Fig 1.
A schematic diagram indicating the passengers’ travel behavior along a rail transit journey in the normal and abnormal conditions.
A detailed description is presented in the previous paragraph and the next paragraph. In addition, this logic diagram is a qualitative summary of passenger travel behavior in a rail transit network and is originally presented in this paper.
Fig 2.
An example of a station closure in the Beijing rail transit network.
As indicated in this example, the Life Science Park station on the Changing Line is out of service. Passenger A is going to depart from this station by rail transit. Passenger B is currently at the South Gate of Forest Park station on Line 8, and his destination is the Life Science Park station.
Fig 3.
An illustration of assumption 2.
For a particular rail passenger, O and D denote the planed origin and destination stations, respectively. O’ denotes the alternative origin station when the planed origin station is closed, and D’ denotes the alternative destination station when the planed destination station is closed. (a) represents the passenger’s planned rail journey in the normal situation. (b) shows that the passenger will take a bus or taxi to the new alternative origin station and will then take rail transit from the new origin station to the planned destination when the planned origin station is closed. (c) shows that the passenger will take rail transit from the planned origin station to the new alternative destination and will then take a bus or taxi to the planned destination station then when the planned origin station is closed. Only the two situations of (b) and (c) are considered in our studies for station closure.
Fig 4.
The framework of the integrated solution algorithm.
There are two core modules in the solution algorithm: the passenger simulator and the model solver. The main inputs of the passenger simulator are the rail transit network, train schedules, smart card data, and bus/taxi data. In addition, the simulator provides instant passenger information, including the current path, station, and train, for the tens of thousands of behavior optimization models. The closure duration and its overestimation are also the inputs of the model solver. Finally, the outputs of the model solver, namely, the updated destination station, origin station, the transport mode and paths, are computed and then become the inputs of the passenger simulator.
Fig 5.
The passenger simulator module.
The parameters are initialized firstly. And then the in each simulation step of each simulation period, each passenger will get the most out of what they can do. One passenger's single rail journey will start from the entering a station, and ends up with exiting a station. The whole process will be tracked by the transitions of passenger states, namely “In”, “Entry”, “Waiting”, “Transfer”, “Boarding”, “Alighting”, “Exit”, or “Out”.
Fig 6.
The basic model solver module.
For each passenger, all stations will be traversed and examined with the objective of passenger behavior optimization model. And then the station with the minimum model objective will be chosen as the alternative station.
Fig 7.
The Beijing rail transit network map for 2015.
This map is originally presented in this paper by the Haodong Yin, based on open access data of the Beijing rail transit using our own developed software.
Table 1.
Example of smart card data.
Table 2.
Example of expected fare and time consumption of buses and taxis between each pair of rail stations.
Fig 8.
The location of JISHUITAN station in the Beijing rail transit network.
The red point is JISHUITAN station.
Fig 9.
The total time consumption, distance and fee between JISHUITAN station and nearby stations.
The parameters (t, d, f) on each arc that are marked by a red arrow are the total journey time (minutes), distance (kilometers) and fee (RMB) by bus, including the walking during the trip. (a) denotes the travel cost from the closed station to some nearby stations. (b) indicates the travel cost from the nearby stations to the closed station. It should be noted that the travel costs on the arcs in the different directions between the pairs of stations are different.
Fig 10.
The location of TIANTONGYUAN station in the Beijing rail transit network.
The red point is the TIANTONGYUAN station.
Fig 11.
The total time consumption, distance and fee between the TIANTONGYUAN station and nearby stations.
The parameters (t, d, f) on each arc that are marked by a red arrow are the total journey time (minutes), distance (kilometers) and fee (RMB) by bus, including the walking during the trip. (a) denotes the travel cost from the closed station to some nearby stations. (b) indicates the travel cost from the nearby stations to the closed station. It should be noted that the travel costs on the bidirectional arcs between the same two stations may be different.
Table 3.
The different values of the parameters in the simulation cases.
Fig 12.
The passenger flow status at every 5 minutes on the rail network from 8:00–8:30.
We can simulate every moment of each passenger in our passenger simulator. In addition, once trains enter the segment, the passengers in the trains is counted by the segment, and the train’s capacity is also merged. If N stands for the total passenger count and Ca stands for the capacity of all the trains passing through the segment, the train load of the segment can be calculated as N/Ca. We use four colors to display the train load of each segment: lime indicates a load range from zero to 80%; yellow indicates a load from 80% to 100%; red indicates a load from 100% to 120%; and black indicates that the load is greater than 120%.
Fig 13.
Online passengers in the rail transit network.
(a) represents the total entries, transfers and exits of the rail transit network at every 5 minutes. (b) shows the number of instantaneous passengers on the rail transit network at the end of each simulation period. The number of passengers reaches its peak, namely, 490,397, at end of the simulation period [8:15, 8:30). The simulation results are computed in the normal situation with no station closure.
Fig 14.
Number of entries in each station every 5 minutes.
This graph has three dimensions: time, stations and the number of passengers. Every point in a colored area donates the entries of a particular station during a particular period. The color indicates the number of passengers entering the station.
Fig 15.
Affected passengers for varying overestimation of the closure duration.
A longer announced closure duration, that is, a larger overestimation of the closure duration, results in more affected passengers.
Fig 16.
The relationship between the closure duration and the passenger behavioral choices.
(a) represents the simulation results in the JISHUITAN case. (b) denotes the simulation results in the TIANTONGYUAN case.
Fig 17.
The relationship between the overestimation of the closure duration and the passenger behavioral choices.
(a) shows the proportion of passenger behavioral choices after the station closure in the JISHUITAN case. (b) shows the proportion of passenger behavioral choices after the TIANTONGYUAN station is closed in the second closure case. With increasing g, the number of passengers taking an alternative origin station or giving up on their rail transit journey gradually increases.
Fig 18.
The main stations that passengers choose as their alternative origin stations after JISHUITAN station is closed.
The red circles represent the alternative origin stations, including the closed JISHUITAN station. The size of each circle represents the number of passengers who choose that station, and a larger radius indicates relatively more passengers.
Fig 19.
The main stations that passengers choose as their alternative origin stations after TIANTONGYUAN station is closed.
The red circles represent the alternative origin stations. The size of each circle represents the number of passengers who choose that station, and a larger radius indicates relatively more passengers.
Fig 20.
The main stations that passengers choose as their alternative destination stations after JISHUITAN station is closed.
The red circles represent the alternative destination stations, and a larger radius indicates a larger proportion.
Fig 21.
The main stations that passengers choose as their alternative destination stations after TIANTONGYUAN station is closed.
The red circles represent the alternative destination stations, and a larger radius indicates a larger proportion.
Fig 22.
The number of entries at the closed stations for varying values of g.
(a) shows the number of entries at JISHUITAN station. (b) represents the number of entries at TIANTONGYUAN station. As shown in the first closure case in Fig 22(a), when g equals 1, JISHUITAN station experiences 2343 more entries than in the no closure situation after 8:30. However, in the case of g equal to 10, this difference is 197, which is 91.7% smaller than in the case of g equal to 1. The duration is 75 minutes in the case of g equal to 10, which is 16.7% more than in the case of g equal to 1. As shown in the second closure case in Fig 22(b), when g equals 1, the TIANTONGYUAN station experiences 3195 more entries than in the no closure situation after 8:30. However, in the case of g equal to 10, this difference is 422, which is 86.8% less than in the case of g equal to 1. The duration is 90 minutes in the case of g equal to 10, which is 38.5% more than the duration in the case of g equal to 1.
Fig 23.
The number of entries at the affected stations for varying values of g.
(a) shows the number of entries at GULOUDAJIE station in the JISHUITAN case. (b) shows the number of entries at TIANTONGYUAN South station in the TIANTONGYUAN case. The inbound capacity of the GULOUDAJIE is 1000 persons per 5 minutes, and the TIANTONGYUAN South station is 1062 persons per 5 minutes. As shown in the first closure case in Fig 23(a), when g equals 1, the GULOUDAJIE station experiences 1,284 more entries than in the no closure case. However, in the case of g equal to 10, this difference is 2,064, which is 60.9% more than that in the case of g equal to 1. The duration in the case of g equal to 10 is 60 minutes, which is 33.3% more than in the case of g equal to 1. As shown in the second closure case in Fig 23(b), when g equals 1, the TIANTONGYUAN South station experiences 4,979 entries more than in the no closure case. However, in the case of g equal to 10, this difference is 7294, which is 46.5% more than that in the case of g equal to 1. The duration in the case of g equal to 10 is 65 minutes, which is 44.4% more than in the case of g equal to 1.
Fig 24.
The comparisons of the model outputs and the manual surveys in the JISHUITAN closure case.
In the manual survey, 80% (119 of 148) of passengers choose to alter their planned origin station (Fig 24(a)) and 87% (104 among the 119) passengers choose the GULOUDAJIE as their new origin station (Fig 24(b)). But our model results show that all the affected passengers will change their origins and choose the GULOUDAJIE station as their new origins, which indicates that there is an error of no more than 20% between the model results and the actual survey results.