Suazo, Dragicevic and Muñoz 1 HOLDING BOARDING PASSENGERS TO IMPROVE TRAIN OPERATION BASED ON AN ECONOMETRIC DWELL TIME MODEL.

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1 Suazo, Dragicevic and Muñoz 0 0 HOLDING BOARDING PASSENGERS TO IMPROVE TRAIN OPERATION BASED ON AN ECONOMETRIC DWELL TIME MODEL. Gonzalo Suazo-Vecino (*) Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile (PUC), Chile. Engineering school, Vicuña Mackenna 0, Macul, Chile. 0. Telephone: +--; Fax: gsuazovecino@uc.cl (*) Corresponding Author Marina Dragicevic Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile (PUC), Chile. Engineering school, Vicuña Mackenna 0, Macul, Chile. 0. Telephone: +--; Fax: mpdragic@uc.cl Juan Carlos Muñoz Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile (PUC), Chile. Engineering school, Vicuña Mackenna 0, Macul, Chile. 0. Telephone: +--0; Fax: jcm@ing.puc.cl Revision Submitted on: November, 0 Word Count: Text (including references) =. Tables 0 words each) =.0 Figures 0 words each) =.0 Total =.

2 Suazo, Dragicevic and Muñoz 0 ABSTRACT This paper aims to explain the factors that determine the dwell time of subway trains in Santiago, Chile. Based on morning rush-hour video-recordings of Line s most critically congested station, Baquedano, explanatory variables were selected to adjust a mathematical model. The purpose behind this model was to identify which factors could be managed to increase the system s overall operation, reducing dwell times and improving the passenger s travelling experience. The model was obtained by adjusting a linear regression that considered the number of boarding passengers, alighting passengers multiplied by the platform s occupancy level before and after the exchange, and the density inside the train (which has an exponential impact on dwell time). The model s correlation coefficient was 0., and the train s passenger density was found to be the most significant variable, explaining.% of the trains average dwell time. In contrast to what could have been expected, the interaction between passengers getting off the train and the platform s occupancy level explains only.% of the total dwell time. The conclusion of this study was that the passenger s overall travelling experience could be improved by implementing a passenger management system throughout the platform, while slightly reducing the dwell time of the trains. Since Baquedano Station is one of the busiest stations of the subways network, reductions in the dwell time of trains could increase overall departure frequencies, increasing the line capacity and improving the network s operation of all downstream stations. Keywords: Dwell time, retention time, econometrics, retention of passenger s train

3 Suazo, Dragicevic and Muñoz 0 0 INTRODUCTION This investigation focuses on understating the factors that determine the detention time of a subway train. Beforehand, the number of passengers boarding and alighting the train and the subway car and platform s occupation levels are expected to be the most relevant factors. However, understanding how each of these factors determine the train s dwell times allows planners to manage those aspects. This leads to improvements in the level of service and the passenger s travelling experience, together with increasing the line s effective frequency given a fixed fleet and reducing travelling times and delays. Other studies have investigated passenger s total service time for bus systems, which has similarities to a subway s system. For example, there are simple linear models dependent on the number of passengers boarding and alighting the buses (). Other models consider different entry times per passenger based on the amount of time needed to enter the bus, depending on the type of payment mechanism (). However, this situation does not apply to the case of Metro systems, since payment is made prior to entering the platform. In another study based on bus systems, the dynamics of boarding and alighting was explored through the use of large smart card data set, including the effect of on-board passengers and its interaction with the passengers boarding and alighting (). However, a different aspect in the case of Metro de Santiago is the high level of friction between passengers that enter and exit the train with passengers on the platform, which is not included in the investigation mentioned before since this effect only rarely occurs in bus services. Chinese studies have concluded that high congestion inside buses considerably affects the amount of time needed for passengers to board and alight the train (). Also, passengers alighting and boarding in metro stations of Beijing have been modeled through simulation (), considering variables such as individual desires, pressure from passengers behind, and personal activity and tendencies. This explains the fundamental traits of alighting and boarding movements. Moreover, passenger restraints implemented in 0 in the Metro de São Paulo, Brazil, were well received by users and decreased the discomfort in the process of getting on and off the train (). This evidences that reducing the friction between passengers, even by delaying their access to the trains, can be well received by them. Finally, the dwell time usually treated as an exogenous parameter is a relevant input in the optimization of public transport services (). In this investigation, a model was calibrated with data gathered at one of the most critically congested stations of Santiago s Subway Network, Baquedano (Line platform). The friction between passengers inside the trains and on the platforms delays the trains, which reduces the system s frequency (and therefore the capacity of the line) and worsens the overall travelling experience. This study focuses on understanding what variables are causing high levels of passenger friction and train delays at the platforms. Once the impact of these factors is understood, a mitigation system is proposed based on the concept of using metering to limit the access to the platform, in a similar way than limited

4 Suazo, Dragicevic and Muñoz 0 access highways avoid an excessive flow of cars from entering at the same time, causing congestion. METHODOLOGY The following section describes the methodology used in this study. The first part includes the process of how data was collected, and then the method through which the model was obtained is explained.. Data collection To model the dwell times of the trains at Baquedano Station, video-recordings of the trains doors, while passengers accessed and exited the subway car, were used. These videos allowed us to count the number of passengers getting on and off the trains during the rush hour. Also, through the footage, the amount of passengers waiting on the platform (before and after the boarding/alighting of passengers) was estimated. A total of observations were used, with each observation being a train s arrival. The videos showed that most of the passengers gather in the center of the platform, since that is the most accessible section for the passenger flow that transfer from Line (another line in Santiago s subway system) to Line. This increases congestion and friction in this part of the platform. Therefore, this research focuses on this section of the platform, since it determines the train s dwell time. The train s doors in this section of the platform were carefully regarded, and the door with the longest passenger exchange time was selected. The total dwell time of the train was measured starting when the doors opened at the platform and ended when the transfer of passengers in the critical door finished. In some cases, the trains did not move as soon as the doors were closed, remaining stopped for other external reasons. This extra time was ignored in the analysis. Table shows the selected explanatory variables used in the model and how they were obtained. TABLE Modelling Variables Variable Boarding Passengers Alighting Passengers Tiles Before Description and method of obtaining Number of passengers boarding the critically congested door.. Number of passengers alighting the critically congested door. The number of tiles occupied by passengers on the platform before the doors were opened. The level of congestion on the platform was

5 Suazo, Dragicevic and Muñoz 0 Tiles After Subway car s Density classified in six levels, ranging from 0 (least congested) to (most congested). Similarly to Tiles Before this variable measures the number of tiles occupied by passengers in the station after the train has left (passengers that were not able to board the train). Indicates the critical subway car s occupation level in passengers/m once it has left the station. This measurement was provided by Metro by weighing the train between Baquedano and the station which is immediately downstream. Regarding the variables Tiles Before and Tiles After, the tile occupation was used instead of counting passengers because it seemed to be more effective and easier to quantify quickly, but still objective.. The model Based on the variables described above, different multiple linear regression models were estimated. A regression approach was chosen over a simulation approach because our objective is to develop a predictive model based on variables, whereas simulations are more useful to obtain performance measures regarding the model behavior based on certain parameters. Graphs were constructed to analyze the individual relationship between the total detention time and each of the variables studied. As expected, these graphs showed a positive correlation with dwell times. Based on these graphs, an initial function describing the detention time was estimated. It was also noted that the effect of the subway car s density over dwell times had an exponential effect rather than a linear one. Subsequently, an iterative process was conducted, starting with a model that included all five variables and the interactions between them. This initial model was progressively adjusted in order to obtain the best fit possible. To avoid collinearity in the model, only independent variables were included. Different models were tested, making sure that the variables included could be logically combined, and that their coefficients were reasonable. We also expected a low constant of the model, since we thought that the explanatory variables chosen would be quite successful in explaining the dwell time. All variables included in the model were required to have a high statistical significance, with t-values over., assuring a % confidence interval. Finally, the coefficient of determination (R ) was sought to be as high as possible. Following these criteria, the model described in Table showed the best fit. TABLE Variables of the Model

6 Suazo, Dragicevic and Muñoz TD BP PT TA ED Variable RESULTS AND DISCUSSION Description Dependent variable: Train s stopping time Number of passengers entering the critical door during the exchange, calculated as Boarding Passengers. Variable that relates the number of passengers exiting the subway car and the tiles occupied before the doors were opened. The interaction was calculated as: (Alighting Passengers Tiles Before) Variable that accounts for the number of passengers on the platform after the doors have been closed. Calculated as Tiles After. A variable that relates to the subway car s density accounting for its exponential behavior. Calculated as e ( :;< ABC@DE<). This section describes the mathematical model obtained. Also, an analysis of how the subway system of Santiago de Chile could improve by using this results is included, together with an analysis of the data.. Analysis of the obtained model The value and statistical significance (t-value) of the coefficients obtained in the selected model, which is able to most accurately predict the total dwell time of the train, are presented in Table. Since the variable ED has an exponential coefficient (θ) associated to it, this parameter was calibrated through a parallel process. This process consisted in calibrating the model for different values of the parameter until the fit was best (i.e. the adjusted R H was maximized). The best model was obtained for θ = 0., and an adjusted R = 0.. TABLE Values of the Coefficients and Statistical Tests t for Each Explanatory Variable Variable Coefficient Statistical t test Constant BP 0.. PT TA 0.0. ED..

7 Suazo, Dragicevic and Muñoz 0 Thus, the dwell time can be modelled as: dwell time = BP PT + 0. TA +. ED () All variables, except for PT and the constant, had a significance level higher that %. Since the constant has a low significance level, it can be concluded that the total dwell time is mostly explained by the chosen explanatory variables. On the other hand, even though the variable PT has t-test lower than the minimum required (.), it is still considered relevant enough to be included in the model, since it represents the friction between alighting passengers and those in the platform. Using average values for the different explanatory variables, the total dwell time can decompose into each variable s independent effect. Since the average dwell time of the train was calculated to be. seconds, the contribution of each of these variables is displayed in Table. TABLE Values of the Statistic t in Each of the Variables Variable Average value of the variable Average time explained by variable (s) BP. pax/exchange. PT. pax/tile 0. TA. occupied tiles on platform. ED. pax/ subway car. These results show that the average dwell time is explained in a.% by the subway car s passenger density. The interaction between the number of passengers exiting the subway car with the congestion on the platform (PT) provide a slight increment on the total dwell time, explaining only its.%. Figure shows a comparison between the observed and modeled dwell times. A degree line is drawn in the Figure for reference, since it represents a perfect match. The figure shows that the variables selected in the model are highly explicative of the detention times for most of the data. However, for detention times over s, the model underestimates the total dwell time. This fact points out that there are certain aspects of the detention time that the model is not able to reflect. Unfortunately, it was not possible to include other variables or modify the model so that it could capture this phenomenon.

8 Suazo, Dragicevic and Muñoz Comparision of modeled v/s observed times 0 Modeled times (s) Observed times (s) FIGURE Graph of modelled vs. observed data in seconds.. Analysis of system improvements Although it would be preferable to intervene those variables that have the most impact on increasing the detention time, it is not always possible to do so. For example, although the subway car s passenger density is relevant in the total detention time, this aspect is a rather fixed factor of operation that cannot be reduced by simple methods. The same happens with the number of passengers boarding and alighting each of the train s passenger cars. These factors could be considered to be fixed, determined by the characteristics of the passenger s trips that the train is serving. However, there are aspects, such as the platforms occupation, which could be modified in order to reduce the total detention time. Therefore, it is possible to develop a scheme to control passenger access and distribution throughout the station s platform, helping reduce the number of passengers waiting to board the train in the most congested sections of the platform. The purpose behind this measure is to reduce friction when passengers are exiting the subway car. From Table, it is evident that PT and TA, are factors that could be modified, potentially accounting for a.% of the train s total dwell time. Therefore, if passengers could be intelligently metered into the platform, the dwell time could be reduced and the passenger s travelling experience would improve. For example, if the platform s passenger density is reduced to half, the total detention time could be decreased in %, which is about. seconds per stop. This may seem as a small figure, but it immediately increases the capacity of the whole line in about.% if accomplished (since the interval between consecutive trains is approximately seconds).

9 Suazo, Dragicevic and Muñoz 0. Analysis of data through validation A data base containing a representative sample of a two-day operation, provided by Metro, was used to validate the model. The difference between the modelled and observed times was calculated to be. s in average. If the train s average dwell time is.s, the model s error is close to.%. Using these results, a platform passenger metering system was developed. Since part of the total detention time is due to the friction between passengers when they board, alight and move throughout the platform, minimizing this friction reduces dwell time. To achieve this, if the number of passengers in the platform exceed a defined threshold, passengers will be held in a separate section before accessing the platform. In this study, it was determined that, if the variable measuring the number of occupied tiles after the exchange (TA) is not greater than level, the friction between passengers allows them to board and alight the train easily, reducing the train s total detention time. Under this scenario, the simulated dwell time would be reduced in.%. Figure shows a comparison between the observed and modeled dwell time of a train, similar to the analysis presented in Figure. A clear correlation between the observed and modeled detention times can be observed for most the cases. Nevertheless, when the total dwelling time exceeds seconds, the model underestimates the actual detention time. 0 Comparision of modeled v/s observed times (validation data) Modeled times (s) Observed times (s) FIGURE Graph of modelled vs. observed with the validation data in seconds time.

10 Suazo, Dragicevic and Muñoz PROPOSAL FOR A PLATFORM PASSENGER METERING SYSTEM In this section we propose a passenger metering system that could keep the east-bounded platform of Baquedano station at the desired level of occupancy, so the train flow in the station (and the passengers in those trains) is maximized. Figure shows the number of passengers arriving at Baquedano Station (east-bounded platform) during the morning peak. The figure also decompose the volume into passengers transferring from crossing line and those coming directly from the surface. 0 FIGURE Average number of passengers arriving to Baquedano s east platform between :0 and :0 a.m. on October th and th, 0. Figure shows that most of the passengers arriving to the platform are transferring from Line. Thus, the passenger metering efforts will be focused in this inflow into the platform, allowing passengers arriving from the surface to flow freely into the platform. To predict the impact of the proposed method, Metro provided the number of trains coming every minutes between :0 and :0 a.m. during seven representative days. The average number of trains visiting the platform during each time interval are shown in Table. Additionally, the average number of passengers entering the trains during these intervals are shown in Figure. TABLE Average Number of Trains Observed Within Minute Intervals Time interval 0:0-0: 0: - 0:00. 0:00-0:. 0:-0:0. 0:0-0:. Average number of trains

11 Suazo, Dragicevic and Muñoz 0:-0:00. 0:00-0: 0:-0:0. 0:0-0:. 0:-0:00. 0:00-0:. 0:-0:0 FIGURE Passengers per train. Given this information, the platform passenger metering system was proposed to start at : a.m., since the earliest congestion at the platform is detected around :0 a.m. It is relevant to start intervening before congestion kicks, since preventing congestion at the platform allows us to increase the number of passengers that can board the trains. By reducing the remaining number of passengers not boarding the trains in this early period, the conditions later on during the peak period are improved. To develop a platform passenger metering system aimed at reducing the dwell time, the following assumptions were made: ) passengers can stand per m ) Two types of trains arrive at the station: NS-0 and NS-. The characteristics of each of these trains are presented in Table. TABLE Train s Characteristics Train Model NS-0 NS-

12 Suazo, Dragicevic and Muñoz Subway car per Train, Number of doors per subway car Length of each subway car. m. m Train s total length. m. m Number of passengers per train (assuming passengers per linear meter) Table presents the average number of passengers boarding a train for each of the minuteintervals. In the Table, the inflow into every train is decomposed into those coming from Line and those coming from the surface. TABLE Number of People Boarding the Line Train Towards Los Domínicos Time (morning) Passengers arriving from the surface boarding the train Transferring passengers (coming from Line ) boarding the train 0:0-0: 0 0:-0:00 0 0:00-0: 0:-0:0 0:0-0: 0:-0:00 0:00-0: 0:-0:0 0:0-0: 0 0:-0:00 0:00-0: 0:-0:0 0 Total passengers boarding the train Based on this information, the following passenger metering system is proposed. The available space to hold passengers is divided into three sections (A, B, and C) of. m wide and. m long each, as shown in the Figure.

13 Suazo, Dragicevic and Muñoz FIGURE Diagram of the passenger holding area. For the proposed metering system, passengers are held before they access the platform (to avoid high congestion, which leads to increasing passenger friction) in an area of 0m approximately. As the platform reduces its occupancy after a train leaves the station, the new available space on the platform will be taken by the passengers waiting in the holding area, as shown in Figure. This area will be designed to fit 0 passengers in section A, 0 passengers in section B and another 0 passengers in section C. Passengers move from C to B and from B to A. FIGURE Diagram of the containment system. When a train approaches the station, we can estimate based on the weight of the train and a fixed origin-destination matrix for the line, the number of passengers that will alight in our platform, and the number of passengers that could board the train there. The metering rate should allow the occupancy of the platform to reach the level in which the train departs with the maximum

14 Suazo, Dragicevic and Muñoz capacity, leaving few passengers behind (so the friction to board and alight is not significant). So once the optimal number of transferring passengers entering the platform is determined, we can decide if just Section A is open, or if sections B or even also C are opened as well. Once these sections are cleared, upstream passengers are allowed to move ahead filing the sections downstream. Assuming that passengers can stand per square meter, section A should be.m long and. m wide. This metering system is needed only during morning rush hours (: to :00 am) so its infrastructure should be light enough to be installed and dismantled daily. The proposed holding area in the context of the entire station is shown in the Figure. 0 FIGURE Waiting area in the context of the entire station. CONCLUSIONS The obtained model shows that the total train dwell time is mostly explained by the subway car s passenger density, the number of boarding and alighting passengers, and the number of passengers on the platform (quantified as the occupied tiles on the platform). The proposed model s correlation coefficient equals 0.. This value is mostly due to the fact that the model underestimates the detention time when it exceeds s. Therefore, for future investigations, other variables should also be included in order to reflect this behavior and increase the correlation coefficient.

15 Suazo, Dragicevic and Muñoz 0 0 Also, the low explanatory power of the variable that relates the number of passengers exiting the subway car and the tiles occupied before the doors were opened may be a focus to improve the model and try alternative formulation. Moreover, other mathematical formulations could be considered and studied, such as the use of a log-linear function instead of a linear regression. These aspects are left as suggestions for future research. By implementing the passenger metering system proposed on this paper, the train s dwell time should be reduced. The comparison between the observed and modeled data showed that the reduction is up to.% of a train s detention time, if the platform s passenger density is kept stable and passengers are held back until free space on the platform and subway car are available for them to use. The basic principle of this proposal is to reduce friction between passengers as they board and alight the train and move through the platform, and this is obtained by holding passengers back in designated areas until there is enough space in the platform, allowing shorter dwell times. Even if the estimated reduction is under %, it would allow passengers to perceive an improvement of their overall travelling experience. Also, as the train s dwell time is reduced, its dispatch frequency can be improved, given a fixed fleet. Finally, since this analysis was made for one of Santiago s most congested subway station, this improvement would positively impact other downstream stations. ACKNOWLEDGEMENTS We thank Santiago s Subway System, Metro, for providing video-recordings of the station and data to correct the estimated models. Finally, we would also like to thank Homero Larraín and Juan de Dios Ortúzar, who helped us with doubts that emerged throughout this investigation. REFERENCES () Pretty, R. L., and Russel D. J. Bus boarding rates. In Australian Road Research (),, pp. -. () Fernández, R., M. del Campo, and C. Swett. Data collection and calibration of passenger service time models for the Transantiago system, In European Transport Conference, the Netherlands, October, 00. () Sun, L., Tirachini, A., Axhausen, K., Erath, A., Lee, D. Models of bus boarding and alighting dynamics. In Transportation Research Part A: Policy and Practice, Volume, November 0. () Liu, J., Deng, W., and Yi, F. Passenger Boarding and Alighting Times at Bus Stops. In International Conference of Chinese Transportation Professionals 0, 0, pp. 0-. () Zhang, Q., Han, B., Li, D. Modeling and simulation of passenger alighting and boarding movement in Beijing metro stations. In Transportation Research Part C: Emerging Technologies, Volume, Issue, October 00.

16 Suazo, Dragicevic and Muñoz () Gerência de Operações Área de Pesquisa. Informações sobre controle de fluxo no metrô sp. Estudos e Informações. In Congresso Nacional de excelencia em gestão, 0. () Jara-Díaz, S., and Tirachini, A. Urban bus transport: open all doors for boarding. In Journal of Transport Economics and Policy (JTEP), (), 0, pp. -.