cases by the exponential distribution, also for weekdays, evenings, and the entire week (Figure 7), confirming the findings of Schwanhäusser (1974). Figure 7. Density estimate and exponential fit of the late arrival delay of IC 1500 Den Haag-Heerlen at station Eindhoven (September 1997) 4.2 Dwell time The behaviour of the dwell times does not differ for different type-of-day or time period. The dwell times can be fitted well by a single normal distribution for the entire week (Figure 8). Early arrivals cause large dwell times. Therefore, also the dwell times for late arrivals have been analysed. The dwell times of the late arrived trains exceeded the scheduled dwell time on the average about 30 sec to 90 sec (Table 2). 8

10 Figure 8. Density estimate and normal fit of the dwell time of IC 1500 Den Haag-Heerlen at station Eindhoven (September 1997) Line Table 2. Dwell times of trains at station Eindhoven (September 1997) Sched. [s] Average [s] St. dev. [s] Average of late trains [s] Share of dwell time prolongation Average prolongation of late trains [s] IC 800 Hlm-Mt IC 800 Mt-Hlm IC1500 Gvc-Hrl IC1500 Hrl-Gvc IR1900 Rtd-Vl IR1900 Vl-Rtd AR5200 Dn-Tbwt There is again no statistical evidence that the dwell times for late arrivals differ for any two time periods or type-of-day. The distribution of the dwell times for late arrivals, in general, fits to a normal distribution (Figure 9). Figure 9. Density estimate and normal fit of the dwell time of late arrivals of IR 1900 Rotterdam-Venlo at station Eindhoven (September 1997) 9

11 4.3 Departure time The average departure delay of the trains of all lines, except IR 3500 Eindhoven-Utrecht, is between 51 sec and 154 sec (Table 3). The mean delays per line, in general, are growing during the stop. The percentage trains with less than 3 minutes departure delay, is situated between 69% and 98%. Surprisingly, the lines with the largest mean departure delay (IC 1500 Den Haag-Heerlen, IR 2700 Eindhoven-Venlo) differ from the lines with the largest mean arrival delay (IC 900 Haarlem-Eindhoven, IR 3500 Utrecht-Eindhoven). The main reason seems to be the scheduled transfer connection of the first ones to frequently delayed trains of other lines. Table 3. Departure delays of the trains at station Eindhoven (September 1997) Line Average [s] St. dev. [s] Share of early departures Share of trains with < 3 min delay IC 800 Hlm-Mt IC 800 Mt-Hlm IC 900 Hlm-Ehv IC1500 Gvc-Hrl IC1500 Hrl-Gvc INT1800 Ehv-Koln IR1900 Rtd-Vl IR1900 Vl-Rtd IR2700 Ehv-Vl IR3500 Ehv-Ut AR5200 Dn-Tbwt AR5200 Tbwt-Dn AR9600 Ehv-Ut Departure delays can be fit well by an exponential distribution (Figure 10). Note that, in general, early departures of railway trains are not allowed. Therefore, this finding is completely in line with the normal distributions of the arrival delay and of the dwell times. There is no statistical evidence that the behaviour of the departure delay is different during any type of day. However, the behaviour of departure delays in the evening peak differs significantly from the other parts of the day (Figure 11). 10

12 Figure 10. Density estimate and exponential fit of the departure delay of late arrivals of IC 1500 Den Haag-Heerlen at station Eindhoven (September 1997) Figure 11. Histograms of the departure delay of IC 1500 Den Haag-Heerlen at station Eindhoven by part of day (September 1997) 5 CONCLUSIONS The importance of high punctuality of train operations is given by the travellers requirements on the quality of service and the competition with other transport modes. The empirical analysis of train delays, so far, was mostly limited to larger delays than 3 minutes for practical reasons. However, modern train detection systems and computing facilities enable a much more precise data collection and analysis than in the past. The estimation of punctuality in railway operations should therefore be done with the same precision as the available data permits. Thus, train delays should be measured and analysed in seconds. This would, of course, result in a much lower punctuality level than reported by railway companies until now. It enables a much more effective search of the reasons of delays and finally would lead to an increased punctuality of the scheduled services. The arrival and departure times of trains at the stop position of the platform tracks can be estimated with a high precision of about a second by means of the recently developed tool TNV-Prepare for the analysis of train detection data of the Dutch Railways. Thus, the precise duration of the dwell times can also be determined on the basis of available standard data. The statistical analysis of arrival times at the Dutch Railways station Eindhoven shows that about 20% to nearly 70% of the trains of the different lines were delayed by more than one minute. The percentage of the IC- and IR-trains with an arrival delay of 3 minutes or less in most cases was significantly lower than the officially aimed 90%. A vast majority of the trains exceeded the scheduled dwell time by up to almost 60 seconds. These facts indicate that the large number of smaller train delays has an important 11

13 impact on the quality of service and regular more detailed investigation is worthwhile in order to increase the level of punctuality of the Dutch Railways. The proven fit of most of the delay times to normal and negative-exponential distributions respectively will allow an improved design of the timetable and more reliable forecasts of train delays during operations based on historic empirical data. Current research focuses on suitable models of train delay propagation in stations and networks. ACKNOWLEDGEMENTS This publication is a result of the research program Seamless Multimodal Mobility, carried out within TRAIL Research School for Transport, Infrastructure and Logistics, and financed by Delft University of Technology. REFERENCES Ackermann, T. (1998), Die Bewertung der Pünktlichkeit als Qualitätsparameter im Schienenpersonenverkehr auf Basis der direkten Nutzenmessung, Heimerl, G. (ed.) Forschungsarbeiten des Verkehrswiss. Instituts Universität Stuttgart 21, pp CRUCC Central Rail Users Consultative Committee (1999), Actual performance of train operating companies: trains delayed, Local Transport Today, p. 7. Edmonds, J. (2000) Creating Railtrack, In: Freeman, R. & Shaw, J. (eds.) All Change British Railway Privatisation, MacGraw-Hill, London, pp Goverde, R.M.P. (2000), Delay Estimation and Filtering of Train Detection Data, In: Proc. TRAIL 6th Annual Congress 2000, Part 2, No. P2000/3, TRAIL Research School, Delft. Goverde, R.M.P., Hooghiemstra, G., Lopuhaä, H.P. (2001), Statistical Analysis of Train Traffic: The Eindhoven Case, TRAIL Studies in Transportation Science, No. S2001/1, Delft University Press, Delft. Goverde, R.M.P., Hansen, I.A. (2000), TNV-Prepare: Analysis of Dutch Railway Operations Based on Train detection Data, In: Allan, J., Hill, R.J., Brebbia, C.A., Sciutto, G., Sone, S. (eds.), Computers in Railways VII, WIT Press, Southampton, pp Netelenbos, T., Huisinga, J.W. (2000), Overgangscontract II Staat-NSR voor het hoofdrailnet, s Gravenhage, pp Schwanhäusser, W. (1974), Die Bemessung der Pufferzeiten im Fahrplangefüge der Eisenbahn, PhD Thesis, RWTH Aachen, p. 13/14. Weigand, W. (1996) Erfolge der japanischen Eisenbahnen im Markt des Personenfernverkehrs, Eisenbahntechnische Rundschau 45, No. 11, pp

14 Wolmar, C. (2000), Creating the Passenger Rail Franchises, In: Freeman, R. & Shaw, J. (eds.), All Change British Railway Privatisation, MacGraw-Hill, London, p.140. Wolmar, C., Ford, R. (2000), Selling the Passenger Railway, In: Freeman, R. & Shaw, J. (eds.), All Change British Railway Privatisation, MacGraw-Hill, London, p.168. Zhu, P. (2000), Betriebliche Leistung von Bahnsystemen unter Störungsbedingungen, Technische Universität Braunschweig, Braunschweig, p. 9 (unpublished draft PhD Thesis). 13