Subway Station Passenger Movement using Pathfinder

This post demonstrates how to use Pathfinder to simulate movement in a subway station, with trains arriving and departing from the station. A growing list of features not specific to evacuation, such as occupant sources and assisted evacuation, make Pathfinder applicable to a much broader range of pedestrian movement problems.

The subway station is illustrated in Figure 1, which shows passengers on the upper platform. Our model will simulate the continuous entry of passengers into the station to board specific trains and the exit of passengers from trains that have arrived at the station. The model includes 10 trains, 6 arrive and depart on the upper platform and 4 on the lower platform. We assume that each train arrives and departs at a 10-minute interval. The arrival times are staggered, so that one train arrives each minute. Each train unloads and then loads 200 passengers, giving a total flow exiting the station of 200 persons/minute or 12000 persons/hour (the same number also arrive at the station). The train loading was chosen to be consistent both with the size and number of cars in each train and with the flow capacity of the stairs and escalators.

Figure 1: Subway model showing platform with passengers arriving and leaving by train.

Brandon Lambrecht, now an architect at Mahlum Architects in Portland, created the subway CAD model while a summer intern at Thunderhead Engineering. The CAD model was drawn in Revit and imported into Pathfinder using the FBX import feature and the extract floor tool. It does not represent a real-world location. To learn more about importing CAD geometry, see the ‘Importing CAD files’ section of the Pathfinder User Manual. There are also videos available that provide examples of the process, entitled Import DWG or DXF File and How do I import existing CAD model geometry into Pathfinder?

Conceptual Model

Before describing the subway model, it is useful to demonstrate the approach using a small conceptual model. Figure 2 shows the train schedule. The train departs at 3-minute intervals, with 30 seconds of unloading and 60 seconds for loading. Passengers enter the station continuously at a rate of 12 pers/min and exit the train at a flow rate of 1.2 pers/s for 30 seconds.

subway movement sequence
Figure 2: Sequence of passenger exit, boarding, and train departure. The flow of passengers entering the station is continuous.

Figure 3 shows the geometry. The door on the right is the station door. This door has an attached source that inserts new passengers into the model, the station door is also an exit for passengers who leave the station. The wait room with its doors and split line are one method of managing queues using the current capabilities of Pathfinder. Passengers who will board the train have a behavior that tells them to go to the wait room and then proceed to the subway door to exit. In addition to being an exit, the subway door has an attached source that inserts passengers who then proceed to the station door to exit. The timing of events is shown in Figure 2, where a continuous flow of passengers enter the station and queue, the subway train then discharges passengers for 30 seconds, and then the wait room exit door opens for 60 seconds and passengers board the train. The cycle then repeats.

Figure 3: Conceptual model used to illustrate passenger arrival and exit.

The details used for the wait room deserve further explanation, since they represent one approach to modeling queues within the current constraints of Pathfinder. As shown in Figure 3, the wait room has a one-way entry door, a one-way exit door, and a split line that extends the entry space. Figure 4 shows how waiting passengers queue at the wait room while passengers exit the subway train. The details of the wait room work together to accomplish this movement. First, the wait room is small so that queuing passengers will try to move as close as possible to the room. This has the effect of moving passengers to the front of the queue. The split line is a barrier that guides the passengers to form a queue, rather than form a semi-circle around the wait room. The one-way entry door ensures that passengers will only leave the wait room using the exit door. Finally, the wait room exit door can be opened and closed, when closed a queue forms and when open the passengers leave the wait room and board the train. The video below demonstrates this movement dynamically. We will use the same conceptual approach to make the more complex subway model.

subway passengers leave subway
Figure 4: Passengers exit the train (blue) while waiting passengers (red) form a queue.

Below is a video showing the Simple Subway Demo.

Subway Model

The subway model is shown in Figure 5 and has five main floors:

  • Floor 0 m – This is the lower platform floor. Four trains connect to this floor. Stairs connect Floor 0 m to Floor 3 m.
  • Floor 3 m – One side of this floor gathers the passengers exiting from Floor 0 m and delivers them by escalator to Floor 18 m. The other side of Floor 3 m is used by passengers descending from Floor 18 m to Floor 0 m to board trains.
  • Floor 15 m – This is the upper platform floor. Six trains connect to this floor. Stairs connect Floor 15 m to Floor 18 m. The stairs on one side of Floor 15 m are used for passengers ascending to exit the station and the other side is for passengers descending to board trains.
  • Floor 18 m – This floor gathers and distributes all flow from and to Floor 3 m and Floor 15 m. Both stairs and escalators connect Floor 18 m to Floor 30 m. One set of stairs and escalators brings flow up to Floor 30 m and one set brings flow down from Floor 30 m.
  • Floor 30 m – This is the main floor level. All passengers enter and leave the station from this level. One side of this floor is for passengers who proceed to trains and the other side is for passengers who arrived by train and are leaving the station.
Figure 5: Subway model navigation mesh.

The stairs and elevators are specified either for flow up or flow down. Figure 6 shows a detail of the flow descending from Floor 18 m, through Floor 3 m, and then down to the lower platform, Floor 0 m. The red arrows show the direction of flow. At the other end of Floor 3 m, the flow is up to Floor 18 m. Floor 18 m connects to the main floor by stairs and escalators.

Figure 6: Flow pattern down to Floor 0 m. Red arrows indicate flow direction.

As illustrated in the simple model, wait rooms with entry and exit doors are used to control the flow of passengers entering trains. Figure 7 shows a combined CAD and navigation mesh view of the end car of Train #6, located on the upper platform. You can see the wait rooms, the one-way doors to enter and leave the wait rooms, and the exits/entrance from the train. The corresponding navigation mesh with details is shown in Figure 8.

Figure 7: CAD and navigation mesh view of the end car of Train #6 on the upper platform.
Figure 8: Detail of navigation mesh showing Train #6, with entry/exit doors and associated wait rooms.

The subway schedule for the first 15 minutes is shown in Figure 9. Each train arrives every 10 minutes and delivers 200 passengers. The passenger exit the train in 30 seconds, then the queued passengers enter the train in one minute, and the train departs. Just to be clear, Pathfinder does not actually animate the train arrival and departure, the arrival and departure is simulated by opening and closing doors for the train and wait rooms.

Figure 9: Subway schedule for each train. Each train unloads and loads every 10 minutes.

The behavior of passengers is determined by their profiles (physical characteristics) and behaviors (specified movement goals). In addition, sources are used to define the entry flow of passengers into the station and the flow of passengers exiting the trains. The profiles, behaviors, and sources used in the model are listed in Figure 10.

The profiles (Figure 10) assign walking speed and other physical characteristics. All passengers are assigned a speed from a uniform distribution with bounds of 0.7 and 1.5 m/s, this range broadly covers the walking speed for most populations (Table 3.4, IMO Circ. 1238, Guidelines for Evacuation Analysis for New and Existing Passenger Ships, 2007). The simplest approach would be to use only one profile to define the walking speed, but multiple profiles are used to assign different colors to passengers, depending on the train they are to board or if they are to exit the station. Alternately, the Pathfinder framework supports defining detailed profiles for each passenger type, for example, a “child” profile could use the child avatar and have a speed range appropriate for children, while a “young male” profile could use an avatar of a young man and have a different appropriate speed range. The approach taken in this model is a compromise between the simple and complex approaches.

The behaviors (Figure 10) define how the passengers will move. Passengers exiting the trains are randomly assigned to go to one of the two station exits. Passengers who are entering the station to board trains are randomly assigned to go to one of the trains, so they first proceed to any of the wait rooms associated with queuing for that train and then board the train when the wait queue exit door opens.

Each occupant source can be assigned a distribution of different profiles and different behaviors. When an occupant is created by the source, the occupant is randomly assigned a profile and behavior from the distribution.

Occupant sources (Figure 10) are associated with the train doors for passenger exiting the trains and with two sources outside the station (the two long green lines in Figure 5) for passengers who enter the station to board trains. The exit flow from the trains is periodic, as shown in Figure 11. Each train has 15 doors and the exit interval from the train is 30 seconds, so a flow rate of 0.4444 pers/s gives a total of 200 passengers every 10 minutes. The sources associated with passengers entering the station (the two long green lines on Level 30 m in Figure 5) have a continuous flow of 0.1666 pers/s per train. Since there are two sources and 10 trains, this gives the arrival of 200 passengers every minute (or 200 passengers for each train every 10 minutes). Thus the total passenger arrival flow entering the station is 12000 pers/hr, which matches the total flow out of the station from the trains.

Figure 10: Lists of the profiles, behaviors, and sources used in the subway model.
Figure 11: Source for one of the train 1 exit doors. The flow is periodic at a rate of 0.444 pers/s for 30 seconds every 10 minutes.

Results

An overview of the results is provided by the Subway Simulation video. This shows the movement from 510 s to 660 s after the start of the simulation.

One way to look at the use of space in more detail is to plot accumulated usage contours. Figure 12 shows accumulated usage contours for the main floor. These contours are at 1800 seconds (30 minutes) and the contour range is 0 to 500 seconds.

Figure 12: Contours of accumulated usage (integrated time at which a space was
occupied).

Let us look in more detail at stairs A and B, which manage flow up from the trains, and at stairs C and D, which manage flow downward to board the trains. The contours show that stair A is used more than B. The reason for this is that stair A is closest to the flow up from the trains from Level 3 m, so more passengers use the closer stairway. But because there is also upward flow on both sides from Level 15 m to Level 18, Stair B also sees significant use. All downward flow enters on the side closest to Stair C, so it is much more heavily used than Stair D.

This is confirmed in plots of flow rates for the stairs. Figure 13 shows the flow up in Stairs A and B, while Figure 14 shows the flow down in Stairs C and D. For comparison, the maximum SFPE flow rate for these stairs is 2.4 pers/s. The upward flow in Stairs A and B is cyclic and reflects the arrival of trains. The peak flow rates on these stairs are about 1 pers/s. The downward flow in Stairs C and D is more steady because of the steady arrival of passengers. Stair C shows a relatively constant flow rate of about 2 pers/s.

Figure 13: Upward flow rates on Stairs A and B (see Figure 12 for stair labeling).
Figure 14: Flow rates for Stairs C and D down to trains (see Figure 12 for definition of stair labels).

Changing Flow Direction Leads to Congestion

In the subway model, the directions of flow of the turnstiles, stairs, and escalators were defined to minimize crossflow between passengers heading to the trains and the passengers leaving the station (Figure 6). To look at the effect of changing the flow directions for movement between Level 30 m and Level 18 m, a case was run in which the turnstile, stair, and escalator flow directions were rearranged. The original and new directions of flow are shown in Figure 15. Now the flow on the right half of the stairs/escalators is in a different direction than the left half.

The change in flow directions means that passengers attempting to go down to trains (mixed colors) must now cross the flow of passengers leaving the station (blue). The space between the stair entry/exit on the main floor is relatively small, so this crossflow leads to congestion.

Figure 15: Change in flow directions to illustrate the difficulty of mixed flow in a tight space.

The movement calculation in Pathfinder is optimized for evacuation, where counterflow and crossflow do not typically occur. The counterflow capability of Pathfinder is documented in the Validation and Verification Manual. The movement algorithm in Pathfinder does include some lane-forming capability, but in general, it is expected that Pathfinder will enhance the congestion in crossflow conditions. Experimental data on crossflow is sparse, so it is difficult to rigorously evaluate the simulation. In one sense, enhanced congestion could also be considered an asset, since it means that the Pathfinder results are conservative.

Summary and Request for Comments

In this post, we demonstrated how to use Pathfinder to simulate movement in a subway station. The model and results show:

  • The use of sources makes it possible to simulate passengers exiting trains at specified time intervals. Sources also support the continuous entry of passengers to the station.
  • The flow of passengers and use of stairs and escalators was consistent with the expected behavior.
  • Peak flow rates on stairs approached the expected SFPE maximum flow rates.
  • Pathfinder makes it possible to study congestion that can result from inadequate or poor design choices.

Since this is a new area of application of Pathfinder, we would appreciate comments and suggestions from pedestrian movement engineers. Please contact support@thunderheadeng.com.

Modeling Hints

This Subway Modeling Hints video demonstrates using tools that can speed model creation and editing.

Download Pathfinder Input Files

Here is a zip file of the Pathfinder input files.

Comments or Questions

This post was written by Daniel Swenson. For comments or questions, send email to support@thunderheadeng.com.


More Tutorials Like This

See all Pathfinder tutorials