Binder cordon probabilities¶
In [1]:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import binom
import ipywidgets as W
In [2]:
@W.interact(duration=(0.0, 4.0), interval=(12, 36), nodes=(1, 8))
def plotit(duration, interval, nodes=4):
# probability that any given node is cordoned
p = 1.0 * duration / interval
p_inverse = 1 - p
# n = for number of nodes available
n = np.arange(0, nodes + 1)
prob = binom.pmf(n, nodes, p)
plt.semilogy(n, prob, '-o')
plt.title("Probability that N nodes are cordoned at any given time")
plt.xticks(n)
plt.xlabel("cordoned nodes")
plt.ylabel("P")
print(f"Probability of N/{nodes} nodes cordoned:")
for i, p_i in zip(n, prob):
print(f"{i}: 1/{1/p_i:.2g}")
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In [3]:
plotit(duration=2, interval=24)
Probability of N/4 nodes cordoned: 0: 1/1.4 1: 1/3.9 2: 1/29 3: 1/4.7e+02 4: 1/2.1e+04
