In [1]:
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
%matplotlib notebook
In [2]:
history = [
[2002, 3/7],
[2003, 3/7],
[2004, 3/7],
[2005, 3/7],
[2006, 3/7],
[2007, 5/7],
[2008, 5/7],
[2009, 5/7],
[2010, 6/7],
[2011, 6/7],
[2012, 1],
[2013, 2],
[2014, 3],
[2015, 3],
[2016, 3],
[2017, 3],
]
history = np.transpose(history)
years = history[0]
limits = history[1]
In [3]:
fig, ax = plt.subplots()
ax.plot(years, limits, marker='o', ls='None')
ax.set_xlabel("Jahr")
ax.set_ylabel("GB pro Tag")
plt.show()
In [4]:
fig, ax = plt.subplots()
ax.plot(years, limits, marker='o', ls='None')
ax.set_xlabel("Jahr")
ax.set_ylabel("GB pro Tag")
ax.plot(2018, 5, 'ro')
ax.set_yscale("log")
plt.show()
In [5]:
def exp_growth(t, y0, A, τ):
return y0 + A * 2**((t-2002)/τ)
In [6]:
years = np.append(years, [2018])
limits = np.append(limits, [5])
[[y0, A, τ], pcov] = curve_fit(exp_growth, years, limits)
perr = np.sqrt(np.diag(pcov))
print("y0 = {:.3f}, A = {:.3f}, τ = {:.3f}".format(y0, A, τ))
In [7]:
# Daten der Bundesnetzagentur, Datenvolumen Breitband in Festnetzen
# https://www.bundesnetzagentur.de/SharedDocs/Downloads/DE/Allgemeines/Presse/Pressemitteilungen/JB2017ZDF.pdf
# Seite 6, Datenvolumen pro Nutzer und Monat in GB
data_BNetzA = [
[2011, 17],
[2012, 21],
[2013, 29],
[2014, 33],
[2015, 47],
[2016, 60], # Prognose
]
data_BNetzA = np.transpose(data_BNetzA)
[[y0_BNetzA, A_BNetzA, τ_BNetzA], _] = curve_fit(exp_growth,
data_BNetzA[0],
data_BNetzA[1])
print("y0 = {:.3f}, A = {:.3f}, τ = {:.3f}".format(y0_BNetzA, A_BNetzA, τ_BNetzA))
In [8]:
# Daten von Statista
# https://de.statista.com/statistik/daten/studie/3564/umfrage/durchschnittliches-datenvolumen-pro-anschluss-seit-2001/
# Durchschnittliches Datenvolumen pro stationärem Breitbandanschluss und Monat in Deutschland von 2001 bis 2017 (in Gigabyte)
data_stat = [
[2000, 1.8],
[2002, 6.6],
[2003, 8.8],
[2004, 7.8],
[2005, 6.5],
[2006, 5.8],
[2007, 6.9],
[2008, 9.4],
[2009, 10.1],
[2010, 11],
[2011, 12],
[2012, 15],
[2013, 20.9],
[2014, 26.6],
[2015, 44.2],
[2016, 59.3],
[2017, 79], # Prognose
]
data_stat = np.transpose(data_stat)
[[y0_stat, A_stat, τ_stat], _] = curve_fit(exp_growth,
data_stat[0],
data_stat[1])
print("y0 = {:.3f}, A = {:.3f}, τ = {:.3f}".format(y0_stat, A_stat, τ_stat))
In [9]:
# Moore's Law
# N_Transistors ~ 2**(year/2) = e**(year/(2/ln(2))) = e**(year/2.9)
In [10]:
fig, ax = plt.subplots()
ax.plot(years, exp_growth(years, y0, A, τ_stat) , marker=',', c='C8',
label='Statista fit: τ = {:.1f}'.format(np.round(τ_stat, decimals=1)), lw=0.5)
ax.plot(years, exp_growth(years, y0, A, 2) , marker=',', c='C3',
label='Moores Law: τ = 2', lw=0.5)
ax.plot(years, exp_growth(years, y0, A, τ_BNetzA) , marker=',', c='C4',
label='BNetzA fit: τ = {:.1f}'.format(np.round(τ_BNetzA, decimals=1)), lw=0.5)
ax.plot(years, exp_growth(years, y0, A, τ) , marker='.', c='C1',
label='Data fit: τ = {:.1f}'.format(np.round(τ, decimals=1)))
ax.plot(years, limits, marker='o', c='C0', ls='None', label='Data')
ax.plot(years, exp_growth(years, y0, A, τ+perr[2]) , marker='None', c='grey', alpha=0.4)
ax.plot(years, exp_growth(years, y0, A, τ-perr[2]) , marker='None', c='grey', alpha=0.4)
ax.fill_between(years, exp_growth(years, y0, A, τ+perr[2]), exp_growth(years, y0, A, τ-perr[2]),
facecolor='grey', alpha=0.1, label='Uncertainty on fit')
ax.set_xlabel("Jahr")
ax.set_ylabel("GB pro Tag")
ax.set_yscale("log")
ax.legend()
plt.show()
In [11]:
def agreement(t):
return np.floor(0.8 + 0.18*2**((t-2002)/3.5))
In [12]:
years_2025 = np.append(years, range(2019, 2026))
fig, ax = plt.subplots()
ax.plot(years, limits, marker='o', ls='None')
ax.plot(years_2025, exp_growth(years_2025, y0, A, τ) , marker='.', label='Data fit')
ax.step(years_2025, agreement(years_2025), marker=',', where='post', label='Future limits')
ax.set_xlabel("Jahr")
ax.set_ylabel("GB pro Tag")
ax.set_yscale("log")
ax.legend()
plt.show()
In [13]:
for [y, d] in np.transpose([years_2025, agreement(years_2025)])[16:]:
print("{:4.0f} beträgt das Limit {:2.0f} GB/Tag".format(y, d))