Run a simulation of a public transport circuit.
The simulation consists of a single circuit (which, in this case, means a list of stops). The number of stops along the circuit as well as their positions can be specified. The simulation performs some basic statistical measurements.
Roadsim is simple, but it can be used as a starting point to handle more complicated scenarios.
To run the simulation, the following packages are required:
- scipy
- numpy
- matplotlib
Start by determining the number of bus stops and their positions.
stop_pos = np.arange(0, 30, 2)
nb_stops = len(stop_pos)
Determine how far passengers want to go. Here, we suppose the number of stops a passenger wants to travel is normally distributed with mean 7.5 and standard deviation 3.75. Obviously, a passenger can't travel a negative number of stops nor travel past the last stop. This is taken care of by using a truncated normal function.
import numpy as np
from scipy.stats import truncnorm
mean_stops = nb_stops / 2.0
std_stops = nb_stops / 4.0
a, b = (1 - mean_stops) / std_stops, (nb_stops - mean_stops) / std_stops
stops_to_dest = lambda: np.round(truncnorm.rvs(a, b, loc=mean_stops,
scale=std_stops))
The simulation is initialized using mostly default values (see below). The time between each bus is set to 40 minutes and passenger arrivals at the stops follow a Poisson process with mean interarrival time set to 5 minutes. Finally, the number of buses in the simulation is set to 40 (which means the simulations will run for roughly 1600 minutes, or 27 hours).
sim = Simulation(bus_stop_positions=stop_pos,
time_between_buses=lambda: 40,
nb_stops_to_dest=stops_to_dest,
passenger_arrival_times=lambda: np.random.exponential(5),
nb_buses=40)
Then the simulation can be started.
sim.run()
After completion, the sim object contains information about various
statistics. It is possible to produce a figure containing lots of interesting
metrics as well as to compute some other statistics.
import matplotlib.pyplot as plt
sim.stats.plot()
plt.show()
print('Mean satisfaction: {:.3f}'.format(np.mean(sim.stats.satisfaction)))
print('Mean number of passengers per bus: '
'{:.2f}'.format(np.mean(sim.stats.total_passengers[-1])))
The default values for the simulation are defined to give something reasonable, but they should be tuned based on available data. By default, a simulation assumes time is measured in minutes, distance in kilometers and speed in kilometers per minute. The full list of initialization options follows.
bus_stop_positions: list or array : Position of all bus stops in the simulation. The number of bus stops is set equal to the length of this list.
Default: 10 stops separated by 3 kilometers; ``np.arange(0, 30, 3)``
passenger_arrival_times: function : Time between two successive arrivals of passengers at a bus stop. This function takes no arguments. For arrivals according to a Poisson process, this should be set to an exponential random variable.
Default: Poisson process with mean interarrival time of 10 minutes; ``lambda: np.random.exponential(10.0)``
hop_in_time: function : Time for a passenger to hop into a bus. This function takes no arguments.
Default: ``lambda: truncnorm.rvs(-1, 8, loc=0.3, scale=0.2)``
hop_out_time: function : Time for a passenger to hop out of a bus. This function takes no arguments.
Default: ``lambda: truncnorm.rvs(-1, 8, loc=0.3, scale=0.2)``
nb_stops_to_dest: function : Number of stops between origin and destination for a passenger. This function takes no arguments.
Default: ``lambda: np.round(truncnorm.rvs(-1, 4, loc=4, scale=3))``
bus_speed: function : Bus speed between two successive stops. This function takes no argument.
Default: ``lambda: truncnorm.rvs(-2, 2, loc=0.83, scale=0.1)``
nb_buses: int : Number of buses in the simulation.
Default: 50
time_between_buses: function : Time between the arrival of two successive buses at the first bus stop. This function takes no argument.
Default: ``lambda: 25``
stats_time: float : Time between measurement of statistics.
Default: 5.0
Once the simulation has finished running, the statistics are available in
the Stats object sim.stats.
The anim_simul.py script will produce a mp4 movie showing the length of
queues, the positions of the buses and the number of passengers in each bus.
To use the script, create a directory named anim and execute the script with
python anim_simul.py
The animation is saved to a file named movie.mp4 in the current directory.