Fig 1.
Relationship between methods (A) General, (B) Self-organizing II and (C) Self-organizing.
This flowchart represents the relation between the methods (blue), real data (black) and an idealized abstract scenario (green).
Fig 2.
Simulator’s main control pseudocode.
Fig 3.
(A) General method (black). (B) Self-Organizing II method (red). Common procedures are shown in blue. See text for explanation.
Fig 4.
Pseudocode of antipheromone update.
Fig 5.
Screenshot of the simulation using the Self-Organizing Method II for 20,000 iterations.
The characteristics of the Line 1 of the MXM are considered. The histogram of the headway frequency shows a mean value around 1.88 min and a small standard deviation, 0.0898 min, which reflects a global stability on the system. Regarding the average travel time of passengers, these are stable and remain constant. The intensity of the green color at stations is proportional to the antipheromone concentration.
Fig 6.
The line of vision value is set to 10 patch units (i.e. 1500 meters). This is an efficient strategy because in most cases is not necessary compute the acceleration (Eq 4) and deceleration (Eq 5) in each step of the simulation.
Fig 7.
“Phantom strategy” with optimal position.
To set the correct position of the “phantom” object considering the train speed, a table of calculated distances are loaded a priori.
Table 1.
Parameters used in Gipps’ model.
Fig 8.
Fragment of the computer simulation of the Line 1 of the MXM.
Stations are marked in blue; traffic lights are circles in red or green; trains show the number of current passenger load, and a person shows the number of passengers waiting in the station. The position of the point of measurement of the headway is marked in orange and shows where the empirical measurements were taken.
Fig 9.
Histograms of the headway frequencies.
The mean headway value in the real system and the GM simulation are (A) 147 and (B) 132 seconds, illustrated with a gray bar.
Fig 10.
Histogram frequency of the Pearson correlation coefficient between the headway distribution data of Line 1 and 100 GM simulations.
Fig 11.
Behavior of the headway with SOM-II.
(A) Distribution of the headway frequencies, keeping the same scale of windows size to compare adequately with MXM Line 1 and GM distribution headway. (B) A typical time series of the headway measured at the simulated Pino Suárez station.
Fig 12.
(A) Average passenger travel time, (B) average passenger system exit, (C) average passenger speed, (D) average train speed. In graph (A) values of λp = {2, 3} are not included because the time increment exponential due to overcrowding.
Fig 13.
Modeling a mechanical failure at a specific time.
The mechanical failure begins and ends in the minutes ti = 209 and tf = 224, respectively. (A) in GM series, the high values of the headway represents the formation of clusters. (B) The SOM-II time series is robust against the perturbation and is capable of restoring the system in a short time.
Fig 14.
Time-space diagram of the trains.
(A) After the mechanical failure in GM, the system exhibits a striped pattern characteristic of the equal headway instability. (B) The SOM-II has a homogeneous pattern and stable before and after the mechanical failure, the trains in front of train0 already wait more at stations even before the failure ends, since the balance between the variables ETNextTrain and antipheromoneStation delay the departure. This improves the resilience and accelerates the recovery of the system.
Fig 15.
The components of the guide signs are: three circles that indicate the way to exit, two vertical lines dividing the waiting area, and two black boxes with sideline arrows to indicate the boarding orientation.
Fig 16.
Regulatory strategy in operation.
Passengers wait in the line the train arrival and the alighting area remains clear.