Visualize the remaining time estimated with a simple algorithm that estimates only based on the total time elapsed so far.

remaining_time_estimates.py

import numpy as np
import matplotlib.pyplot as plt

scenarios = [('constant', [1., 2., 3., 4., 5., 6., 7., 8., 9., 10.],  # elapsed time
                          [.1, .2, .3, .4, .5, .6, .7, .8, .9, 1.]),  # fraction of simulation completed
             ('varying', [1., 2., 3., 4., 5., 6., 7., 8., 9., 10.],
                         [.1, .175, .3, .375, .5, .575, .7, .775, .9, 1.]),
             ('slow start', [1., 2., 3., 4., 5., 6., 7., 8., 9., 10.],
                            [.05, 0.1, 0.15, 0.2, 0.25, 0.4, 0.55, 0.7, 0.85, 1.0]),
             ('slow end', [1., 2., 3., 4., 5., 6., 7., 8., 9., 10.],
                          [.15, .3, .45, .6, .75, .8, .85, .9, .95, .1])
             ]

def estimate(elapsed, completed):
    # Normally this is rounded to the next second for display
    return (1 - completed) / completed * elapsed

vectorized_estimate = np.vectorize(estimate)

fig, axes = plt.subplots(len(scenarios), 1, sharex=True)
for ax, (name, elapsed, completed) in zip(axes, scenarios):
    estimated_remaining_time = vectorized_estimate(elapsed[:-1], completed[:-1])
    real_remaining_time = elapsed[-1] - np.array(elapsed[:-1])

    ax.plot(100*np.array(elapsed[:-1])/elapsed[-1], real_remaining_time, color='gray', lw=2)
    ax.plot(100*np.array(elapsed[:-1])/elapsed[-1], estimated_remaining_time, 'o')
    ax.set_title(name)
axes[-1].set_xlabel('elapsed time (%)')
axes[-1].set_ylabel('remaining time')
fig.tight_layout()
plt.show()