A Study of Train Dwelling Time at the Hong Kong Mass Transit Railway System. William H. K, Lam C.Y. Cheung Y.F Poon. Introduction

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1 Journal ofadvanced Transportation, Vol. 32, NO. 3, pp A Study of Train Dwelling Time at the Hong Kong Mass Transit Railway System William H. K, Lam C.Y. Cheung Y.F Poon This paper investigates the relationship between the dwelling time of trains and the crowding situations at Mass Transit Railway (h4tr) stations in Hong Kong. Regression models were established for the dwelling delays of trains due to congestion at stations, and a simulation model making use of the Monte-Carlo technique is developed to assess the reliability of the estimated train dwelling time. Therefore, the distribution and the confidence interval of the train dwelling time can be predicted on the basis of observed boarding and alighting distributions. Introduction The Mass Transit Railway is a metropolitan undergroundelevated railway network comprising three lines with a combined route length of 43.2 kilometers. It is operated by the government-owned Mass Transit Rail\vay Corporation (MTRC). The nehvork has 38 stations and is sened by 759 cars assembled into eight-car trains. Each car has five automatic doors and is connected together to comprise a 40-door train. The average number of weekday passengers is 2.4 million. In relation to its length, it is the busiest metro in the world. During peak periods trains are loaded with 2,500 passengers, operate at two-minutes intervals and spend about 30 seconds at each stations. Despite the system's hourly capacity of 75,000 passengers in each &ection, the peak hour passenger demand has already reached the maximum design limit in The introduction of a peak hour congestion fare surcharge and discount policy during off-peak were prompted to constrain the peak hour demand to the design limit. This was considered necessary to ensure passanger safety. PolyTechnic University, H William H.K. Lam, C.Y. Cheung and Y.F. Poon are at the Department ofcivil and Structural Engineering, The Hong Kong ong Kong. Received AugwI Accepted Mach 1998

2 286 William H.K. Lam, C.Y. Cheung and Y.F. Poon In order to study the crowding effects during peak periods, mathematical models were established to estimate the dwelling delays of train due to congestion, and a reliability analysis was performed to assess the reliability of the estimated train dwelling time. Data Collection Observation Survey To establish mathematical models for estimating the dwelling time of trains with respect to the crowding situations on station s platform, the following data were collected on MTR platforms: (1) (ii) (i i i) Number olboarding passengers The numbers of boarding passengers were recorded for each train during the surveyed period. Number of alighting passengers The numbers of alighting passengers were recorded for each train during the sweyed period. Arrival, departure and dwelling time of rrains The arrival and the departure times of trains were recorded in elapsed second. The arrival time is the time when the train stop at the platform, the departure time is the time when the train begins to move away from the station, and the dwelling time is the duration between the train doors start to open and close completely. Selection of Swfied Stations There are 38 MTR stations in total. It is necessary to set a selection criterion in order to choose suitable and representative stations for survey. For the purpose of h s study, the selection criterion should be the crowding situation at the station. In the other words, stations with critical crowding conditions are selected for study. In view to the levels of congestion, three stations have been recommended by Mass Transit Railway Corporation (MTRC). These stations were Quany Bay Station, Kowloon Tong Station and Mongkok Station. Figure 1 shows the locations of the selected stations. There is a common characteristic among these three stations. They all are transfer stations. In these stations, the crowding situation is critical. The survey carried out in these stations would be appropriate so as to collect representative data for the critical crowding situations.

3 A Study of Train Dwelling Time Results Train Dwelling Time Model Figure 1. Location of MTR stations Train dwelling time DT has two components (S. C. Wirasinghe and D. Szplett, 1984): (i) a fixed time for opening and closing doors T,, and (ii) door utilization time T, for boarding and alighmg passengers. The general form is:

4 288 William H. K. Lam, C. Y. Cheung and Y.E Poon Door utilization time could be af ected by a number of factors such as number of boarding and alighting of passengers, crowding in vehicle and congestion on platform as well as the number of passengers arriving the platform. To decide which independent variables should be included in the model, the technique of correlation and regression analysis was used. Considering the results of correlation and regression analysis, it was found that the train dwelling time is mainly governed by the number of boarand alighting of the passengers at station, which is: Tu = f(a1, Bo) Therefore, to establish a dwelling time model for estimating the train dwelling time with different crowding situations at stations, two independent variables were used, i.e., number of boarding passengers and number of alighting passengers per train. Hence, the mathematical model to estimate the dwelling time of trains in relation to the crowding situations at the three selected stations is given as follow: T=C,+C, AI+C, BO (3 ) where DT is the dwelling time of train in seconds; A1 is the number of alighting passengers per train; Bo is the number of boarding passengers per train; C, is a constant (in seconds); and C, and C, are coefficients. The train dwelling time models for the three stations are summarized in Table 1, together with their coefficients of determination R'. These train dweiling time models were developed based on the data collected during the morning peak. It was found at these three stations that the distributions of passenger boarding and alighting among the train doors are quite uniform during the survey periods. In Table 1, the regression constants C, are the fixed time for opening and closing doors at these three stations. In other words, if there is no passenger boarding on or alighting from a train, the train will stop with the minimum fixed time.

5 Table 1. Dwelling time models for the selected MTR stations Station Sampleshe C, Cr cz R' Dwelling time model Qunrry f3ny O!KHj or= 9.21 t 0.02cjo~1 t 0.01rlin0 Kowloon Tong DT. = A/ B0 McwMc DT= AI Bo

6 290 William H.K. Lam, C. Y. Cheurig and Y. F. Poon Comparing the models for the three selected stations, it can be found that the constants and the coefficients for the number of boarding passengers are of the same order and approximate to one another. Therefore, combining all the data collected at the three stations, a generalized equation for the train dwelling time at MTR stations is given as below: DT= L4 I +O.O 16Bo (R* 4.75) Similar research for Canada LRT line can be found in Wirasinghe and Szplett (1984). The coefilcients for alighting passengers (Al) for the Canada LRT line ranged fiom 0.4 to 1.4 seconds per passenger, while coefficients for boarding passengers Po) ranged fiom 1.4 to 2.4 seconds per passenger. The coefficients obtained for Hong Kong MTR are comparatively lower than that obtained for Canada LRT as door dimension, platform configuration and passenger behavior are different. Dwelling Time Reliabilitw at MTR Stations (4) With making use of the generalized equation (4) given in 3.1, the reliability of the train dwelling time can be estimated. The methodology used for the estimation of the train dwelling time is described as follows: (1) Derivation of the probability distribution for the boarding and alighting passengers on the basis of the survey results. (2) Estimation of the combined probability of the train dwelling time. The estimation of the combined probability of the train dwelling time makes use of the Monte-Carlo technique (Ross, 1991) to consider a number of outcomes of the key variables (i.e. boarding and alighting passengers) randomly selected within their probability distributions. A convergence test is used to determine the adequacy of the number of simulations. By using goodness of fit test, hypothesis tests of the boarding and alighting distributions with various probability distributions were performed at 5% level of significant. Hence, the probability distributions of the boarding and alighting passengers at 95 % level of confidence are given in Table 2.

7 A Study of Train Dwelling Time Table 2. Probability distributions of boarding and alighting passengers m Alighbng Norm( ) Triang( ) It was observed that the probability distribution ofthe boardlng passengers is normal distributed and the alighting passengers is triangular distributed. The probability distributions of train dwelling time can then be estimated by the Monte-Carlo simulation using the derived boarding and alighting distribution. A convergence test was used to determine the number of simulations required. 1,000, 5,000, 10,000 and 15,000 simulations were carried out to investigate whether the adequate simulation is achieved. The results are illustrated in Figure 2. It can be seen that the curve of 1,000 simulations is different from the others, while the other three curves are approximate with each other. Therefore, it was decided to simulate 10,000 times for the reliability analysis of the train dwelling time. The probability density hnction and cumulative distribution of the simulated train dwelling time are displayed in Figures 3 and 4 respectively. The results of the reliability test of the train dwelling time are tabulated in Table 3.

8 292 William H.K. Lam, C.Y. Cheung and Y.F. Poon 40 Figure 2. Probability density function of train dwelling time with different number of simulations Y) 40 Train Iholtig TCD. (seconds) Figure 3. Probability density function of train dwelling time

9 A Study of Train Dwelling Time Figure 4. Cumulative distribution function of train dwelling time Table 3. Results of the reliability of the train dwelling time Observed mean train dwelling time (seconds) % confident interval ofthe estimated train dwellingtime <train dwelling time < Probability of reaching observed mean value Estimated mean train dwelling time (seconds) Probability of reaching estimated mean value 50% Estimate median train dwelling time (seconds) By using Chi-square test, the estimated dwelling time is found to be normal distributed. When compared the estimated and observed train dwelling time using Kolmogorov-Smirnov two-sample test (Romano. 1977), it was observed that there is no sigruficant differences between these two distribution at 95% level of confidence. The generalized model (4) gives a reasonable estimate for the average train dwelling time, and the reliability analysis can be used to give a reliable range for the estimated train dwelling time for assessment.

10 294 William H.K. Lam, C.Y. Cheung and Y.F. Poon Conclusions Due to the saturated conditions at Hong Kong MTR stations, attention has been given by the planners and engineers to tackle the congestion problems by using station modelling. Station modelling is particular important when the demand is greater than the capacity of the station facilities. In this paper, disaggregated models were developed to estimate the crowding effects in MTR stations particularly on the platform sides, while the overall pedestrian flows within the station can now be estimated by an aggregated pedestrian model e.g., PEDROUTE (Halcrow Fox and Associates, 1994). The train dwelling time models provide a reasonable estimate for the dwelling time of trains at MTR stations. However, it is impossible for the dwelling time to increase infinitely with the increase in passenger demands. Train headway also governs the m a. m allowable dwelling time of trains, an average value of train headway in Hong Kong is around 3 minutes. A reliability analysis for the train dwelling time model is given to consider the variation of the key variables (boarding and alighting passengers) for forecasting of the train dwelling time. With different boarding and alighting distributions, the distribution of train dwelling time can be predicted by Monte-Carlo simulation and the confident intend of the train dwelling time can also be obtained. Acknowledgements The authors wish to thank Mr. Eddie So, Transport Planning Manager, Miss Y. W. Lai, Market Research Officer, and Mr. H. L. Ho. Transport Planning Assistant of the Mass Transit Railway Corporation Marketing and Planning Department Transport Planning Section for their assistance, advice and resources supplied. References Halcrow Fox and Associates (1994) User Guide to PEDROUTE version Halcrow Fox and Associates. Romano, A. (1977) Applied Statistics for Science and Industry. Alljn and Bacon, Inc., Boston. Ross, S. M. (1991) A Course in Simulation. MacMillan Publishg Company, New York.

11 A Study of Train Dwelling Time S. C. Wirasinghe and D. Szplett (1984) An investigation of passenger interchange and train stanhg time at LRT stations: (ii) estimation of standing time. Journal ofadvanced Transportation, 18: 1, pp