SCIENCE & RESEARCH Rail operations International Transportation (71) 1 | 2019 34 Dwell time forecast in-railbound traffic Procedure and first evaluation Dwell time, Timetable planning, Passenger service time, Quality of service, Dispatching, Highly stressed passenger transport systems Due to their extend and their variability the dwell times at scheduled stops remain a challenge to operational planning and controlling in railbound traffic. For this purpose an approach will be presented, which allows a prediction of the expected dwell times as well as their variations for the individual stops in the course of a whole train run, based on input parameters describing the infrastructure, the vehicle and the traffic volume. Finally, a first validation will be discussed. Johannes Uhl, Ullrich Martin T ransport operators all over the world are faced with various challenges concerning dwell times at scheduled stops in railbound traffic. While the times required for scheduled stops are increasing due to the rising number of passengers and safety requirements, the growing occupancy rate of the infrastructure and the resulting shorter train headways prevent an expansion of the dwell times. This and the increasing passenger and operational requirements on operating quality require a reliable forecast of the expected dwell times and their variations [1]. At the Institute of Railway and Transportation Engineering of the University of Stuttgart, a model for course-related forecast of dwell times at scheduled stops in railbound transport systems is being developed. Below the basic functions and relationships of this model will be introduced and furthermore some model results will be compared with measured values from practice. State of research Various modeling proposals already supply forecasts of dwell times. One example is the dwell time model based on regression analysis of Weston [2]. The investigations on station stops and passenger exchange processes carried out by Weidmann [3] and Heinz [4] as well as their models inspired by fluid mechanics are also significant. Furthermore, several researchers approached the topic by pedestrian flow simulations (e. g., [4, 5]). Currently investigations on dwell time modeling shows high dynamic in Asia, while the postulated models are often regression models for specific transportation systems (e. g., [6]). The model presented below predicts the time required for the individual stops in the course of a train run. It builds on a model forecasting the passenger exchange times which was developed at the same institute (compare [7, 8]). By using queueing-theoretical approaches to calculate the time required for boarding and alighting, the dwell time model takes special account of the stochastic properties of passenger exchange processes. This analytic approach allows an estimation of the dwell time variations without needing extended computation time as required e.g. for pedestrian flow simulations. Thereby the model not only predicts the expected mean of the required dwell times but also the associated distribution functions. The approach is applicable to all railbound transport systems and to ensure the models practicability its data requirements are limited to data typically available in transport companies. As a prototype, the proposed model was implemented in Matlab [9]. Course-related dwell time modeling As can be seen in figure 1, the dwell time modeling for a course starts with the input of the required data by the user. Hereby, infrastructure data (e. g. properties and facilities of the platforms, stop positions), vehicle data (e. g. length, door and capacity distribution, door closing times) and traffic data (e. g. passenger volume) are queried for the investigated train run. The required infrastructure data can be obtained from station plans or from online aerial photographs and the needed vehicle data from the vehicle type sheets. The traffic data cover mainly the numbers of boarders and alighters at the individual stops of the investigated train run which can be received form traffic models or passenger counts. If available, the user can furthermore input the origindestination matrix of the train run. Otherwise, the model itself estimates this matrix based on the numbers of boarders and alighters. In addition, the operational program of parallel running lines can be indicated. PEER REVIEW Received: : 1 Apr 2019 Accepted: 13 May 2019 Rail operations SCIENCE & RESEARCH International Transportation (71) 1 | 2019 35 The calculation process consists of three sub steps - namely the modeling of the expected number of boarding passengers, the distribution of the boarding and alighting passengers among the vehicle doors and finally the time required for the passenger exchange and the other processes of a stop. These three sub-steps are calculated consecutively for every station in the course of a train run, building up on the results of the previous scheduled stops. The procedure within the sub-steps will be explained in more detail below. Figure 1 also elucidates that this procedure is embedded in two repetitive loops. The superior loop takes into account the stochastic daily variations of factors such as delays, passenger volume, and behavior of the passengers. Therefore, random numbers of these variables are generated for about 100 to 200 days of operation. Furthermore, the use of queueing-theoretical approaches also allows the utilization of a probability of non-exceedance. Among others, this concerns the determination of the amount of boarding passengers arriving at the platform non-timetable-oriented. Therefore, about 5 to 20-probability steps are calculated for each day of operation. The results of the individual of both loops are aggregated by averaging. Finally, the model provides the distribution functions of the dwell times expected for each scheduled stop as well as additional statistical information such as mean values and standard deviations. Furthermore, there are additional outputs that support the understanding of the results and especially allow identifying potentials for optimizations concerning the dwell times. Expected amount of boarding passengers As can be seen from equation (1), the modeling of the amount of boarding passengers at a scheduled stop is carried out separately for each destination reachable from this stop on the considered line. Thereby the passengers arriving at the platform are distinguished between passengers arriving randomly and timetableoriented. Their ratio A is inter alia depending on the scheduled headway on the respective origin-destinationrelation [10]. First of all the average arrival rate AR m,p of boarders on the current origin-destination relation is calculated from the amount of passengers on this relation. Then, the current headway CHW m,p occurring in the considered operating situation is calculated for each relation. Therefore, the randomly generated delays of the evaluated line and parallel running lines are considered. Further delays due to exceeding the planned dwell times at previous stops are also taken into account. The number of passengers arriving randomly BR m,p depends on the duration since the last travel opportunity on the considered relation and is modeled as a queueingtheoretical birth process, whereby the current headway and the respective probability are taken into account. The number of timetable-oriented passengers BT m,p is determined directly from the general number of boarders at the stop. Only if the current headway is longer than 1.5 times the scheduled headway, it is taken into account that there are already passengers arriving for the next trip. Finally, the expected amount of arriving passengers of the individual relations are summed up to get the total amount of boarding passengers B m at the considered stop. B A SHW BR SHW BT AR AR CHW PS A m m p m p m p m p m p m p m = ( ) ⋅ ( ) ( ) + − ( ) ⋅ , , , , , , ; ; 1 " , , ; ; p m p m p p m M SHW CHW ( )   = + ∑ 1 B A SHW BR SHW BT AR AR CHW PS A m m p m p m p m p m p m p m = ( ) ⋅ ( ) ( ) + − ( ) ⋅ , , , , , , ; ; 1 " , , ; ; p m p m p p m M SHW CHW ( )   = + ∑ 1 (1) B m Number of boarders at stop m [-] BR m,p Number of randomly arriving boarders at stop m with destination p [-] BT m,p Number of timetable-oriented arriving boarders at stop m with destination p [-] A Ratio of randomly arriving boarders [-] AR m,p Average arrival rate of boarders at stop m with destination p [Pass/ h] SHW m,p Scheduled headway on the origin-destinationrelation from m to p [sec] CHW m,p Current headway on the origin-destinationrelation from m to p [sec] PS Probability step [-] M Total number of stops [-] Ini tial Query input data from the user Determine random numbers for the variables delays, passenger volume, passenger behavior parameters, stopping accuracy for current day of operation Determine the number of boarding passengeres at the current scheduled stop Determine the distribution of boarding passengers among the vehicle doors at the current scheduled stop Determine the cumulative distribution function of the dwell time at the current scheduled stop Calculate the weighted mean of the CDFs of all probability steps per scheduled stop Calculate the mean of the CDFs of all days of operation per scheduled stop Provide results to user Final Done for al l days of operati on? Done for al l scheduled stop? Done for al l probabi lity steps? Choose next scheduled stop Choose next probability step Choose next day of operation yes n o yes yes n o n o Figure 1: Procedure of the presented dwell time model Source: Authors SCIENCE & RESEARCH Rail operations International Transportation (71) 1 | 2019 36 This procedure allows the modelling of busy line sections with short headways (mainly in the city centers), where passengers predominant arrive randomly and thus almost low delays result in a significant increase of the amount of boarders. Hence, modelling of the building up of delays can be done. The use of the parameter A also enables the modelling of line sections with long headways (mainly outside the city center), where this effect is less important. Passenger distribution among the vehicle doors For the passenger exchange time at a stop, the distribution of the passengers among the vehicle doors is of particular importance, whereby a uniform distribution minimizes the time required [3, 4]. Since, however, it cannot be assumed that the users of the model know the distribution of waiting passengers along the platform length at each stop, this is also modeled. In order to determine the distribution of passengers, it is assumed that passengers, when positioning on the platform of their departure point, orient either towards the circumstances of their departure (platform accesses, weather protection, usual vehicle stop position) or their destination point (platform exits). Using the existing knowledge (e. g., [11, 12]) as well as results of further investigations about the factors influencing passengers’ distribution along the length of a platform carried out at our institute [13], an analytic model was developed, which allows to predict the passengers´ distribution for a certain platform situation. Thereby based on the infrastructure data entered by the user, a density function of the probability of the position chosen by a waiting passenger among the platform can be derived for the respective stop. Taking into account the vehicles door arrangement and stop position, this can be used to distribute the boarding passengers at a stop among the doors. Hence, the vehicle occupancy and the numbers of alighting passengers are determined based on the results of previous stops. Three redistribution steps then adjust the calculated numbers of boarders and alighters as well as the vehicle occupancy. These redistribution steps are simulating the reactions of passengers to the different occupancy rates of the individual platform areas before the arrival of the vehicle, in the case of overfilling of individual vehicle entry sections as well as to the different occupancy rate after boarding in the various areas of the vehicle. Therefore, the situation is modeled as a classical study of transport theory, whereby the number of supernumerary or missing passengers in the individual areas is regarded as supply or demand quantity and the distances between the sections as the transportation costs. Cumulative distribution function of-the-dwell-time To determine the cumulative distribution function (CDF) of the dwell time at a scheduled stop, the CDFs of the time required for the partial processes are first determined and then summarized by convolution. First the method used for door opening is determined considering the technical possibilities of the vehicle and the specific operating situation. Hence the CDF of the vehicle-specific time requirement before the start of the passenger exchange (inter alia door release) is determined. Subsequently, the CDF of the period up to the end of the regular boarding process is calculated separately for each door of the vehicle. This is determined by convoluting the CDFs of the time required for the doorspecific processes before the passenger exchange (inter alia door opening), the alighting process and the boarding process. The CDF of the alighting as well as the boarding process are modeled as a queueing-theoretical pure death process. This assumes that there are initially a definite amount of jobs (in this case boarders or alighters) which have to be processed (in this case pass the door) one after the other with a specific rate. This so called death-rate as well as whose variation are adjusted by the model to fit the death-process matching with varying situations at a platform. Thereby the effects of geometric constraints (inter alia door width and height difference) and interactions between passengers (inter alia congestion at high occupancy, interactions between boarders and alighters) on the boarding or alighting rate are considered by varying the death rate [7]. In practice, however, not all boarders are already waiting on the platform when the vehicle arrives, but there also late runners, who arrive only at the platform when the boarding already has begun. The amount of Figure 2: Comparison of the model calculated mean values with at least 20 measured values per stop for the center part of a suburban railway line (one direction) at seven stops Source: Authors Figure 3: Comparison of the model calculated CDF with 54 measured values for a busy station of a suburban railway line (one direction) Source: Authors Rail operations SCIENCE & RESEARCH International Transportation (71) 1 | 2019 37 those late runners at a certain stop is calculated inter alia considering the scheduled headway and then distributed among the vehicle doors depending on the location of the platform accesses. At doors where late runners are expected, the CDF of the boarding process is not modeled as a pure death process but instead as a queueing-theoretical birth-death process with focus on the duration of the busy period. Thereby the death rate is specified as the boarding rate described above, while the birth rate is specified as the arrival rate of late runners at a vehicle door. This allows the calculation of the duration until the door first time has the possibility to be closed completely. Hence, the door closing procedure is also taken into account, which is determined considering the technical possibilities of the vehicle and the platform, the number of late runners and the current delay of the train. Overall, it is also possible to model the recurrent interruption of the door closing process by late runners. Finally, the CDFs of the individual doors are aggregated by maximum formation and then, considering the CDF of the time required for dispatch, the CDF of the dwell time at the scheduled stop is determined. Comparison of the model results with measured data Using the example of one direction of a suburban railway line in Stuttgart, the results of the model are compared with dwell times measured in real operation. The considered line is a cross-city route and shows a high passenger volume, especially in the extended city center. Figure 2 shows the mean values of the measured and modeled dwell times for the stops around the city center. Although the model is not fully calibrated yet, the comparison elucidates that the dwell times calculated by the model correspond well to the measured values. The average deviation of the measured and calculated mean values over all stops of the considered line is 2.7 seconds or 9.8 %. Figure 3 shows the CDFs based on the calculated and measured values for station 6, which is one of the stops located in the city center. A close match can be seen as it is the case for the other evaluated stations. Also first validations for light rail and commuter train courses let expect a high degree of forecasting quality. Conclusion and outlook The presented model enables a precise forecast of the distribution functions of dwell times in railbound systems. The model results can be used for timetable planning as well as due to the consideration of the relationship between delay and the dwell time extension for dispatching and performance investigation [14]. Because of the additional outputs, optimization potentials regarding vehicle, infrastructure and operating program can also be derived. The remaining discrepancies between the measured and the predicted values indicate further need for research regarding the arrival of passengers at the scheduled stops, the distribution of passengers along the platform and the behavior of late runners. Therefore as well as for model calibrations based on extensive data sets of light rail systems, suburban railways trains and commuter train systems further investigations are already running. ■ LITERATURE [1] Lin, T. (1990): Dwell time relationships for urban rail systems, Massachusetts, Masterthesis [2] Weston, J. (1989): Train service model - technical guide, London [3] Weidmann, U. (1994): Der Fahrgastwechsel im öffentlichen Personenverkehr, Zürich [4] Heinz, W. (2003): Passenger service times on trains, Stockholm [5] Buchmüller, S. (2005): Planung von Umsteigeanlagen, Zürich, Diplomarbeit [6] Lam, W.; Cheung, C.; Poon, Y. (1998): A study of train dwelling time at the Hong Kong mass transit railway system. In: Journal of advanced transportation, Jg. 32, H. 3, S. 285-296 [7] Uhl, J.; Martin, U.; Hantsch, F. (2018): Entwicklung eines bedienungstheoretischen Modells zur Bestimmung von Fahrgastwechselzeiten im spurgeführten Verkehr. In: Schönberger, J.; Nerlich, S. (Hrsg.): Tagungsband der 26. Verkehrswissenschaftliche Tage, Dresden, S. 625-640 [8] Uhl, J. (2018): Entwicklung eines bedienungstheoretischen Modells zur Bestimmung von Fahrgastwechselzeiten im spurgeführten Verkehr, Stuttgart, Masterthesis [9] Mathworks (2018): MATLAB - Matrix Laboratory, Version 2018a [10] Lüthi, M.; Weidmann, U.; Nash, A. (2007): Passenger Arrival Rates at Public Transport Stations. ETH Zürich - Research Collection. Zürich [11] Kim, H. et al. (2014): Why do passengers choose a specific car of a metro train during the morning peak hours? In: Transportation Research Part, Jg. 61, S. 249-258 [12] Rüger, B. (2017): Influence of Passenger Behaviour on Railway-Station Infrastructure. In: Fraszczyk, A.; Marinov, M. (Hrsg): Sustainable Rail Transport, S. 127-160 [13] Klose, M. (2019): Untersuchung der Einflussfaktoren auf die Verteilung der wartenden Fahrgäste über die Längsausdehnung eines Bahnsteigs. Stuttgart, Bachelorthesis [14] Steiner, J. (2019): Untersuchung der Zusammenhänge zwischen der Haltezeitcharakteristik und der Betriebsqualität auf einem Streckenabschnitt des spurgeführten Verkehrs. Stuttgart, Bachelorthesis Ullrich Martin, Prof. Dr.-Ing. Director, Institute of Railway and Transportation Engineering (IEV), University of Stuttgart, Stuttgart (DE) ullrich.martin@ievvwi.uni-stuttgart.de Johannes Uhl, M.Sc. Doctoral student, Institute of Railway and Transportation Engineering (IEV), University of Stuttgart, Stuttgart (DE) johannes.uhl@ievvwi.uni-stuttgart.de AUF EINEN BLICK Das vorgestellte Modell ermöglicht auf Basis von Eingabeparametern zur Infrastruktur, dem Fahrzeug sowie dem Fahrgastaufkommen eine linienbezogene Prognose der Verteilungsfunktionen von Haltezeiten spurgeführter Verkehrssysteme. Hierzu wird für jede Station zunächst das zu erwartende Einsteigeraufkommen sowie die Verteilung der Einsteiger auf die Fahrzeugtüren modelliert. Mit diesen Ergebnissen werden anschließend unter Verwendung bedienungstheoretischer Zusammenhänge die Zeitbedarfe für den Fahrgastwechsel sowie die weiteren Haltezeitprozesse ermittelt. Neben stochastischen Einflüssen werden auch Zusammenhänge zwischen den planmäßigen Halten sowie das Unterbrechen des Türschließprozesses durch Einsteigernachzügler berücksichtig. Erste Validierungen der Modellergebnisse am Beispiel einer S-Bahnlinie lassen auf eine hohe Prognosegüte schließen.