## 3 Estimating Observed Dwell Time of Train When Departure Information Is Missing  
This paper utilizes the real-time operation data of the metro trains. The collected data have relatively well-recorded arrival times of trains, while often missing the departure times. Therefore, in cases where the departure times are missing, the observed dwell time for each train at each station was estimated by using typical travel times between stations.  
As illustrated in Figure 5, the train arrival times at station S and S + 1 is easily determined from the train operation data. The arrival time refers to the time when a train passes 400 m upstream of an associated station. The time difference between the 2 stations consists of the braking time at station S (\(\mathrm{B_{S}}\)), dwell time at station S (\(\mathrm{DW_{S}}\)), and the travel time between the station S and 400 m upstream location of station S + 1. If we assume the braking times are similar for all stations, the braking time at station S (\(\mathrm{B_{S}}\)) can be subtracted from the time difference between the two stations S and S + 1 in order to estimate the actual dwell time. The S line, from which the data were collected, is specifically suitable for such assumptions, because it is autonomously operated and has constant braking times at stations with a large headway of 4 min, and has a relatively low chance of congestion occurring due to the influence of trains downstream. The assumption of constant braking times was verified visually with video cameras installed on all trains. Figure 6 shows the time difference between arrivals of trains at all stations (solid black and red lines), and average travel times visually observed from trains equipped with video cameras (blue dotted line). The difference, \(\mathrm{DW_{S}}\), between the \(\mathrm{TT_{S}}\) and \(\mathrm{TD_{S}}\) is the estimated dwell time for each train at each station in the case of missing departure data. It is noted that the red lines represent time difference between arrivals at stations of the first 5 trains in the early morning period, where there are no delays, while black lines represent for all other trains.  
Figure 5: Time components of railway operation between stations and definitions of \(\mathrm{TT_{S}}\) and \(\mathrm{TD_{S}}\).  
Figure 7 shows a relationship between the estimation of observed dwell times for all trains at all stations versus the sum of boarding and alighting passenger counts. The \(x\)-axis represents the sum of boarding and alighting passengers while the \(y\)-axis represents the estimation of observed dwell times. Each symbol represents a station, as illustrated in Table 1. The minimum observed dwell time is 16 s. The variability of dwell times is found to be larger when the passenger counts are smaller, and smaller when the passenger counts are larger. In addition, it is found that the minimum dwell time increases as the passenger counts increase. It is interesting to note that many observed dwell times at certain stations seem to have constant dwell times regardless of passenger counts. This is a result of enforced dwell times at some major stations being assisted by dedicated employees on the platforms, limiting the number of boarding passengers.  
Figure 6: TT\({}_{\text{S}}\) and TDS\({}_{\text{S}}\) at each station and the concept of estimating the DW\({}_{\text{S}}\) at each station.  
Figure 7: Relationship between estimated dwell time and the number of boarding and alighting passengers at each station of S line.