jpasquier · December 17, 2022 18:08
diff --git a/rush.py b/rush.py
 #!/bin/python3

 import numpy as np
 import matplotlib.pyplot as plt
 from multiprocessing import Pool, cpu_count

 np.random.seed(666)

 # Function that calculates (by simulation) the overflow probability of the
 # system
 def prob(
    n = 80,    # Number of employees likely to clock out during the rush period
    p = 300,   # Duration of rush period (seconds)
    d = 5,     # Time required for clocking out (seconds)
    k = 16,    # Number of time clocks
    s = 10**5  # Number of simulations
    ):
    # Each employee arrives randomly in the rush period according to a uniform
    # distribution. The clocking out times are stored in a list of arrays.
    t = [np.random.uniform(low=0, high=p, size=n) for i in range(s)]
    # Sort each array of the clocking out time list (sorting by time for each
    # simulation)
    t = [np.sort(x) for x in t]
    # For each employee sorted in the order of arrival, we calculate the time
    # difference with the employee with k more ranks in the order of arrival.
    # If one of these time differences is less than the time needed to clocking
    # out, then the system is overflowed.
    o = [[t[i][j + k] - t[i][j] <= d for j in range(n - k)] for i in range(s)]
    # Proportion of overflowding
    return np.mean([any(x) for x in o])

 # Probability of overflowding according to the number of devices. The other
 # parameters are fixed. Default values are defined in the function.
 def prob_k(k):
    return prob(k=k)
 devices = range(2, 17)
 with Pool(processes=cpu_count()) as P:
    probs = P.map(prob_k, devices)

 # Figure
 plt.plot(devices, probs)
 plt.xlabel('Number of devices')
 plt.ylabel('Probability of overflowding')
 plt.show()
	#!/bin/python3

	import numpy as np
	import matplotlib.pyplot as plt
	from multiprocessing import Pool, cpu_count

	np.random.seed(666)

	# Function that calculates (by simulation) the overflow probability of the
	# system
	def prob(
	n = 80, # Number of employees likely to clock out during the rush period
	p = 300, # Duration of rush period (seconds)
	d = 5, # Time required for clocking out (seconds)
	k = 16, # Number of time clocks
	s = 10**5 # Number of simulations
	):
	# Each employee arrives randomly in the rush period according to a uniform
	# distribution. The clocking out times are stored in a list of arrays.
	t = [np.random.uniform(low=0, high=p, size=n) for i in range(s)]
	# Sort each array of the clocking out time list (sorting by time for each
	# simulation)
	t = [np.sort(x) for x in t]
	# For each employee sorted in the order of arrival, we calculate the time
	# difference with the employee with k more ranks in the order of arrival.
	# If one of these time differences is less than the time needed to clocking
	# out, then the system is overflowed.
	o = [[t[i][j + k] - t[i][j] <= d for j in range(n - k)] for i in range(s)]
	# Proportion of overflowding
	return np.mean([any(x) for x in o])

	# Probability of overflowding according to the number of devices. The other
	# parameters are fixed. Default values are defined in the function.
	def prob_k(k):
	return prob(k=k)
	devices = range(2, 17)
	with Pool(processes=cpu_count()) as P:
	probs = P.map(prob_k, devices)

	# Figure
	plt.plot(devices, probs)
	plt.xlabel('Number of devices')
	plt.ylabel('Probability of overflowding')
	plt.show()